The Hubbard dimer: a density functional case study of a many-body problem

Carrascal, D. J.; Ferrer, J.; Smith, J. C.; Burke, K.

doi:10.1088/0953-8984/27/39/393001

Title: The Hubbard dimer: a density functional case study of a many-body problem

Abstract

This review explains the relationship between density functional theory and strongly correlated models using the simplest possible example, the two-site Hubbard model. The relationship to traditional quantum chemistry is included. Even in this elementary example, where the exact ground-state energy and site occupations can be found analytically, there is much to be explained in terms of the underlying logic and aims of density functional theory. Although the usual solution is analytic, the density functional is given only implicitly. We overcome this difficulty using the Levy–Lieb construction to create a parametrization of the exact function with negligible errors. The symmetric case is most commonly studied, but we find a rich variation in behavior by including asymmetry, as strong correlation physics vies with charge-transfer effects. We explore the behavior of the gap and the many-body Green's function, demonstrating the 'failure' of the Kohn–Sham (KS) method to reproduce the fundamental gap. We perform benchmark calculations of the occupation and components of the KS potentials, the correlation kinetic energies, and the adiabatic connection. We test several approximate functionals (restricted and unrestricted Hartree–Fock and Bethe ansatz local density approximation) to show their successes and limitations. Here, we also discuss and illustrate the concept of themore »« less

Authors:

Carrascal, D. J. ^[1]; Ferrer, J. ^[1]; Smith, J. C. ^[2]; Burke, K. ^[2]

Univ. de Oviedo (Spain); Nanomaterials and Nanotechnology Research Center, Oviedo (Spain)
Univ. of California, Irvine, CA (United States)

Publication Date:: 2015-09-17

Research Org.:: Univ. of California, Irvine, CA (United States)

Sponsoring Org.:: USDOE Office of Science (SC), Basic Energy Sciences (BES)

OSTI Identifier:: 1595136

Grant/Contract Number:: FG02-08ER46496; FIS2012-34858; DGE-1321846

Resource Type:: Accepted Manuscript

Journal Name:: Journal of Physics. Condensed Matter

Additional Journal Information:: Journal Volume: 27; Journal Issue: 39; Journal ID: ISSN 0953-8984

Publisher:: IOP Publishing

Country of Publication:: United States

Language:: English

Subject:: 75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND SUPERFLUIDITY; density functional theory; Hubbard model; strongly correlated electron systems

Citation Formats


                    Carrascal, D. J., Ferrer, J., Smith, J. C., and Burke, K. The Hubbard dimer: a density functional case study of a many-body problem.  United States: N. p., 2015. 
Web.  doi:10.1088/0953-8984/27/39/393001.

Copy to clipboard


                    Carrascal, D. J., Ferrer, J., Smith, J. C., & Burke, K. The Hubbard dimer: a density functional case study of a many-body problem.  United States.  https://doi.org/10.1088/0953-8984/27/39/393001

Copy to clipboard


                    Carrascal, D. J., Ferrer, J., Smith, J. C., and Burke, K. Thu .  
"The Hubbard dimer: a density functional case study of a many-body problem".  United States.  https://doi.org/10.1088/0953-8984/27/39/393001.  https://www.osti.gov/servlets/purl/1595136.

Copy to clipboard


                    
@article{osti_1595136,

  title        = {The Hubbard dimer: a density functional case study of a many-body problem},

  author       = {Carrascal, D. J. and Ferrer, J. and Smith, J. C. and Burke, K.},

  abstractNote = {This review explains the relationship between density functional theory and strongly correlated models using the simplest possible example, the two-site Hubbard model. The relationship to traditional quantum chemistry is included. Even in this elementary example, where the exact ground-state energy and site occupations can be found analytically, there is much to be explained in terms of the underlying logic and aims of density functional theory. Although the usual solution is analytic, the density functional is given only implicitly. We overcome this difficulty using the Levy–Lieb construction to create a parametrization of the exact function with negligible errors. The symmetric case is most commonly studied, but we find a rich variation in behavior by including asymmetry, as strong correlation physics vies with charge-transfer effects. We explore the behavior of the gap and the many-body Green's function, demonstrating the 'failure' of the Kohn–Sham (KS) method to reproduce the fundamental gap. We perform benchmark calculations of the occupation and components of the KS potentials, the correlation kinetic energies, and the adiabatic connection. We test several approximate functionals (restricted and unrestricted Hartree–Fock and Bethe ansatz local density approximation) to show their successes and limitations. Here, we also discuss and illustrate the concept of the derivative discontinuity. Useful appendices include analytic expressions for density functional energy components, several limits of the exact functional (weak- and strong-coupling, symmetric and asymmetric), various adiabatic connection results, proofs of exact conditions for this model, and the origin of the Hubbard model from a minimal basis model for stretched H2.},

  doi          = {10.1088/0953-8984/27/39/393001},

  journal      = {Journal of Physics. Condensed Matter},

  number       = 39,

  volume       = 27,

  place        = {United States},

  year         = {2015},

  month        = {9}

}

Copy to clipboard

Journal Article:

Free Publicly Available Full Text

Accepted Manuscript (DOE)

Publisher's Version of Record

https://doi.org/10.1088/0953-8984/27/39/393001

Other availability

Search WorldCat to find libraries that may hold this journal

Citation Metrics:

Cited by: 48 works

Citation information provided by
Web of Science

Save / Share:

Export Metadata

Save to My Library

Works referenced in this record:

Lattice density-functional theory on graphene
journal, December 2010

Ijäs, Mari; Harju, Ari
Physical Review B, Vol. 82, Issue 23
DOI: 10.1103/PhysRevB.82.235111

Component separation of two-component fermion clouds in a spin-dependent external potential by spin-density-functional theory
journal, February 2013

Xianlong, Gao
Physical Review A, Vol. 87, Issue 2
DOI: 10.1103/PhysRevA.87.023628

Strictly correlated electrons in density-functional theory
journal, January 1999

Seidl, Michael; Perdew, John P.; Levy, Mel
Physical Review A, Vol. 59, Issue 1
DOI: 10.1103/PhysRevA.59.51

Libxc: A library of exchange and correlation functionals for density functional theory
journal, October 2012

Marques, Miguel A. L.; Oliveira, Micael J. T.; Burnus, Tobias
Computer Physics Communications, Vol. 183, Issue 10
DOI: 10.1016/j.cpc.2012.05.007

A density functional study of the simplest hydrogen abstraction reaction. Effect of self-interaction correction
journal, April 1994

Johnson, Benny G.; Gonzales, Carlos A.; Gill, Peter M. W.
Chemical Physics Letters, Vol. 221, Issue 1-2
DOI: 10.1016/0009-2614(94)87024-1

A full coupled‐cluster singles and doubles model: The inclusion of disconnected triples
journal, February 1982

Purvis, George D.; Bartlett, Rodney J.
The Journal of Chemical Physics, Vol. 76, Issue 4
DOI: 10.1063/1.443164

Exchange-correlation kernel in time-dependent density functional theory
journal, October 2002

Aryasetiawan, F.; Gunnarsson, O.
Physical Review B, Vol. 66, Issue 16
DOI: 10.1103/PhysRevB.66.165119

Density-functional exchange-correlation potentials and orbital eigenvalues for light atoms
journal, May 1984

Almbladh, C. O.; Pedroza, A. C.
Physical Review A, Vol. 29, Issue 5
DOI: 10.1103/PhysRevA.29.2322

Perspective: Treating electron over-delocalization with the DFT+U method
journal, June 2015

Kulik, Heather J.
The Journal of Chemical Physics, Vol. 142, Issue 24
DOI: 10.1063/1.4922693

Influence of next-nearest-neighbor electron hopping on the static and dynamical properties of the two-dimensional Hubbard model
journal, December 1995

Duffy, Daniel; Moreo, Adriana
Physical Review B, Vol. 52, Issue 21
DOI: 10.1103/PhysRevB.52.15607

Ground and excited-state fermions in a one-dimensional double-well: Exact and density-functional solutions
journal, May 2009

Magyar, R. J.
Physical Review B, Vol. 79, Issue 19
DOI: 10.1103/PhysRevB.79.195127

Density-Functional Theory for Fractional Particle Number: Derivative Discontinuities of the Energy
journal, December 1982

Perdew, John P.; Parr, Robert G.; Levy, Mel
Physical Review Letters, Vol. 49, Issue 23
DOI: 10.1103/PhysRevLett.49.1691

Strictly correlated electrons in density-functional theory: A general formulation with applications to spherical densities
journal, April 2007

Seidl, Michael; Gori-Giorgi, Paola; Savin, Andreas
Physical Review A, Vol. 75, Issue 4
DOI: 10.1103/PhysRevA.75.042511

Resistance Minimum in Dilute Magnetic Alloys
journal, July 1964

Kondo, J.
Progress of Theoretical Physics, Vol. 32, Issue 1, p. 37-49
DOI: 10.1143/PTP.32.37

Accurate exchange-correlation potentials and total-energy components for the helium isoelectronic series
journal, November 1994

Umrigar, C. J.; Gonze, Xavier
Physical Review A, Vol. 50, Issue 5
DOI: 10.1103/PhysRevA.50.3827

Multiconfiguration wave functions for quantum Monte Carlo calculations of first‐row diatomic molecules
journal, July 1996

Filippi, Claudia; Umrigar, C. J.
The Journal of Chemical Physics, Vol. 105, Issue 1
DOI: 10.1063/1.471865

The Resonating Valence Bond State in La2CuO4 and Superconductivity
journal, March 1987

Anderson, P. W.
Science, Vol. 235, Issue 4793
DOI: 10.1126/science.235.4793.1196

Interacting Fermi gases in disordered one-dimensional lattices
journal, April 2006

Xianlong, Gao; Polini, M.; Tanatar, B.
Physical Review B, Vol. 73, Issue 16
DOI: 10.1103/PhysRevB.73.161103

Why CCSD(T) works: a different perspective
journal, December 1997

Stanton, John F.
Chemical Physics Letters, Vol. 281, Issue 1-3
DOI: 10.1016/S0009-2614(97)01144-5

Persistent current and Drude weight for the one-dimensional Hubbard model from current lattice density functional theory
journal, February 2012

Akande, A.; Sanvito, S.
Journal of Physics: Condensed Matter, Vol. 24, Issue 9
DOI: 10.1088/0953-8984/24/9/099601

DFT: A Theory Full of Holes?
journal, April 2015

Pribram-Jones, Aurora; Gross, David A.; Burke, Kieron
Annual Review of Physical Chemistry, Vol. 66, Issue 1
DOI: 10.1146/annurev-physchem-040214-121420

Derivative discontinuity, bandgap and lowest unoccupied molecular orbital in density functional theory
journal, May 2012

Yang, Weitao; Cohen, Aron J.; Mori-Sánchez, Paula
The Journal of Chemical Physics, Vol. 136, Issue 20
DOI: 10.1063/1.3702391

The Kohn–Sham gap, the fundamental gap and the optical gap: the physical meaning of occupied and virtual Kohn–Sham orbital energies
journal, January 2013

Baerends, E. J.; Gritsenko, O. V.; van Meer, R.
Physical Chemistry Chemical Physics, Vol. 15, Issue 39
DOI: 10.1039/c3cp52547c

Difference between the quasiparticle and the Kohn-Sham-Fermi surfaces
journal, February 1988

Schonhammer, K.; Gunnarsson, O.
Physical Review B, Vol. 37, Issue 6
DOI: 10.1103/PhysRevB.37.3128

Levy–Lieb principle: The bridge between the electron density of Density Functional Theory and the wavefunction of Quantum Monte Carlo
journal, January 2015

Delle Site, Luigi
Chemical Physics Letters, Vol. 619
DOI: 10.1016/j.cplett.2014.11.060

Atomic-orbital-based approximate self-interaction correction scheme for molecules and solids
journal, January 2007

Pemmaraju, C. D.; Archer, T.; Sánchez-Portal, D.
Physical Review B, Vol. 75, Issue 4
DOI: 10.1103/PhysRevB.75.045101

Ab initio quantum chemistry: Methodology and applications
journal, May 2005

Friesner, R. A.
Proceedings of the National Academy of Sciences, Vol. 102, Issue 19
DOI: 10.1073/pnas.0408036102

Adiabatic connection forms in density functional theory: H2 and the He isoelectronic series
journal, August 2008

Peach, Michael J. G.; Miller, Adam M.; Teale, Andrew M.
The Journal of Chemical Physics, Vol. 129, Issue 6
DOI: 10.1063/1.2965531

Universal variational functionals of electron densities, first-order density matrices, and natural spin-orbitals and solution of the v-representability problem
journal, December 1979

Levy, M.
Proceedings of the National Academy of Sciences, Vol. 76, Issue 12
DOI: 10.1073/pnas.76.12.6062

Quasiparticle Self-Consistent $G W$ Theory
journal, June 2006

van Schilfgaarde, M.; Kotani, Takao; Faleev, S.
Physical Review Letters, Vol. 96, Issue 22
DOI: 10.1103/PhysRevLett.96.226402

Density Functionals Not Based on the Electron Gas: Local-Density Approximation for a Luttinger Liquid
journal, April 2003

Lima, N. A.; Silva, M. F.; Oliveira, L. N.
Physical Review Letters, Vol. 90, Issue 14
DOI: 10.1103/PhysRevLett.90.146402

Metallic ferromagnetism in a single-band model
journal, August 1989

Hirsch, J. E.
Physical Review B, Vol. 40, Issue 4
DOI: 10.1103/PhysRevB.40.2354

Density-matrix functional study of the Hubbard model on one- and two-dimensional bipartite lattices
journal, July 2011

Saubanère, Matthieu; Pastor, G. M.
Physical Review B, Vol. 84, Issue 3
DOI: 10.1103/PhysRevB.84.035111

The GW method
journal, March 1998

Aryasetiawan, F.; Gunnarsson, O.
Reports on Progress in Physics, Vol. 61, Issue 3
DOI: 10.1088/0034-4885/61/3/002

Spin-independent V-representability of Wigner crystal oscillations in one-dimensional Hubbard chains: The role of spin-charge separation
journal, August 2012

Vieira, Daniel
Physical Review B, Vol. 86, Issue 7
DOI: 10.1103/PhysRevB.86.075132

Density-Functional Theory of the Electronic Structure of Molecules
journal, October 1995

Parr, Robert G.; Yang, Weitao
Annual Review of Physical Chemistry, Vol. 46, Issue 1
DOI: 10.1146/annurev.pc.46.100195.003413

Atoms, molecules, solids, and surfaces: Applications of the generalized gradient approximation for exchange and correlation
journal, September 1992

Perdew, John P.; Chevary, J. A.; Vosko, S. H.
Physical Review B, Vol. 46, Issue 11
DOI: 10.1103/PhysRevB.46.6671

Ferromagnetic transition and phase diagram of the one-dimensional Hubbard model with next-nearest-neighbor hopping
journal, August 1998

Daul, S.; Noack, R. M.
Physical Review B, Vol. 58, Issue 5
DOI: 10.1103/PhysRevB.58.2635

A local exchange-correlation potential for the spin polarized case. i
journal, July 1972

Barth, U. von; Hedin, L.
Journal of Physics C: Solid State Physics, Vol. 5, Issue 13
DOI: 10.1088/0022-3719/5/13/012

Hubbard Hamiltonian for the hydrogen molecule
journal, May 2007

Chiappe, G.; Louis, E.; SanFabián, E.
Physical Review B, Vol. 75, Issue 19
DOI: 10.1103/PhysRevB.75.195104

The analog of Koopmans’ theorem in spin-density functional theory
journal, November 2002

Gritsenko, O. V.; Baerends, E. J.
The Journal of Chemical Physics, Vol. 117, Issue 20
DOI: 10.1063/1.1516800

Discontinuity of the exchange-correlation potential: Support for assumptions used to find it
journal, January 2008

Sagvolden, Espen; Perdew, John P.
Physical Review A, Vol. 77, Issue 1
DOI: 10.1103/PhysRevA.77.012517

Doping a Mott insulator: Physics of high-temperature superconductivity
journal, January 2006

Lee, Patrick A.; Nagaosa, Naoto; Wen, Xiao-Gang
Reviews of Modern Physics, Vol. 78, Issue 1
DOI: 10.1103/RevModPhys.78.17

A Variational Approach to the Unipotential Many-Electron Problem
journal, April 1953

Sharp, R. T.; Horton, G. K.
Physical Review, Vol. 90, Issue 2
DOI: 10.1103/PhysRev.90.317

Energy differences between Kohn-Sham and Hartree-Fock wave functions yielding the same electron density
journal, June 1995

Görling, Andreas; Ernzerhof, Matthias
Physical Review A, Vol. 51, Issue 6
DOI: 10.1103/PhysRevA.51.4501

Comparative study of many-body perturbation theory and time-dependent density functional theory in the out-of-equilibrium Anderson model
journal, September 2011

Uimonen, A. -M.; Khosravi, E.; Stan, A.
Physical Review B, Vol. 84, Issue 11
DOI: 10.1103/PhysRevB.84.115103

Bethe ansatz density-functional theory of ultracold repulsive fermions in one-dimensional optical lattices
journal, April 2006

Xianlong, Gao; Polini, Marco; Tosi, M. P.
Physical Review B, Vol. 73, Issue 16
DOI: 10.1103/PhysRevB.73.165120

Perspective on density functional theory
journal, April 2012

Burke, Kieron
The Journal of Chemical Physics, Vol. 136, Issue 15
DOI: 10.1063/1.4704546

The adiabatic connection method: a non-empirical hybrid
journal, January 1997

Burke, Kieron; Ernzerhof, Matthias; Perdew, John P.
Chemical Physics Letters, Vol. 265, Issue 1-2
DOI: 10.1016/S0009-2614(96)01373-5

Two-dimensional Hubbard model with nearest- and next-nearest-neighbor hopping
journal, March 1987

Lin, H. Q.; Hirsch, J. E.
Physical Review B, Vol. 35, Issue 7
DOI: 10.1103/PhysRevB.35.3359

Communication: Self-interaction correction with unitary invariance in density functional theory
journal, March 2014

Pederson, Mark R.; Ruzsinszky, Adrienn; Perdew, John P.
The Journal of Chemical Physics, Vol. 140, Issue 12
DOI: 10.1063/1.4869581

Dynamical Correction to Linear Kohn-Sham Conductances from Static Density Functional Theory
journal, July 2013

Kurth, S.; Stefanucci, G.
Physical Review Letters, Vol. 111, Issue 3
DOI: 10.1103/PhysRevLett.111.030601

Density-matrix functional theory of strongly correlated lattice fermions
journal, October 2002

López-Sandoval, R.; Pastor, G. M.
Physical Review B, Vol. 66, Issue 15
DOI: 10.1103/PhysRevB.66.155118

Density-functional theory of strongly correlated Fermi gases in elongated harmonic traps
journal, March 2006

Xianlong, Gao; Polini, Marco; Asgari, Reza
Physical Review A, Vol. 73, Issue 3
DOI: 10.1103/PhysRevA.73.033609

The surface energy of a bounded electron gas
journal, August 1974

Harris, J.; Jones, R. O.
Journal of Physics F: Metal Physics, Vol. 4, Issue 8
DOI: 10.1088/0305-4608/4/8/013

Density functional theory for strongly-interacting electrons: perspectives for physics and chemistry
journal, January 2010

Gori-Giorgi, Paola; Seidl, Michael
Physical Chemistry Chemical Physics, Vol. 12, Issue 43
DOI: 10.1039/c0cp01061h

Competition between local potentials and attractive particle–particle interactions in superlattices
journal, December 2007

Lima, N. A.; Malvezzi, A. L.; Capelle, K.
Solid State Communications, Vol. 144, Issue 12
DOI: 10.1016/j.ssc.2007.03.057

Fractional charge perspective on the band gap in density-functional theory
journal, March 2008

Cohen, Aron J.; Mori-Sánchez, Paula; Yang, Weitao
Physical Review B, Vol. 77, Issue 11
DOI: 10.1103/PhysRevB.77.115123

A bird's-eye view of density-functional theory
journal, January 2006

Capelle, Klaus
Brazilian Journal of Physics, Vol. 36, Issue 4a
DOI: 10.1590/S0103-97332006000700035

Density functional theory based many-body analysis of electron transport through molecules
journal, January 2011

Mirjani, F.; Thijssen, J. M.
Physical Review B, Vol. 83, Issue 3
DOI: 10.1103/PhysRevB.83.035415

Reference electronic structure calculations in one dimension
journal, January 2012

Wagner, Lucas O.; Stoudenmire, E. M.; Burke, Kieron
Physical Chemistry Chemical Physics, Vol. 14, Issue 24
DOI: 10.1039/c2cp24118h

Exchange-correlation energy and potential as approximate functionals of occupied and virtual Kohn–Sham orbitals: Application to dissociating H[sub 2]
journal, January 2003

Grüning, M.; Gritsenko, O. V.; Baerends, E. J.
The Journal of Chemical Physics, Vol. 118, Issue 16
DOI: 10.1063/1.1562197

Exchange and correlation in atoms, molecules, and solids by the spin-density-functional formalism
journal, May 1976

Gunnarsson, O.; Lundqvist, B. I.
Physical Review B, Vol. 13, Issue 10
DOI: 10.1103/PhysRevB.13.4274

Zur Theorie der Kernmassen
journal, July 1935

Weizs�cker, C. F. v.
Zeitschrift f�r Physik, Vol. 96, Issue 7-8
DOI: 10.1007/BF01337700

Excitation energies from time-dependent density-functional formalism for small systems
journal, March 2002

Aryasetiawan, F.; Gunnarsson, O.; Rubio, A.
Europhysics Letters (EPL), Vol. 57, Issue 5
DOI: 10.1209/epl/i2002-00517-6

Electric field response of strongly correlated one-dimensional metals: A Bethe ansatz density functional theory study
journal, December 2010

Akande, A.; Sanvito, S.
Physical Review B, Vol. 82, Issue 24
DOI: 10.1103/PhysRevB.82.245114

Density-functional theory for one-dimensional harmonically trapped Bose-Fermi mixture
journal, May 2012

Wang, Hongmei; Hao, Yajiang; Zhang, Yunbo
Physical Review A, Vol. 85, Issue 5
DOI: 10.1103/PhysRevA.85.053630

First-principles calculations of the electronic structure and spectra of strongly correlated systems: the LDA + U method
journal, January 1997

Anisimov, Vladimir I.; Aryasetiawan, F.; Lichtenstein, A. I.
Journal of Physics: Condensed Matter, Vol. 9, Issue 4, p. 767-808
DOI: 10.1088/0953-8984/9/4/002

Adiabatic connection for strictly correlated electrons
journal, September 2009

Liu, Zhen-Fei; Burke, Kieron
The Journal of Chemical Physics, Vol. 131, Issue 12
DOI: 10.1063/1.3239472

Electronic excitations: density-functional versus many-body Green’s-function approaches
journal, June 2002

Onida, Giovanni; Reining, Lucia; Rubio, Angel
Reviews of Modern Physics, Vol. 74, Issue 2
DOI: 10.1103/RevModPhys.74.601

Eine statistische Methode zur Bestimmung einiger Eigenschaften des Atoms und ihre Anwendung auf die Theorie des periodischen Systems der Elemente
journal, January 1928

Fermi, E.
Zeitschrift f�r Physik, Vol. 48, Issue 1-2
DOI: 10.1007/BF01351576

What do the Kohn-Sham Orbital Energies Mean? How do Atoms Dissociate?
book,

Perdew, John P.
DOI: 10.1007/978-1-4757-0818-9_10

Effective action for strongly correlated fermions from functional integrals
journal, November 1990

Schulz, H. J.
Physical Review Letters, Vol. 65, Issue 19
DOI: 10.1103/PhysRevLett.65.2462

Electronic Structure
book, January 2004

Martin, Richard M.
DOI: 10.1017/CBO9780511805769

Exact Kohn-Sham eigenstates versus quasiparticles in simple models of strongly correlated electrons
journal, January 2012

Carrascal, D. J.; Ferrer, J.
Physical Review B, Vol. 85, Issue 4
DOI: 10.1103/PhysRevB.85.045110

Density-Functional Theory of the Energy Gap
journal, November 1983

Sham, L. J.; Schlüter, M.
Physical Review Letters, Vol. 51, Issue 20
DOI: 10.1103/PhysRevLett.51.1888

Assessment of the GW approximation using Hubbard chains
journal, February 1998

Pollehn, Thomas J.; Schindlmayr, Arno; Godby, R. W.
Journal of Physics: Condensed Matter, Vol. 10, Issue 6
DOI: 10.1088/0953-8984/10/6/011

Coupled-cluster theory in quantum chemistry
journal, February 2007

Bartlett, Rodney J.; Musiał, Monika
Reviews of Modern Physics, Vol. 79, Issue 1
DOI: 10.1103/RevModPhys.79.291

Density-functional theory of two-component Bose gases in one-dimensional harmonic traps
journal, October 2009

Hao, Yajiang; Chen, Shu
Physical Review A, Vol. 80, Issue 4
DOI: 10.1103/PhysRevA.80.043608

Relationship of Kohn–Sham eigenvalues to excitation energies
journal, May 1998

Savin, A.; Umrigar, C. J.; Gonze, Xavier
Chemical Physics Letters, Vol. 288, Issue 2-4
DOI: 10.1016/S0009-2614(98)00316-9

Static correlation beyond the random phase approximation: Dissociating H ₂ with the Bethe-Salpeter equation and time-dependent GW
journal, April 2014

Olsen, Thomas; Thygesen, Kristian S.
The Journal of Chemical Physics, Vol. 140, Issue 16
DOI: 10.1063/1.4871875

Physical Content of the Exact Kohn-Sham Orbital Energies: Band Gaps and Derivative Discontinuities
journal, November 1983

Perdew, John P.; Levy, Mel
Physical Review Letters, Vol. 51, Issue 20
DOI: 10.1103/PhysRevLett.51.1884

Hubbard-corrected DFT energy functionals: The LDA+U description of correlated systems
journal, July 2013

Himmetoglu, Burak; Floris, Andrea; de Gironcoli, Stefano
International Journal of Quantum Chemistry, Vol. 114, Issue 1
DOI: 10.1002/qua.24521

A Comparison of Model Chemistries
journal, November 1995

Ochterski, Joseph W.; Petersson, George A.; Wiberg, Kenneth B.
Journal of the American Chemical Society, Vol. 117, Issue 45
DOI: 10.1021/ja00150a030

The self-energy beyond GW: Local and nonlocal vertex corrections
journal, October 2009

Romaniello, P.; Guyot, S.; Reining, L.
The Journal of Chemical Physics, Vol. 131, Issue 15
DOI: 10.1063/1.3249965

Density‐functional thermochemistry. III. The role of exact exchange
journal, April 1993

Becke, Axel D.
The Journal of Chemical Physics, Vol. 98, Issue 7, p. 5648-5652
DOI: 10.1063/1.464913

One-Dimensional Continuum Electronic Structure with the Density-Matrix Renormalization Group and Its Implications for Density-Functional Theory
journal, August 2012

Stoudenmire, E. M.; Wagner, Lucas O.; White, Steven R.
Physical Review Letters, Vol. 109, Issue 5
DOI: 10.1103/PhysRevLett.109.056402

Investigation of Self-Interaction Corrections for an Exactly Solvable Model System: Orbital Dependence and Electron Localization
journal, October 2010

Vieira, Daniel; Capelle, K.
Journal of Chemical Theory and Computation, Vol. 6, Issue 11
DOI: 10.1021/ct100352r

Bethe Ansatz Approach to the Kondo Effect within Density-Functional Theory
journal, February 2012

Bergfield, Justin P.; Liu, Zhen-Fei; Burke, Kieron
Physical Review Letters, Vol. 108, Issue 6
DOI: 10.1103/PhysRevLett.108.066801

Systematic approximations to the optimized effective potential: Application to orbital-density-functional theory
journal, November 1992

Krieger, J. B.; Li, Yan; Iafrate, G. J.
Physical Review A, Vol. 46, Issue 9
DOI: 10.1103/PhysRevA.46.5453

Orbital-dependent density functionals: Theory and applications
journal, January 2008

Kümmel, Stephan; Kronik, Leeor
Reviews of Modern Physics, Vol. 80, Issue 1
DOI: 10.1103/RevModPhys.80.3

A low-cost, high-efficiency solar cell based on dye-sensitized colloidal TiO₂ films
journal, October 1991

O'Regan, Brian; Grätzel, Michael
Nature, Vol. 353, Issue 6346, p. 737-740
DOI: 10.1038/353737a0

Lattice density functional theory at finite temperature with strongly density-dependent exchange-correlation potentials
journal, December 2012

Xianlong, Gao; Chen, A-Hai; Tokatly, I. V.
Physical Review B, Vol. 86, Issue 23
DOI: 10.1103/PhysRevB.86.235139

Forces in Molecules
journal, August 1939

Feynman, R. P.
Physical Review, Vol. 56, Issue 4
DOI: 10.1103/PhysRev.56.340

Beyond the $G W$ approximation: Combining correlation channels
journal, April 2012

Romaniello, Pina; Bechstedt, Friedhelm; Reining, Lucia
Physical Review B, Vol. 85, Issue 15
DOI: 10.1103/PhysRevB.85.155131

Localized Magnetic States in Metals
journal, October 1961

Anderson, P. W.
Physical Review, Vol. 124, Issue 1
DOI: 10.1103/PhysRev.124.41

Density-functional approximation for the correlation energy of the inhomogeneous electron gas
journal, June 1986

Perdew, John P.
Physical Review B, Vol. 33, Issue 12
DOI: 10.1103/PhysRevB.33.8822

Localization and Delocalization Errors in Density Functional Theory and Implications for Band-Gap Prediction
journal, April 2008

Mori-Sánchez, Paula; Cohen, Aron J.; Yang, Weitao
Physical Review Letters, Vol. 100, Issue 14
DOI: 10.1103/PhysRevLett.100.146401

Escaping the symmetry dilemma through a pair-density interpretation of spin-density functional theory
journal, June 1995

Perdew, John P.; Savin, Andreas; Burke, Kieron
Physical Review A, Vol. 51, Issue 6
DOI: 10.1103/PhysRevA.51.4531

Interactions and Phase Transitions on Graphene’s Honeycomb Lattice
journal, October 2006

Herbut, Igor F.
Physical Review Letters, Vol. 97, Issue 14
DOI: 10.1103/PhysRevLett.97.146401

Density-Functional Theory for Time-Dependent Systems
journal, March 1984

Runge, Erich; Gross, E. K. U.
Physical Review Letters, Vol. 52, Issue 12
DOI: 10.1103/PhysRevLett.52.997

Toward reliable density functional methods without adjustable parameters: The PBE0 model
journal, April 1999

Adamo, Carlo; Barone, Vincenzo
The Journal of Chemical Physics, Vol. 110, Issue 13
DOI: 10.1063/1.478522

Assessment of the Perdew–Burke–Ernzerhof exchange-correlation functional
journal, March 1999

Ernzerhof, Matthias; Scuseria, Gustavo E.
The Journal of Chemical Physics, Vol. 110, Issue 11
DOI: 10.1063/1.478401

Time-dependent density functional theory on a lattice
journal, September 2012

Farzanehpour, M.; Tokatly, I. V.
Physical Review B, Vol. 86, Issue 12
DOI: 10.1103/PhysRevB.86.125130

'Luttinger liquid theory' of one-dimensional quantum fluids. I. Properties of the Luttinger model and their extension to the general 1D interacting spinless Fermi gas
journal, July 1981

Haldane, F. D. M.
Journal of Physics C: Solid State Physics, Vol. 14, Issue 19
DOI: 10.1088/0022-3719/14/19/010

Inhomogeneous Electron Gas
journal, November 1964

Hohenberg, P.; Kohn, W.
Physical Review, Vol. 136, Issue 3B, p. B864-B871
DOI: 10.1103/PhysRev.136.B864

Optimized effective atomic central potential
journal, July 1976

Talman, James D.; Shadwick, William F.
Physical Review A, Vol. 14, Issue 1
DOI: 10.1103/PhysRevA.14.36

Charge transfer in time-dependent density-functional theory: Insights from the asymmetric Hubbard dimer
journal, June 2014

Fuks, J. I.; Maitra, N. T.
Physical Review A, Vol. 89, Issue 6
DOI: 10.1103/PhysRevA.89.062502

Conserving Approximations for Strongly Correlated Electron Systems: Bethe-Salpeter Equation and Dynamics for the Two-Dimensional Hubbard Model
journal, February 1989

Bickers, N. E.; Scalapino, D. J.; White, S. R.
Physical Review Letters, Vol. 62, Issue 8
DOI: 10.1103/PhysRevLett.62.961

Hellmann-Feynman, virial, and scaling requisites for the exact universal density functionals. Shape of the correlation potential and diamagnetic susceptibility for atoms
journal, October 1985

Levy, Mel; Perdew, John P.
Physical Review A, Vol. 32, Issue 4
DOI: 10.1103/PhysRevA.32.2010

XXXIV. Notes on the molecular orbital treatment of the hydrogen molecule
journal, April 1949

Coulson, C. A.; Fischer, I.
The London, Edinburgh, and Dublin Philosophical Magazine and Journal of Science, Vol. 40, Issue 303
DOI: 10.1080/14786444908521726

Spin gaps and spin-flip energies in density-functional theory
journal, March 2010

Capelle, K.; Vignale, G.; Ullrich, C. A.
Physical Review B, Vol. 81, Issue 12
DOI: 10.1103/PhysRevB.81.125114

Time-Dependent Density-Functional Theory Meets Dynamical Mean-Field Theory: Real-Time Dynamics for the 3D Hubbard Model
journal, March 2011

Karlsson, Daniel; Privitera, Antonio; Verdozzi, Claudio
Physical Review Letters, Vol. 106, Issue 11
DOI: 10.1103/PhysRevLett.106.116401

New exactly solvable model of strongly correlated electrons motivated by high- $T_{c}$ superconductivity
journal, May 1992

Essler, Fabian H. L.; Korepin, Vladimir E.; Schoutens, Kareljan
Physical Review Letters, Vol. 68, Issue 19
DOI: 10.1103/PhysRevLett.68.2960

The one-dimensional Hubbard model: a reminiscence
journal, April 2003

Lieb, Elliott H.; Wu, F. Y.
Physica A: Statistical Mechanics and its Applications, Vol. 321, Issue 1-2
DOI: 10.1016/S0378-4371(02)01785-5

Evaluation of $GW$ Approximations for the Self-Energy of a Hubbard Cluster
journal, March 1995

Verdozzi, C.; Godby, R. W.; Holloway, S.
Physical Review Letters, Vol. 74, Issue 12
DOI: 10.1103/PhysRevLett.74.2327

Thermal Properties of the Inhomogeneous Electron Gas
journal, March 1965

Mermin, N. David
Physical Review, Vol. 137, Issue 5A
DOI: 10.1103/PhysRev.137.A1441

Two Fermions in a Double Well: Exploring a Fundamental Building Block of the Hubbard Model
journal, February 2015

Murmann, Simon; Bergschneider, Andrea; Klinkhamer, Vincent M.
Physical Review Letters, Vol. 114, Issue 8
DOI: 10.1103/PhysRevLett.114.080402

Time-Dependent Density-Functional Theory and Strongly Correlated Systems: Insight from Numerical Studies
journal, October 2008

Verdozzi, Claudio
Physical Review Letters, Vol. 101, Issue 16
DOI: 10.1103/PhysRevLett.101.166401

Ground-state properties of the one-dimensional attractive Hubbard model with confinement: A comparative study
journal, July 2010

Hu, Ji-Hong; Wang, Jing-Jing; Xianlong, Gao
Physical Review B, Vol. 82, Issue 1
DOI: 10.1103/PhysRevB.82.014202

Density-matrix functional theory of the Hubbard model: An exact numerical study
journal, January 2000

López-Sandoval, R.; Pastor, G. M.
Physical Review B, Vol. 61, Issue 3
DOI: 10.1103/PhysRevB.61.1764

Direct Method for Optimized Effective Potentials in Density-Functional Theory
journal, September 2002

Yang, Weitao; Wu, Qin
Physical Review Letters, Vol. 89, Issue 14
DOI: 10.1103/PhysRevLett.89.143002

Density functional theory for a model quantum dot: Beyond the local-density approximation
journal, March 2011

Schenk, S.; Schwab, P.; Dzierzawa, M.
Physical Review B, Vol. 83, Issue 11
DOI: 10.1103/PhysRevB.83.115128

Successes and failures of Bethe ansatz density functional theory
journal, October 2008

Schenk, Stefan; Dzierzawa, Michael; Schwab, Peter
Physical Review B, Vol. 78, Issue 16
DOI: 10.1103/PhysRevB.78.165102

Generalized Gradient Approximation Made Simple
journal, October 1996

Perdew, John P.; Burke, Kieron; Ernzerhof, Matthias
Physical Review Letters, Vol. 77, Issue 18, p. 3865-3868
DOI: 10.1103/PhysRevLett.77.3865

Orbital- and state-dependent functionals in density-functional theory
journal, August 2005

Görling, Andreas
The Journal of Chemical Physics, Vol. 123, Issue 6
DOI: 10.1063/1.1904583

Electron- and hole-hopping amplitudes in a diatomic molecule
journal, August 1993

Hirsch, J. E.
Physical Review B, Vol. 48, Issue 5
DOI: 10.1103/PhysRevB.48.3327

Density-functional theory for the spin-1 bosons in a one-dimensional harmonic trap
journal, August 2013

Wang, Hongmei; Zhang, Yunbo
Physical Review A, Vol. 88, Issue 2
DOI: 10.1103/PhysRevA.88.023626

Hybrid functionals based on a screened Coulomb potential
journal, May 2003

Heyd, Jochen; Scuseria, Gustavo E.; Ernzerhof, Matthias
The Journal of Chemical Physics, Vol. 118, Issue 18
DOI: 10.1063/1.1564060

Time-dependent density functional theory: Past, present, and future
journal, August 2005

Burke, Kieron; Werschnik, Jan; Gross, E. K. U.
The Journal of Chemical Physics, Vol. 123, Issue 6
DOI: 10.1063/1.1904586

Strongly Correlated Materials: Insights From Dynamical Mean-Field Theory
journal, March 2004

Kotliar, Gabriel; Vollhardt, Dieter
Physics Today, Vol. 57, Issue 3
DOI: 10.1063/1.1712502

A priori calculation of molecular properties to chemical accuracy
journal, August 2004

Helgaker, Trygve; Ruden, Torgeir A.; Jørgensen, Poul
Journal of Physical Organic Chemistry, Vol. 17, Issue 11
DOI: 10.1002/poc.841

Densities, operators, and basis sets
journal, July 1986

Harriman, John E.
Physical Review A, Vol. 34, Issue 1
DOI: 10.1103/PhysRevA.34.29

Accuracy of density functionals for molecular electronics: The Anderson junction
journal, April 2012

Liu, Zhen-Fei; Bergfield, Justin P.; Burke, Kieron
Physical Review B, Vol. 85, Issue 15
DOI: 10.1103/PhysRevB.85.155117

$2 k_{F}$ -Friedel to $4 k_{F}$ -Wigner oscillations in one-dimensional Fermi gases under confinement
journal, August 2012

Xianlong, Gao
Physical Review A, Vol. 86, Issue 2
DOI: 10.1103/PhysRevA.86.023616

Lattice density functional theory of the single-impurity Anderson model: Development and applications
journal, June 2011

Töws, W.; Pastor, G. M.
Physical Review B, Vol. 83, Issue 23
DOI: 10.1103/PhysRevB.83.235101

Nonadiabatic time-dependent spin-density functional theory for strongly correlated systems
journal, November 2013

Turkowski, Volodymyr; Rahman, Talat S.
Journal of Physics: Condensed Matter, Vol. 26, Issue 2
DOI: 10.1088/0953-8984/26/2/022201

Ab initio determination of the crystalline benzene lattice energy to sub-kilojoule/mole accuracy
journal, August 2014

Yang, J.; Hu, W.; Usvyat, D.
Science, Vol. 345, Issue 6197
DOI: 10.1126/science.1254419

Phase diagram of harmonically confined one-dimensional fermions with attractive and repulsive interactions
journal, December 2005

Campo, V. L.; Capelle, K.
Physical Review A, Vol. 72, Issue 6
DOI: 10.1103/PhysRevA.72.061602

Collective excitations in one-dimensional ultracold Fermi gases: Comparative study
journal, November 2008

Li, Wei; Xianlong, Gao; Kollath, Corinna
Physical Review B, Vol. 78, Issue 19
DOI: 10.1103/PhysRevB.78.195109

CO Chemisorption at Metal Surfaces and Overlayers
journal, March 1996

Hammer, B.; Morikawa, Y.; Nørskov, J. K.
Physical Review Letters, Vol. 76, Issue 12
DOI: 10.1103/PhysRevLett.76.2141

Strong Correlation in Kohn-Sham Density Functional Theory
journal, December 2012

Malet, Francesc; Gori-Giorgi, Paola
Physical Review Letters, Vol. 109, Issue 24
DOI: 10.1103/PhysRevLett.109.246402

Density Functional Theory of Electronic Structure
journal, January 1996

Kohn, W.; Becke, A. D.; Parr, R. G.
The Journal of Physical Chemistry, Vol. 100, Issue 31
DOI: 10.1021/jp960669l

Nobel Lecture: Electronic structure of matter—wave functions and density functionals
journal, October 1999

Kohn, W.
Reviews of Modern Physics, Vol. 71, Issue 5
DOI: 10.1103/RevModPhys.71.1253

Insights into Current Limitations of Density Functional Theory
journal, August 2008

Cohen, A. J.; Mori-Sanchez, P.; Yang, W.
Science, Vol. 321, Issue 5890
DOI: 10.1126/science.1158722

Physical interpretation and evaluation of the Kohn–Sham and Dyson components of the ε–I relations between the Kohn–Sham orbital energies and the ionization potentials
journal, July 2003

Gritsenko, O. V.; Braïda, B.; Baerends, E. J.
The Journal of Chemical Physics, Vol. 119, Issue 4
DOI: 10.1063/1.1582839

Correlation effects in bistability at the nanoscale: Steady state and beyond
journal, February 2012

Khosravi, E.; Uimonen, A. -M.; Stan, A.
Physical Review B, Vol. 85, Issue 7
DOI: 10.1103/PhysRevB.85.075103

Three-dimensional dynamics of a fermionic Mott wedding-cake in clean and disordered optical lattices
journal, September 2013

Kartsev, A.; Karlsson, D.; Privitera, A.
Scientific Reports, Vol. 3, Issue 1
DOI: 10.1038/srep02570

Self-Consistent Equations Including Exchange and Correlation Effects
journal, November 1965

Kohn, W.; Sham, L. J.
Physical Review, Vol. 140, Issue 4A, p. A1133-A1138
DOI: 10.1103/PhysRev.140.A1133

Guaranteed Convergence of the Kohn-Sham Equations
journal, August 2013

Wagner, Lucas O.; Stoudenmire, E. M.; Burke, Kieron
Physical Review Letters, Vol. 111, Issue 9
DOI: 10.1103/PhysRevLett.111.093003

Interaction-energy functional for lattice density functional theory: Applications to one-, two-, and three-dimensional Hubbard models
journal, February 2004

López-Sandoval, R.; Pastor, G. M.
Physical Review B, Vol. 69, Issue 8
DOI: 10.1103/PhysRevB.69.085101

Some open questions in TDDFT: Clues from lattice models and Kadanoff–Baym dynamics
journal, November 2011

Verdozzi, C.; Karlsson, D.; Puig von Friesen, M.
Chemical Physics, Vol. 391, Issue 1
DOI: 10.1016/j.chemphys.2011.04.035

Density-functional theory on a lattice: Comparison with exact numerical results for a model with strongly correlated electrons
journal, July 1995

Schönhammer, K.; Gunnarsson, O.; Noack, R. M.
Physical Review B, Vol. 52, Issue 4
DOI: 10.1103/PhysRevB.52.2504

Systematic study of first-row transition-metal diatomic molecules: A self-consistent DFT+U approach
journal, September 2010

Kulik, Heather J.; Marzari, Nicola
The Journal of Chemical Physics, Vol. 133, Issue 11
DOI: 10.1063/1.3489110

Development of the Colle-Salvetti correlation-energy formula into a functional of the electron density
journal, January 1988

Lee, Chengteh; Yang, Weitao; Parr, Robert G.
Physical Review B, Vol. 37, Issue 2
DOI: 10.1103/PhysRevB.37.785

Discontinuity of the exchange-correlation potential in density functional theory
journal, August 1987

Schonhammer, K.; Gunnarsson, O.
Journal of Physics C: Solid State Physics, Vol. 20, Issue 24
DOI: 10.1088/0022-3719/20/24/010

Solving lattice density functionals close to the Mott regime
journal, May 2014

Ying, Zu-Jian; Brosco, Valentina; Lorenzana, José
Physical Review B, Vol. 89, Issue 20
DOI: 10.1103/PhysRevB.89.205130

Density functionals and model Hamiltonians: Pillars of many-particle physics
journal, July 2013

Capelle, Klaus; Campo, Vivaldo L.
Physics Reports, Vol. 528, Issue 3
DOI: 10.1016/j.physrep.2013.03.002

Discontinuous Nature of the Exchange-Correlation Functional in Strongly Correlated Systems
journal, February 2009

Mori-Sánchez, Paula; Cohen, Aron J.; Yang, Weitao
Physical Review Letters, Vol. 102, Issue 6
DOI: 10.1103/PhysRevLett.102.066403

Toward Computational Materials Design: The Impact of Density Functional Theory on Materials Research
journal, September 2006

Hafner, Jürgen; Wolverton, Christopher; Ceder, Gerbrand
MRS Bulletin, Vol. 31, Issue 9
DOI: 10.1557/mrs2006.174

Correlated electrons in high-temperature superconductors
journal, July 1994

Dagotto, Elbio
Reviews of Modern Physics, Vol. 66, Issue 3
DOI: 10.1103/RevModPhys.66.763

Self-interaction-free exchange-correlation functional for thermochemistry and kinetics
journal, March 2006

Mori-Sánchez, Paula; Cohen, Aron J.; Yang, Weitao
The Journal of Chemical Physics, Vol. 124, Issue 9
DOI: 10.1063/1.2179072

Atomic-Scale Structure and Catalytic Reactivity of the RuO2(110) Surface
journal, February 2000

Over, H.
Science, Vol. 287, Issue 5457
DOI: 10.1126/science.287.5457.1474

Adiabatic connection in the low-density limit
journal, June 2009

Liu, Zhen-Fei; Burke, Kieron
Physical Review A, Vol. 79, Issue 6
DOI: 10.1103/PhysRevA.79.064503

Time-dependent bond-current functional theory for lattice Hamiltonians: Fundamental theorem and application to electron transport
journal, November 2011

Kurth, S.; Stefanucci, G.
Chemical Physics, Vol. 391, Issue 1
DOI: 10.1016/j.chemphys.2011.01.016

Density functional formulations for quantum chains
journal, July 2007

Alcaraz, Francisco C.; Capelle, Klaus
Physical Review B, Vol. 76, Issue 3
DOI: 10.1103/PhysRevB.76.035109

Describing static correlation in bond dissociation by Kohn–Sham density functional theory
journal, March 2005

Fuchs, M.; Niquet, Y. -M.; Gonze, X.
The Journal of Chemical Physics, Vol. 122, Issue 9
DOI: 10.1063/1.1858371

Wechselwirkung neutraler Atome und hom�opolare Bindung nach der Quantenmechanik
journal, June 1927

Heitler, W.; London, F.
Zeitschrift f�r Physik, Vol. 44, Issue 6-7
DOI: 10.1007/BF01397394

Absence of Mott Transition in an Exact Solution of the Short-Range, One-Band Model in One Dimension
journal, June 1968

Lieb, Elliott H.; Wu, F. Y.
Physical Review Letters, Vol. 20, Issue 25
DOI: 10.1103/PhysRevLett.20.1445

Density-Functional Theory for Strongly Interacting Electrons
journal, October 2009

Gori-Giorgi, Paola; Seidl, Michael; Vignale, G.
Physical Review Letters, Vol. 103, Issue 16
DOI: 10.1103/PhysRevLett.103.166402

Challenging adiabatic time-dependent density functional theory with a Hubbard dimer: the case of time-resolved long-range charge transfer
journal, January 2014

Fuks, Johanna I.; Maitra, Neepa T.
Phys. Chem. Chem. Phys., Vol. 16, Issue 28
DOI: 10.1039/C4CP00118D

Conserving approximations for strongly fluctuating electron systems. I. Formalism and calculational approach
journal, July 1989

Bickers, N. E.; Scalapino, D. J.
Annals of Physics, Vol. 193, Issue 1
DOI: 10.1016/0003-4916(89)90359-X

Effects of disorder on atomic density waves and spin-singlet dimers in one-dimensional optical lattices
journal, August 2008

Xianlong, Gao
Physical Review B, Vol. 78, Issue 8
DOI: 10.1103/PhysRevB.78.085108

Lattice density-functional theory of the attractive Hubbard model
journal, September 2014

Saubanère, Matthieu; Pastor, G. M.
Physical Review B, Vol. 90, Issue 12
DOI: 10.1103/PhysRevB.90.125128

The spin-unrestricted molecular Kohn–Sham solution and the analogue of Koopmans’s theorem for open-shell molecules
journal, May 2004

Gritsenko, O. V.; Baerends, E. J.
The Journal of Chemical Physics, Vol. 120, Issue 18
DOI: 10.1063/1.1698561

Time-dependent exchange-correlation functional for a Hubbard dimer: Quantifying nonadiabatic effects
journal, December 2013

Fuks, Johanna I.; Farzanehpour, Mehdi; Tokatly, Ilya V.
Physical Review A, Vol. 88, Issue 6
DOI: 10.1103/PhysRevA.88.062512

Density-functional exchange-energy approximation with correct asymptotic behavior
journal, September 1988

Becke, A. D.
Physical Review A, Vol. 38, Issue 6
DOI: 10.1103/PhysRevA.38.3098

Density functionals for coulomb systems
journal, September 1983

Lieb, Elliott H.
International Journal of Quantum Chemistry, Vol. 24, Issue 3
DOI: 10.1002/qua.560240302

Fulde-Ferrell-Larkin-Ovchinnikov critical polarization in one-dimensional fermionic optical lattices
journal, September 2012

França, Vivian V.; Hörndlein, Dominik; Buchleitner, Andreas
Physical Review A, Vol. 86, Issue 3
DOI: 10.1103/PhysRevA.86.033622

Theory of the Insulating State
journal, January 1964

Kohn, Walter
Physical Review, Vol. 133, Issue 1A
DOI: 10.1103/PhysRev.133.A171

Proof that $\frac{\partial E}{\partial n_{i}} = ε$ in density-functional theory
journal, December 1978

Janak, J. F.
Physical Review B, Vol. 18, Issue 12
DOI: 10.1103/PhysRevB.18.7165

Probing the limits of accuracy in electronic structure calculations: Is theory capable of results uniformly better than “chemical accuracy”?
journal, March 2007

Feller, David; Peterson, Kirk A.
The Journal of Chemical Physics, Vol. 126, Issue 11
DOI: 10.1063/1.2464112

The exchange-correlation energy of a metallic surface
journal, December 1975

Langreth, D. C.; Perdew, J. P.
Solid State Communications, Vol. 17, Issue 11
DOI: 10.1016/0038-1098(75)90618-3

First-principles calculations of the electronic structure and spectra of strongly correlated systems: dynamical mean-field theory
journal, September 1997

Anisimov, V. I.; Poteryaev, A. I.; Korotin, M. A.
Journal of Physics: Condensed Matter, Vol. 9, Issue 35
DOI: 10.1088/0953-8984/9/35/010

Density-functional theory and the v -representability problem for model strongly correlated electron systems
journal, April 1995

Schindlmayr, Arno; Godby, R. W.
Physical Review B, Vol. 51, Issue 16
DOI: 10.1103/PhysRevB.51.10427

The derivative discontinuity of the exchange–correlation functional
journal, January 2014

Mori-Sánchez, Paula; Cohen, Aron J.
Phys. Chem. Chem. Phys., Vol. 16, Issue 28
DOI: 10.1039/c4cp01170h

Exact results for the charge and spin densities, exchange-correlation potentials, and density-functional eigenvalues
journal, March 1985

Almbladh, C. -O.; von Barth, U.
Physical Review B, Vol. 31, Issue 6
DOI: 10.1103/PhysRevB.31.3231

Electronic structure calculations with dynamical mean-field theory
journal, August 2006

Kotliar, G.; Savrasov, S. Y.; Haule, K.
Reviews of Modern Physics, Vol. 78, Issue 3
DOI: 10.1103/RevModPhys.78.865

Possible critical behavior driven by the confining potential in optical lattices with ultra-cold fermions
journal, October 2009

Campo, V. L.; Quintanilla, J.; Hooley, C.
Physica B: Condensed Matter, Vol. 404, Issue 19
DOI: 10.1016/j.physb.2009.07.089

Time-dependent current density functional theory on a lattice
journal, January 2011

Tokatly, I. V.
Physical Review B, Vol. 83, Issue 3
DOI: 10.1103/PhysRevB.83.035127

Dynamical self-stabilization of the Mott insulator: Time evolution of the density and entanglement entropy of out-of-equilibrium cold fermion gases
journal, January 2011

Karlsson, D.; Verdozzi, C.; Odashima, M. M.
EPL (Europhysics Letters), Vol. 93, Issue 2
DOI: 10.1209/0295-5075/93/23003

Exchange and correlation energies in density-functional theory: Bounds from available data
journal, March 1986

Sahni, Viraht; Levy, Mel
Physical Review B, Vol. 33, Issue 6
DOI: 10.1103/PhysRevB.33.3869

Simple parameterization for the ground-state energy of the infinite Hubbard chain incorporating Mott physics, spin-dependent phenomena and spatial inhomogeneity
journal, July 2012

França, Vivian V.; Vieira, Daniel; Capelle, Klaus
New Journal of Physics, Vol. 14, Issue 7
DOI: 10.1088/1367-2630/14/7/073021

Emergence of Wigner molecules in one-dimensional systems of repulsive fermions under harmonic confinement
journal, January 2007

Abedinpour, Saeed H.; Polini, Marco; Xianlong, Gao
Physical Review A, Vol. 75, Issue 1
DOI: 10.1103/PhysRevA.75.015602

Dynamical Coulomb Blockade and the Derivative Discontinuity of Time-Dependent Density Functional Theory
journal, June 2010

Kurth, S.; Stefanucci, G.; Khosravi, E.
Physical Review Letters, Vol. 104, Issue 23
DOI: 10.1103/PhysRevLett.104.236801

Adiabatic and local approximations for the Kohn-Sham potential in time-dependent Hubbard chains
journal, May 2014

Mancini, L.; Ramsden, J. D.; Hodgson, M. J. P.
Physical Review B, Vol. 89, Issue 19
DOI: 10.1103/PhysRevB.89.195114

Density-functional study of the Mott gap in the Hubbard model
journal, November 2002

Lima, N. A.; Oliveira, L. N.; Capelle, K.
Europhysics Letters (EPL), Vol. 60, Issue 4
DOI: 10.1209/epl/i2002-00261-y

Phase behaviors of strongly correlated Fermi gases in one-dimensional confinements
journal, February 2007

Abedinpour, S. H.; Bakhtiari, M. R.; Xianlong, G.
Laser Physics, Vol. 17, Issue 2
DOI: 10.1134/S1054660X0702020X

Adiabatic connection from accurate wave-function calculations
journal, March 2000

Frydel, Derek; Terilla, William M.; Burke, Kieron
The Journal of Chemical Physics, Vol. 112, Issue 12
DOI: 10.1063/1.481099

Exchange-correlation energy of a metallic surface: Wave-vector analysis
journal, March 1977

Langreth, David C.; Perdew, John P.
Physical Review B, Vol. 15, Issue 6
DOI: 10.1103/PhysRevB.15.2884

Strong Correlations in Density-Functional Theory: A Model of Spin-Charge and Spin–Orbital Separations
journal, August 2014

Vieira, Daniel
Journal of Chemical Theory and Computation, Vol. 10, Issue 9
DOI: 10.1021/ct400223d

Thermal versus quantum fluctuations of optical-lattice fermions
journal, March 2012

Campo, V. L.; Capelle, K.; Hooley, C.
Physical Review A, Vol. 85, Issue 3
DOI: 10.1103/PhysRevA.85.033644

Kohn-Sham calculations with the exact functional
journal, July 2014

Wagner, Lucas O.; Baker, Thomas E.; Stoudenmire, E. M.
Physical Review B, Vol. 90, Issue 4
DOI: 10.1103/PhysRevB.90.045109

Electronic properties of the dimerized one-dimensional Hubbard model using lattice density-functional theory
journal, January 2003

López-Sandoval, R.; Pastor, G. M.
Physical Review B, Vol. 67, Issue 3
DOI: 10.1103/PhysRevB.67.035115

Generalized Kohn-Sham system in one-matrix functional theory
journal, June 2008

Requist, Ryan; Pankratov, Oleg
Physical Review B, Vol. 77, Issue 23
DOI: 10.1103/PhysRevB.77.235121

Correlation-energy functional and its high-density limit obtained from a coupling-constant perturbation expansion
journal, May 1993

Görling, Andreas; Levy, Mel
Physical Review B, Vol. 47, Issue 20
DOI: 10.1103/PhysRevB.47.13105

Effects of nanoscale spatial inhomogeneity in strongly correlated systems
journal, March 2005

Silva, M. F.; Lima, N. A.; Malvezzi, A. L.
Physical Review B, Vol. 71, Issue 12
DOI: 10.1103/PhysRevB.71.125130

Interacting fermions in one-dimensional disordered lattices: Exploring localization and transport properties with lattice density-functional theories
journal, March 2013

Vettchinkina, V.; Kartsev, A.; Karlsson, D.
Physical Review B, Vol. 87, Issue 11
DOI: 10.1103/PhysRevB.87.115117

Self-interaction correction for density-functional theory of electronic energy bands of solids
journal, November 1983

Heaton, Richard A.; Harrison, Joseph G.; Lin, Chun C.
Physical Review B, Vol. 28, Issue 10
DOI: 10.1103/PhysRevB.28.5992

DFT in a nutshell
journal, July 2012

Burke, Kieron; Wagner, Lucas O.
International Journal of Quantum Chemistry, Vol. 113, Issue 2
DOI: 10.1002/qua.24259

Accurate and simple analytic representation of the electron-gas correlation energy
journal, June 1992

Perdew, John P.; Wang, Yue
Physical Review B, Vol. 45, Issue 23, p. 13244-13249
DOI: 10.1103/PhysRevB.45.13244

Dynamical mean-field theory of strongly correlated fermion systems and the limit of infinite dimensions
journal, January 1996

Georges, Antoine; Kotliar, Gabriel; Krauth, Werner
Reviews of Modern Physics, Vol. 68, Issue 1
DOI: 10.1103/RevModPhys.68.13

The calculation of atomic fields
journal, January 1927

Thomas, L. H.
Mathematical Proceedings of the Cambridge Philosophical Society, Vol. 23, Issue 5
DOI: 10.1017/S0305004100011683

Density-Functional Treatment of an Exactly Solvable Semiconductor Model
journal, May 1986

Gunnarsson, O.; Schönhammer, K.
Physical Review Letters, Vol. 56, Issue 18
DOI: 10.1103/PhysRevLett.56.1968

Combining DFT and many-body methods to understand correlated materials
journal, June 2008

Solovyev, I. V.
Journal of Physics: Condensed Matter, Vol. 20, Issue 29
DOI: 10.1088/0953-8984/20/29/293201

Exact Exchange-Correlation Treatment of Dissociated $H_{2}$ in Density Functional Theory
journal, September 2001

Baerends, E. J.
Physical Review Letters, Vol. 87, Issue 13
DOI: 10.1103/PhysRevLett.87.133004

Friedel oscillations in one-dimensional metals: From Luttinger's theorem to the Luttinger liquid
journal, July 2008

Vieira, Daniel; Freire, Henrique J. P.; Campo, V. L.
Journal of Magnetism and Magnetic Materials, Vol. 320, Issue 14
DOI: 10.1016/j.jmmm.2008.02.077

Self-interaction correction to density-functional approximations for many-electron systems
journal, May 1981

Perdew, J. P.; Zunger, Alex
Physical Review B, Vol. 23, Issue 10, p. 5048-5079
DOI: 10.1103/PhysRevB.23.5048

Rationale for mixing exact exchange with density functional approximations
journal, December 1996

Perdew, John P.; Ernzerhof, Matthias; Burke, Kieron
The Journal of Chemical Physics, Vol. 105, Issue 22, p. 9982-9985
DOI: 10.1063/1.472933

Electrical energy storage for transportation—approaching the limits of, and going beyond, lithium-ion batteries
journal, January 2012

Thackeray, Michael M.; Wolverton, Christopher; Isaacs, Eric D.
Energy & Environmental Science, Vol. 5, Issue 7
DOI: 10.1039/c2ee21892e

Adiabatic approximation in time-dependent reduced-density-matrix functional theory
journal, April 2010

Requist, Ryan; Pankratov, Oleg
Physical Review A, Vol. 81, Issue 4
DOI: 10.1103/PhysRevA.81.042519

Why semilocal functionals work: Accuracy of the on-top pair density and importance of system averaging
journal, September 1998

Burke, Kieron; Perdew, John P.; Ernzerhof, Matthias
The Journal of Chemical Physics, Vol. 109, Issue 10
DOI: 10.1063/1.476976

Configuration Interaction in the Hydrogen Molecule—The Ground State
journal, April 1960

McLean, A. D.; Weiss, A.; Yoshimine, M.
Reviews of Modern Physics, Vol. 32, Issue 2
DOI: 10.1103/RevModPhys.32.211

A Mott insulator of fermionic atoms in an optical lattice
journal, September 2008

Jördens, Robert; Strohmaier, Niels; Günter, Kenneth
Nature, Vol. 455, Issue 7210
DOI: 10.1038/nature07244

On the Non‐Orthogonality Problem Connected with the Use of Atomic Wave Functions in the Theory of Molecules and Crystals
journal, March 1950

Löwdin, Per‐Olov
The Journal of Chemical Physics, Vol. 18, Issue 3
DOI: 10.1063/1.1747632

Absence of Mott Transition in an Exact Solution of the Short-Range, One-Band Model in One Dimension
journal, July 1968

Lieb, Elliott H.; Wu, F. Y.
Physical Review Letters, Vol. 21, Issue 3
DOI: 10.1103/physrevlett.21.192.2

The Many-Body Problem
journal, January 2016

Moorjani, Kishin
Samuel Beckett Today / Aujourd’hui, Vol. 28, Issue 1
DOI: 10.1163/18757405-02801007

Fractional charge perspective on the band-gap in density-functional theory
text, January 2007

Cohen, Aron J.; Mori-Sánchez, Paula; Yang, Weitao
arXiv
DOI: 10.48550/arxiv.0708.3175

A Mott insulator of fermionic atoms in an optical lattice
text, January 2008

Jördens, Robert; Strohmaier, Niels; Günter, Kenneth
arXiv
DOI: 10.48550/arxiv.0804.4009

Collective excitations in one-dimensional ultracold Fermi gases: a comparative study
text, January 2008

Li, Wei; Xianlong, Gao; Kollath, Corinna
arXiv
DOI: 10.48550/arxiv.0805.4743

Time-dependent current density functional theory on a lattice
text, January 2010

Tokatly, I. V.
arXiv
DOI: 10.48550/arxiv.1011.2715

Lattice density-functional theory on graphene
text, January 2010

Ijäs, M.; Harju, A.
arXiv
DOI: 10.48550/arxiv.1011.2892

Persistent current and Drude weight for the one-dimensional Hubbard model from current lattice density functional theory
preprint, January 2010

Akande, A.; Sanvito, S.
arXiv
DOI: 10.48550/arxiv.1012.5908

Fulde-Ferrell-Larkin-Ovchinnikov critical polarization in one-dimensional fermionic optical lattices
text, January 2011

França, Vivian V.; Hördlein, Dominik; Buchleitner, Andreas
arXiv
DOI: 10.48550/arxiv.1103.2951

Correlation effects in bistability at the nanoscale: steady state and beyond
text, January 2011

Khosravi, E.; Uimonen, A. -M.; Stan, A.
arXiv
DOI: 10.48550/arxiv.1112.2871

Perspective on density functional theory
text, January 2012

Burke, Kieron
arXiv
DOI: 10.48550/arxiv.1201.3679

Lattice density functional theory at finite temperature with strongly density-dependent exchange-correlation potentials
text, January 2012

Xianlong, Gao; Chen, A-Hai; Tokatly, I. V.
arXiv
DOI: 10.48550/arxiv.1209.3145

Nonadiabatic Time-Dependent Spin-Density Functional Theory for strongly correlated systems
text, January 2012

Turkowski, Volodymyr; Rahman, Talat S.
arXiv
DOI: 10.48550/arxiv.1210.6397

Guaranteed convergence of the Kohn-Sham equations
text, January 2013

Wagner, Lucas O.; Stoudenmire, E. M.; Burke, Kieron
arXiv
DOI: 10.48550/arxiv.1305.2967

Three-dimensional dynamics of a fermionic Mott wedding-cake in clean and disordered optical lattices
preprint, January 2013

Kartsev, A.; Karlsson, D.; Privitera, A.
arXiv
DOI: 10.48550/arxiv.1308.4382

Hubbard-corrected DFT energy functionals: the LDA+U description of correlated systems
text, January 2013

Himmetoglu, Burak; Floris, Andrea; de Gironcoli, Stefano
arXiv
DOI: 10.48550/arxiv.1309.3355

Component separation of two-component fermion clouds in a spin-dependent external potential by spin-density-functional theory
text, January 2013

Xianlong, Gao
arXiv
DOI: 10.48550/arxiv.1309.5198

Charge-Transfer in Time-Dependent Density Functional Theory: Insights from the Asymmetric Hubbard Dimer
text, January 2013

Fuks, J. I.; Maitra, N. T.
arXiv
DOI: 10.48550/arxiv.1312.6880

Solving lattice density functionals close to the Mott regime
text, January 2014

Ying, Zu-Jian; Brosco, Valentina; Lorenzana, José
arXiv
DOI: 10.48550/arxiv.1403.5080

A bird's-eye view of density-functional theory
preprint, January 2002

Capelle, Klaus
arXiv
DOI: 10.48550/arxiv.cond-mat/0211443

Describing static correlation in bond dissociation by Kohn-Sham density functional theory
text, January 2004

Fuchs, M.; Niquet, Y. -M.; Gonze, X.
arXiv
DOI: 10.48550/arxiv.cond-mat/0410482

Density-functional formulations for quantum chains
text, January 2007

Alcaraz, Francisco C.; Capelle, Klaus
arXiv
DOI: 10.48550/arxiv.cond-mat/0702080

Correlated Electrons in High Temperature Superconductors
text, January 1993

Dagotto, Elbio
arXiv
DOI: 10.48550/arxiv.cond-mat/9311013

Works referencing / citing this record:

Multiple impurities and combined local density approximations in site-occupation embedding theory
journal, November 2018

Senjean, Bruno; Nakatani, Naoki; Tsuchiizu, Masahisa
Theoretical Chemistry Accounts, Vol. 137, Issue 12
DOI: 10.1007/s00214-018-2368-z

Accurate double excitations from ensemble density functional calculations
journal, October 2018

Sagredo, Francisca; Burke, Kieron
The Journal of Chemical Physics, Vol. 149, Issue 13
DOI: 10.1063/1.5043411

On the performance of natural orbital functional approximations in the Hubbard model
journal, September 2017

Mitxelena, I.; Piris, M.; Rodríguez-Mayorga, M.
Journal of Physics: Condensed Matter, Vol. 29, Issue 42
DOI: 10.1088/1361-648x/aa80ca

(Spin-)density-functional theory for open-shell systems: Exact magnetization density functional for the half-filled Hubbard trimer
journal, July 2019

Ullrich, Carsten A.
Physical Review A, Vol. 100, Issue 1
DOI: 10.1103/physreva.100.012516

Unified formulation of fundamental and optical gap problems in density-functional theory for ensembles
journal, August 2018

Senjean, Bruno; Fromager, Emmanuel
Physical Review A, Vol. 98, Issue 2
DOI: 10.1103/physreva.98.022513

Projected site-occupation embedding theory
journal, July 2019

Senjean, Bruno
Physical Review B, Vol. 100, Issue 3
DOI: 10.1103/physrevb.100.035136

Exchange-correlation magnetic fields in spin-density-functional theory
journal, September 2019

Pluhar, Edward A.; Ullrich, Carsten A.
Physical Review B, Vol. 100, Issue 12
DOI: 10.1103/physrevb.100.125135

Reduced density-matrix functionals applied to the Hubbard dimer
journal, February 2016

Kamil, Ebad; Schade, Robert; Pruschke, Thomas
Physical Review B, Vol. 93, Issue 8
DOI: 10.1103/physrevb.93.085141

Quantifying the effect of interactions in quantum many-body systems
journal, September 2018

Pachos, Jiannis; Papic, Zlatko
SciPost Physics Lecture Notes
DOI: 10.21468/scipostphyslectnotes.4

Density functional theory of electron transfer beyond the Born-Oppenheimer approximation: Case study of LiF
journal, February 2018

Li, Chen; Requist, Ryan; Gross, E. K. U.
The Journal of Chemical Physics, Vol. 148, Issue 8
DOI: 10.1063/1.5011663

Exact ensemble density functional theory for excited states in a model system: Investigating the weight dependence of the correlation energy
journal, January 2017

Deur, Killian; Mazouin, Laurent; Fromager, Emmanuel
Physical Review B, Vol. 95, Issue 3
DOI: 10.1103/physrevb.95.035120

Ground and excited energy levels can be extracted exactly from a single ensemble density-functional theory calculation
journal, March 2019

Deur, Killian; Fromager, Emmanuel
The Journal of Chemical Physics, Vol. 150, Issue 9
DOI: 10.1063/1.5084312

Many-body effects on the thermodynamics of closed quantum systems
journal, November 2019

Skelt, A. H.; Zawadzki, K.; D’Amico, I.
Journal of Physics A: Mathematical and Theoretical, Vol. 52, Issue 48
DOI: 10.1088/1751-8121/ab4fb6

Site-occupation Green's function embedding theory: A density functional approach to dynamical impurity solvers
journal, November 2019

Mazouin, Laurent; Saubanère, Matthieu; Fromager, Emmanuel
Physical Review B, Vol. 100, Issue 19
DOI: 10.1103/physrevb.100.195104

Diverging Exchange Force and Form of the Exact Density Matrix Functional
journal, January 2019

Schilling, Christian; Schilling, Rolf
Physical Review Letters, Vol. 122, Issue 1
DOI: 10.1103/physrevlett.122.013001

Local density approximation in site-occupation embedding theory
journal, May 2016

Senjean, Bruno; Tsuchiizu, Masahisa; Robert, Vincent
Molecular Physics, Vol. 115, Issue 1-2
DOI: 10.1080/00268976.2016.1182224

An efficient method for strongly correlated electrons in one dimension
journal, January 2020

Mitxelena, Ion; Piris, Mario
Journal of Physics: Condensed Matter, Vol. 32, Issue 17
DOI: 10.1088/1361-648x/ab6d11

Quantifying the effect of interactions in quantum many-body systems
text, January 2018

Pachos, Jiannis K.; Papić, Zlatko
arXiv
DOI: 10.48550/arxiv.1803.06812

Many-body effects on the thermodynamics of closed quantum systems
text, January 2019

Skelt, A. H.; Zawadzki, K.; D'Amico, I.
arXiv
DOI: 10.48550/arxiv.1905.00318

Similar Records in DOE PAGES and OSTI.GOV collections:

Linear response time-dependent density functional theory of the Hubbard dimer

Journal Article Carrascal, Diego J. ; Ferrer, Jaime ; Maitra, Neepa ; ... - European Physical Journal. B, Condensed Matter and Complex Systems

The asymmetric Hubbard dimer is used to study the density-dependence of the exact frequency-dependent kernel of linear-response time-dependent density functional theory. The exact form of the kernel is given, and the limitations of the adiabatic approximation utilizing the exact ground-state functional are shown. The oscillator strength sum rule is proven for lattice Hamiltonians, and relative oscillator strengths are defined appropriately. The method of Casida for extracting oscillator strengths from a frequency-dependent kernel is demonstrated to yield the exact result with this kernel. An unambiguous way of labelling the nature of excitations is given. The fluctuation-dissipation theorem is proven for themore »« less
Cited by 12
https://doi.org/10.1140/epjb/e2018-90114-9

Full Text Available
Exact thermal density functional theory for a model system: Correlation components and accuracy of the zero-temperature exchange-correlation approximation

Journal Article Smith, J. C. ; Pribram-Jones, A. ; Burke, K. - Physical Review B

Thermal density functional theory calculations often use the Mermin-Kohn-Sham scheme, but employ ground-state approximations to the exchange-correlation (XC) free energy. In the simplest solvable nontrivial model, an asymmetric Hubbard dimer, we calculate the exact many-body energies and the exact Mermin-Kohn-Sham functionals for this system and extract the exact XC free energy. For moderate temperatures and weak correlation, we find this approximation to be excellent. Here we extract various exact free-energy correlation components and the exact adiabatic connection formula.
Cited by 1
https://doi.org/10.1103/PhysRevB.93.245131

Full Text Available
η-pairing in Hubbard models: From spectrum generating algebras to quantum many-body scars

Journal Article Moudgalya, Sanjay ; Regnault, Nicolas ; Bernevig, B. Andrei - Physical Review B

In this work, we revisit the η-pairing states in Hubbard models and explore their connections to quantum many-body scars to discover a universal scars mechanism. η-pairing occurs due to an algebraic structure known as a spectrum generating algebra (SGA), giving rise to equally spaced towers of eigenstates in the spectrum. We generalize the original η-pairing construction and show that several Hubbard-like models on arbitrary graphs exhibit SGAs, including ones with disorder and spin-orbit coupling. We further define a restricted spectrum generating algebra (RSGA) and give examples of perturbations to the Hubbard-like models that preserve an equally spaced tower of themore »« less
https://doi.org/10.1103/physrevb.102.085140

Full Text Available
Comparing correlation components and approximations in Hartree–Fock and Kohn–Sham theories via an analytical test case study

Journal Article Giarrusso, Sara ; Pribram-Jones, Aurora - Journal of Chemical Physics

The asymmetric Hubbard dimer is a model that allows for explicit expressions of the Hartree–Fock (HF) and Kohn–Sham (KS) states as analytical functions of the external potential, Δ v, and of the interaction strength, U. We use this unique circumstance to establish a rigorous comparison between the individual contributions to the correlation energies stemming from the two theories in the { U, Δ v} parameter space. Within this analysis of the Hubbard dimer, we observe a change in the sign of the HF kinetic correlation energy, compare the indirect repulsion energies, and derive an expression for the “traditional” correlation energy, i.e.,more »« less
https://doi.org/10.1063/5.0097095
Magnetic properties of alternating Hubbard ladders

Journal Article Essalah, Kaouther ; Benali, Ali ; Abdelwahab, Anas ; ... - Physical Review B

We explore the Hubbard Hamiltonian on ladders where the number of sites per rung alternates between two and three. These geometries are bipartite with nonequal or equal number of sites on the two sublattices. Thus they share a key feature of the Hubbard model in a class of lattices which Lieb has shown analytically to exhibit long-range ferrimagnetic order while being amenable to powerful numeric approaches developed for quasi-one-dimensional geometries. The density matrix renormalization group (DMRG) method is used to obtain the groundstate properties, e.g., excitation gaps, charge and spin densities as well as their correlation functions at half filling.more »« less
https://doi.org/10.1103/physrevb.103.165127

Full Text Available

Similar Records

Title: The Hubbard dimer: a density functional case study of a many-body problem

Abstract

Citation Formats

Lattice density-functional theory on graphene journal, December 2010

Component separation of two-component fermion clouds in a spin-dependent external potential by spin-density-functional theory journal, February 2013

Strictly correlated electrons in density-functional theory journal, January 1999

Libxc: A library of exchange and correlation functionals for density functional theory journal, October 2012

A density functional study of the simplest hydrogen abstraction reaction. Effect of self-interaction correction journal, April 1994

A full coupled‐cluster singles and doubles model: The inclusion of disconnected triples journal, February 1982

Exchange-correlation kernel in time-dependent density functional theory journal, October 2002

Density-functional exchange-correlation potentials and orbital eigenvalues for light atoms journal, May 1984

Perspective: Treating electron over-delocalization with the DFT+U method journal, June 2015

Influence of next-nearest-neighbor electron hopping on the static and dynamical properties of the two-dimensional Hubbard model journal, December 1995

Ground and excited-state fermions in a one-dimensional double-well: Exact and density-functional solutions journal, May 2009

Density-Functional Theory for Fractional Particle Number: Derivative Discontinuities of the Energy journal, December 1982

Strictly correlated electrons in density-functional theory: A general formulation with applications to spherical densities journal, April 2007

Resistance Minimum in Dilute Magnetic Alloys journal, July 1964

Accurate exchange-correlation potentials and total-energy components for the helium isoelectronic series journal, November 1994

Multiconfiguration wave functions for quantum Monte Carlo calculations of first‐row diatomic molecules journal, July 1996

The Resonating Valence Bond State in La2CuO4 and Superconductivity journal, March 1987

Interacting Fermi gases in disordered one-dimensional lattices journal, April 2006

Why CCSD(T) works: a different perspective journal, December 1997

Persistent current and Drude weight for the one-dimensional Hubbard model from current lattice density functional theory journal, February 2012

DFT: A Theory Full of Holes? journal, April 2015

Derivative discontinuity, bandgap and lowest unoccupied molecular orbital in density functional theory journal, May 2012

The Kohn–Sham gap, the fundamental gap and the optical gap: the physical meaning of occupied and virtual Kohn–Sham orbital energies journal, January 2013

Difference between the quasiparticle and the Kohn-Sham-Fermi surfaces journal, February 1988

Levy–Lieb principle: The bridge between the electron density of Density Functional Theory and the wavefunction of Quantum Monte Carlo journal, January 2015

Atomic-orbital-based approximate self-interaction correction scheme for molecules and solids journal, January 2007

Ab initio quantum chemistry: Methodology and applications journal, May 2005

Adiabatic connection forms in density functional theory: H2 and the He isoelectronic series journal, August 2008

Universal variational functionals of electron densities, first-order density matrices, and natural spin-orbitals and solution of the v-representability problem journal, December 1979

Quasiparticle Self-Consistent G W Theory journal, June 2006

Density Functionals Not Based on the Electron Gas: Local-Density Approximation for a Luttinger Liquid journal, April 2003

Metallic ferromagnetism in a single-band model journal, August 1989

Density-matrix functional study of the Hubbard model on one- and two-dimensional bipartite lattices journal, July 2011

The GW method journal, March 1998

Spin-independent V-representability of Wigner crystal oscillations in one-dimensional Hubbard chains: The role of spin-charge separation journal, August 2012

Density-Functional Theory of the Electronic Structure of Molecules journal, October 1995

Atoms, molecules, solids, and surfaces: Applications of the generalized gradient approximation for exchange and correlation journal, September 1992

Ferromagnetic transition and phase diagram of the one-dimensional Hubbard model with next-nearest-neighbor hopping journal, August 1998

A local exchange-correlation potential for the spin polarized case. i journal, July 1972

Hubbard Hamiltonian for the hydrogen molecule journal, May 2007

The analog of Koopmans’ theorem in spin-density functional theory journal, November 2002

Discontinuity of the exchange-correlation potential: Support for assumptions used to find it journal, January 2008

Doping a Mott insulator: Physics of high-temperature superconductivity journal, January 2006

A Variational Approach to the Unipotential Many-Electron Problem journal, April 1953

Energy differences between Kohn-Sham and Hartree-Fock wave functions yielding the same electron density journal, June 1995

Comparative study of many-body perturbation theory and time-dependent density functional theory in the out-of-equilibrium Anderson model journal, September 2011

Bethe ansatz density-functional theory of ultracold repulsive fermions in one-dimensional optical lattices journal, April 2006

Perspective on density functional theory journal, April 2012

The adiabatic connection method: a non-empirical hybrid journal, January 1997

Two-dimensional Hubbard model with nearest- and next-nearest-neighbor hopping journal, March 1987

Communication: Self-interaction correction with unitary invariance in density functional theory journal, March 2014

Dynamical Correction to Linear Kohn-Sham Conductances from Static Density Functional Theory journal, July 2013

Density-matrix functional theory of strongly correlated lattice fermions journal, October 2002

Density-functional theory of strongly correlated Fermi gases in elongated harmonic traps journal, March 2006

The surface energy of a bounded electron gas journal, August 1974

Density functional theory for strongly-interacting electrons: perspectives for physics and chemistry journal, January 2010

Competition between local potentials and attractive particle–particle interactions in superlattices journal, December 2007

Fractional charge perspective on the band gap in density-functional theory journal, March 2008

A bird's-eye view of density-functional theory journal, January 2006

Density functional theory based many-body analysis of electron transport through molecules journal, January 2011

Reference electronic structure calculations in one dimension journal, January 2012

Exchange-correlation energy and potential as approximate functionals of occupied and virtual Kohn–Sham orbitals: Application to dissociating H[sub 2] journal, January 2003

Exchange and correlation in atoms, molecules, and solids by the spin-density-functional formalism journal, May 1976

Zur Theorie der Kernmassen journal, July 1935

Excitation energies from time-dependent density-functional formalism for small systems journal, March 2002

Electric field response of strongly correlated one-dimensional metals: A Bethe ansatz density functional theory study journal, December 2010

Density-functional theory for one-dimensional harmonically trapped Bose-Fermi mixture journal, May 2012

First-principles calculations of the electronic structure and spectra of strongly correlated systems: the LDA + U method journal, January 1997

Adiabatic connection for strictly correlated electrons journal, September 2009

Electronic excitations: density-functional versus many-body Green’s-function approaches journal, June 2002

Eine statistische Methode zur Bestimmung einiger Eigenschaften des Atoms und ihre Anwendung auf die Theorie des periodischen Systems der Elemente journal, January 1928

What do the Kohn-Sham Orbital Energies Mean? How do Atoms Dissociate? book,

Effective action for strongly correlated fermions from functional integrals journal, November 1990

Electronic Structure book, January 2004

Exact Kohn-Sham eigenstates versus quasiparticles in simple models of strongly correlated electrons journal, January 2012

Density-Functional Theory of the Energy Gap journal, November 1983

Assessment of the GW approximation using Hubbard chains journal, February 1998

Lattice density-functional theory on graphene
journal, December 2010

Component separation of two-component fermion clouds in a spin-dependent external potential by spin-density-functional theory
journal, February 2013

Strictly correlated electrons in density-functional theory
journal, January 1999

Libxc: A library of exchange and correlation functionals for density functional theory
journal, October 2012

A density functional study of the simplest hydrogen abstraction reaction. Effect of self-interaction correction
journal, April 1994

A full coupled‐cluster singles and doubles model: The inclusion of disconnected triples
journal, February 1982

Exchange-correlation kernel in time-dependent density functional theory
journal, October 2002

Density-functional exchange-correlation potentials and orbital eigenvalues for light atoms
journal, May 1984

Perspective: Treating electron over-delocalization with the DFT+U method
journal, June 2015

Influence of next-nearest-neighbor electron hopping on the static and dynamical properties of the two-dimensional Hubbard model
journal, December 1995

Ground and excited-state fermions in a one-dimensional double-well: Exact and density-functional solutions
journal, May 2009

Density-Functional Theory for Fractional Particle Number: Derivative Discontinuities of the Energy
journal, December 1982

Strictly correlated electrons in density-functional theory: A general formulation with applications to spherical densities
journal, April 2007

Resistance Minimum in Dilute Magnetic Alloys
journal, July 1964

Accurate exchange-correlation potentials and total-energy components for the helium isoelectronic series
journal, November 1994

Multiconfiguration wave functions for quantum Monte Carlo calculations of first‐row diatomic molecules
journal, July 1996

The Resonating Valence Bond State in La2CuO4 and Superconductivity
journal, March 1987

Interacting Fermi gases in disordered one-dimensional lattices
journal, April 2006

Why CCSD(T) works: a different perspective
journal, December 1997

Persistent current and Drude weight for the one-dimensional Hubbard model from current lattice density functional theory
journal, February 2012

DFT: A Theory Full of Holes?
journal, April 2015

Derivative discontinuity, bandgap and lowest unoccupied molecular orbital in density functional theory
journal, May 2012

The Kohn–Sham gap, the fundamental gap and the optical gap: the physical meaning of occupied and virtual Kohn–Sham orbital energies
journal, January 2013

Difference between the quasiparticle and the Kohn-Sham-Fermi surfaces
journal, February 1988

Levy–Lieb principle: The bridge between the electron density of Density Functional Theory and the wavefunction of Quantum Monte Carlo
journal, January 2015

Atomic-orbital-based approximate self-interaction correction scheme for molecules and solids
journal, January 2007

Ab initio quantum chemistry: Methodology and applications
journal, May 2005

Adiabatic connection forms in density functional theory: H2 and the He isoelectronic series
journal, August 2008

Universal variational functionals of electron densities, first-order density matrices, and natural spin-orbitals and solution of the v-representability problem
journal, December 1979

Quasiparticle Self-Consistent $G W$ Theory
journal, June 2006

Density Functionals Not Based on the Electron Gas: Local-Density Approximation for a Luttinger Liquid
journal, April 2003

Metallic ferromagnetism in a single-band model
journal, August 1989

Density-matrix functional study of the Hubbard model on one- and two-dimensional bipartite lattices
journal, July 2011

The GW method
journal, March 1998

Spin-independent V-representability of Wigner crystal oscillations in one-dimensional Hubbard chains: The role of spin-charge separation
journal, August 2012

Density-Functional Theory of the Electronic Structure of Molecules
journal, October 1995

Atoms, molecules, solids, and surfaces: Applications of the generalized gradient approximation for exchange and correlation
journal, September 1992

Ferromagnetic transition and phase diagram of the one-dimensional Hubbard model with next-nearest-neighbor hopping
journal, August 1998

A local exchange-correlation potential for the spin polarized case. i
journal, July 1972

Hubbard Hamiltonian for the hydrogen molecule
journal, May 2007

The analog of Koopmans’ theorem in spin-density functional theory
journal, November 2002

Discontinuity of the exchange-correlation potential: Support for assumptions used to find it
journal, January 2008

Doping a Mott insulator: Physics of high-temperature superconductivity
journal, January 2006

A Variational Approach to the Unipotential Many-Electron Problem
journal, April 1953

Energy differences between Kohn-Sham and Hartree-Fock wave functions yielding the same electron density
journal, June 1995

Comparative study of many-body perturbation theory and time-dependent density functional theory in the out-of-equilibrium Anderson model
journal, September 2011

Bethe ansatz density-functional theory of ultracold repulsive fermions in one-dimensional optical lattices
journal, April 2006

Perspective on density functional theory
journal, April 2012

The adiabatic connection method: a non-empirical hybrid
journal, January 1997

Two-dimensional Hubbard model with nearest- and next-nearest-neighbor hopping
journal, March 1987

Communication: Self-interaction correction with unitary invariance in density functional theory
journal, March 2014

Dynamical Correction to Linear Kohn-Sham Conductances from Static Density Functional Theory
journal, July 2013

Density-matrix functional theory of strongly correlated lattice fermions
journal, October 2002

Density-functional theory of strongly correlated Fermi gases in elongated harmonic traps
journal, March 2006

The surface energy of a bounded electron gas
journal, August 1974

Density functional theory for strongly-interacting electrons: perspectives for physics and chemistry
journal, January 2010

Competition between local potentials and attractive particle–particle interactions in superlattices
journal, December 2007

Fractional charge perspective on the band gap in density-functional theory
journal, March 2008

A bird's-eye view of density-functional theory
journal, January 2006

Density functional theory based many-body analysis of electron transport through molecules
journal, January 2011

Reference electronic structure calculations in one dimension
journal, January 2012

Exchange-correlation energy and potential as approximate functionals of occupied and virtual Kohn–Sham orbitals: Application to dissociating H[sub 2]
journal, January 2003

Exchange and correlation in atoms, molecules, and solids by the spin-density-functional formalism
journal, May 1976

Zur Theorie der Kernmassen
journal, July 1935

Excitation energies from time-dependent density-functional formalism for small systems
journal, March 2002

Electric field response of strongly correlated one-dimensional metals: A Bethe ansatz density functional theory study
journal, December 2010

Density-functional theory for one-dimensional harmonically trapped Bose-Fermi mixture
journal, May 2012

First-principles calculations of the electronic structure and spectra of strongly correlated systems: the LDA + U method
journal, January 1997

Adiabatic connection for strictly correlated electrons
journal, September 2009

Electronic excitations: density-functional versus many-body Green’s-function approaches
journal, June 2002

Eine statistische Methode zur Bestimmung einiger Eigenschaften des Atoms und ihre Anwendung auf die Theorie des periodischen Systems der Elemente
journal, January 1928

What do the Kohn-Sham Orbital Energies Mean? How do Atoms Dissociate?
book,

Effective action for strongly correlated fermions from functional integrals
journal, November 1990

Electronic Structure
book, January 2004

Exact Kohn-Sham eigenstates versus quasiparticles in simple models of strongly correlated electrons
journal, January 2012

Density-Functional Theory of the Energy Gap
journal, November 1983

Assessment of the GW approximation using Hubbard chains
journal, February 1998

Coupled-cluster theory in quantum chemistry
journal, February 2007

Density-functional theory of two-component Bose gases in one-dimensional harmonic traps
journal, October 2009

Relationship of Kohn–Sham eigenvalues to excitation energies
journal, May 1998