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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 » 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 H 2.« less

Authors:
 [1];  [1];  [2];  [2]
  1. Univ. de Oviedo (Spain); Nanomaterials and Nanotechnology Research Center, Oviedo (Spain)
  2. Univ. of California, Irvine, CA (United States)
Publication Date:
Research Org.:
Univ. of California, Irvine, CA (United States)
Sponsoring Org.:
USDOE Office of Science (SC), Basic Energy Sciences (BES) (SC-22)
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.
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. doi:10.1088/0953-8984/27/39/393001.
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. doi:10.1088/0953-8984/27/39/393001. https://www.osti.gov/servlets/purl/1595136.
@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}
}

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Works referenced in this record:

Lattice density-functional theory on graphene
journal, December 2010


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

  • 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


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


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

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

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

  • 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


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


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

  • 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


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

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

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


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


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

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

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


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

  • 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


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

  • 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


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

  • 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


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

  • 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


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


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

  • 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


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


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

  • 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


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


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


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

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


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


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


Forces in Molecules
journal, August 1939


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


Localized Magnetic States in Metals
journal, October 1961


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


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


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


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


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


Inhomogeneous Electron Gas
journal, November 1964


Optimized effective atomic central potential
journal, July 1976


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


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


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


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


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


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


Thermal Properties of the Inhomogeneous Electron Gas
journal, March 1965


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


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


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


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


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


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


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


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


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


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


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


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


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


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


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


CO Chemisorption at Metal Surfaces and Overlayers
journal, March 1996


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


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


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


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


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


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


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


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


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

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


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


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


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


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


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


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


Density functional formulations for quantum chains
journal, July 2007


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

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


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


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


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


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


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


Proof that E n i = ε in density-functional theory
journal, December 1978


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


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


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


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


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


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


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


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


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


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


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


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


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


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


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


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


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


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


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


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


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


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


Exact Exchange-Correlation Treatment of Dissociated H 2 in Density Functional Theory
journal, September 2001


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

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


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


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