## This content will become publicly available on February 12, 2021

# Off-shell effective energy theory: A unified treatment of the Hubbard model from $d\phantom{\rule{0ex}{0ex}}=\phantom{\rule{0ex}{0ex}}1$ to $d\phantom{\rule{0ex}{0ex}}=\phantom{\rule{0ex}{0ex}}\infty $

- Authors:

- Publication Date:

- Sponsoring Org.:
- USDOE

- OSTI Identifier:
- 1599489

- Grant/Contract Number:
- SC0016507; AC02-05CH11231

- Resource Type:
- Publisher's Accepted Manuscript

- Journal Name:
- Physical Review B

- Additional Journal Information:
- Journal Name: Physical Review B Journal Volume: 101 Journal Issue: 8; Journal ID: ISSN 2469-9950

- Publisher:
- American Physical Society

- Country of Publication:
- United States

- Language:
- English

### Citation Formats

```
Cheng, Zhengqian, and Marianetti, Chris A. Off-shell effective energy theory: A unified treatment of the Hubbard model from d = 1 to d = ∞. United States: N. p., 2020.
Web. doi:10.1103/PhysRevB.101.081105.
```

```
Cheng, Zhengqian, & Marianetti, Chris A. Off-shell effective energy theory: A unified treatment of the Hubbard model from d = 1 to d = ∞. United States. doi:10.1103/PhysRevB.101.081105.
```

```
Cheng, Zhengqian, and Marianetti, Chris A. Thu .
"Off-shell effective energy theory: A unified treatment of the Hubbard model from d = 1 to d = ∞". United States. doi:10.1103/PhysRevB.101.081105.
```

```
@article{osti_1599489,
```

title = {Off-shell effective energy theory: A unified treatment of the Hubbard model from d = 1 to d = ∞},

author = {Cheng, Zhengqian and Marianetti, Chris A.},

abstractNote = {},

doi = {10.1103/PhysRevB.101.081105},

journal = {Physical Review B},

number = 8,

volume = 101,

place = {United States},

year = {2020},

month = {2}

}

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Works referenced in this record:

##
Rotationally invariant slave-boson and density matrix embedding theory: Unified framework and comparative study on the one-dimensional and two-dimensional Hubbard model

journal, March 2019

- Lee, Tsung-Han; Ayral, Thomas; Yao, Yong-Xin
- Physical Review B, Vol. 99, Issue 11

##
Dynamical mean-field theory, density-matrix embedding theory, and rotationally invariant slave bosons: A unified perspective

journal, December 2017

- Ayral, Thomas; Lee, Tsung-Han; Kotliar, Gabriel
- Physical Review B, Vol. 96, Issue 23

##
Energy resolution and discretization artifacts in the numerical renormalization group

journal, February 2009

- Žitko, Rok; Pruschke, Thomas
- Physical Review B, Vol. 79, Issue 8

##
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

##
Quantum Monte Carlo simulations of solids

journal, January 2001

- Foulkes, W. M. C.; Mitas, L.; Needs, R. J.
- Reviews of Modern Physics, Vol. 73, Issue 1

##
Structure of Fermionic Density Matrices: Complete $N$ -Representability Conditions

journal, June 2012

- Mazziotti, David A.
- Physical Review Letters, Vol. 108, Issue 26

##
Strongly Correlated Materials: Insights From Dynamical Mean-Field Theory

journal, March 2004

- Kotliar, Gabriel; Vollhardt, Dieter
- Physics Today, Vol. 57, Issue 3

##
Density Matrix Embedding: A Simple Alternative to Dynamical Mean-Field Theory

journal, November 2012

- Knizia, Gerald; Chan, Garnet Kin-Lic
- Physical Review Letters, Vol. 109, Issue 18

##
Local reduced-density-matrix-functional theory: Incorporating static correlation effects in Kohn-Sham equations

journal, September 2014

- Lathiotakis, Nektarios N.; Helbig, Nicole; Rubio, Angel
- Physical Review A, Vol. 90, Issue 3

##
Effect of Correlation on the Ferromagnetism of Transition Metals

journal, May 1964

- Gutzwiller, Martin C.
- Physical Review, Vol. 134, Issue 4A

##
Continuous-time Monte Carlo methods for quantum impurity models

journal, May 2011

- Gull, Emanuel; Millis, Andrew J.; Lichtenstein, Alexander I.
- Reviews of Modern Physics, Vol. 83, Issue 2

##
Reduction of the *N* ‐Particle Variational Problem

journal, December 1964

- Garrod, Claude; Percus, Jerome K.
- Journal of Mathematical Physics, Vol. 5, Issue 12

##
Density-matrix functionals from Green's functions

journal, November 2013

- Blöchl, Peter E.; Pruschke, Thomas; Potthoff, Michael
- Physical Review B, Vol. 88, Issue 20

##
Adaptive cluster approximation for reduced density-matrix functional theory

journal, June 2018

- Schade, Robert; Blöchl, Peter E.
- Physical Review B, Vol. 97, Issue 24

##
Electron doping and superconductivity in the two-dimensional Hubbard model

journal, March 2009

- Eichenberger, D.; Baeriswyl, D.
- Physical Review B, Vol. 79, Issue 10

##
Dynamical mean-field theory for correlated electrons

journal, November 2011

- Vollhardt, D.
- Annalen der Physik, Vol. 524, Issue 1

##
Superconductivity and antiferromagnetism in the two-dimensional Hubbard model: A variational study

journal, November 2007

- Eichenberger, D.; Baeriswyl, D.
- Physical Review B, Vol. 76, Issue 18

##
Structure of Fermion Density Matrices

journal, July 1963

- Coleman, A. J.
- Reviews of Modern Physics, Vol. 35, Issue 3

##
The density functional formalism, its applications and prospects

journal, July 1989

- Jones, R. O.; Gunnarsson, O.
- Reviews of Modern Physics, Vol. 61, Issue 3

##
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

##
Global Method for Electron Correlation

journal, August 2017

- Piris, Mario
- Physical Review Letters, Vol. 119, Issue 6

##
Solutions of the Two-Dimensional Hubbard Model: Benchmarks and Results from a Wide Range of Numerical Algorithms

journal, December 2015

- LeBlanc, J. P. F.; Antipov, Andrey E.; Becca, Federico
- Physical Review X, Vol. 5, Issue 4

##
Method to include explicit correlations into density-functional calculations based on density-matrix functional theory

journal, November 2011

- Blöchl, Peter E.; Walther, Christian F. J.; Pruschke, Thomas
- Physical Review B, Vol. 84, Issue 20

##
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

##
New Functional Integral Approach to Strongly Correlated Fermi Systems: The Gutzwiller Approximation as a Saddle Point

journal, September 1986

- Kotliar, Gabriel; Ruckenstein, Andrei E.
- Physical Review Letters, Vol. 57, Issue 11

##
Sign-Problem-Free Fermionic Quantum Monte Carlo: Developments and Applications

journal, March 2019

- Li, Zi-Xiang; Yao, Hong
- Annual Review of Condensed Matter Physics, Vol. 10, Issue 1

##
Effect of Correlation on the Ferromagnetism of Transition Metals

journal, March 1963

- Gutzwiller, Martin C.
- Physical Review Letters, Vol. 10, Issue 5

##
Computational Complexity and Fundamental Limitations to Fermionic Quantum Monte Carlo Simulations

journal, May 2005

- Troyer, Matthias; Wiese, Uwe-Jens
- Physical Review Letters, Vol. 94, Issue 17

##
Local density approximation combined with Gutzwiller method for correlated electron systems: Formalism and applications

journal, February 2009

- Deng, XiaoYu; Wang, Lei; Dai, Xi
- Physical Review B, Vol. 79, Issue 7

##
Rigorous symmetry adaptation of multiorbital rotationally invariant slave-boson theory with application to Hund's rules physics

journal, March 2018

- Piefke, Christoph; Lechermann, Frank
- Physical Review B, Vol. 97, Issue 12

##
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

##
Zero Temperature Metal-Insulator Transition in the Infinite-Dimensional Hubbard Model

journal, July 1999

- Bulla, R.
- Physical Review Letters, Vol. 83, Issue 1

##
Application of the numerical renormalization group method to the hubbard model in infinite dimensions

journal, January 1994

- Sakai, O.; Kuramoto, Y.
- Solid State Communications, Vol. 89, Issue 4

##
Phase Diagram and Electronic Structure of Praseodymium and Plutonium

journal, January 2015

- Lanatà, Nicola; Yao, Yongxin; Wang, Cai-Zhuang
- Physical Review X, Vol. 5, Issue 1

##
Generalized density-functional theory: Conquering theN-representability problem with exact functionals for the electron pair density and the second-order reduced density matrix

journal, September 2005

- Ayers, Paul W.; Levy, Mel
- Journal of Chemical Sciences, Vol. 117, Issue 5

##
Inhomogeneous Electron Gas

journal, November 1964

- Hohenberg, P.; Kohn, W.
- Physical Review, Vol. 136, Issue 3B, p. B864-B871

##
The reduced density matrix method for electronic structure calculations and the role of three-index representability conditions

journal, February 2004

- Zhao, Zhengji; Braams, Bastiaan J.; Fukuda, Mituhiro
- The Journal of Chemical Physics, Vol. 120, Issue 5

##
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

##
Rotationally invariant slave-boson formalism and momentum dependence of the quasiparticle weight

journal, October 2007

- Lechermann, Frank; Georges, Antoine; Kotliar, Gabriel
- Physical Review B, Vol. 76, Issue 15

##
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

##
Linear Inequalities for Density Matrices

journal, April 1969

- Davidson, Ernest R.
- Journal of Mathematical Physics, Vol. 10, Issue 4

##
Approximate solution of variational wave functions for strongly correlated systems: Description of bound excitons in metals and insulators

journal, September 2010

- Hetényi, Balázs
- Physical Review B, Vol. 82, Issue 11

##
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

##
Variational Monte Carlo Studies of the Hubbard Model in One- and Two-Dimensions –Off-Diagonal Intersite Correlation Effects–

journal, May 1992

- Otsuka, Hiromi
- Journal of the Physical Society of Japan, Vol. 61, Issue 5

##
The renormalization group and critical phenomena

journal, July 1983

- Wilson, Kenneth G.
- Reviews of Modern Physics, Vol. 55, Issue 3

##
Analytic calculation of ground-state properties of correlated fermions with the Gutzwiller wave function

journal, May 1988

- Metzner, Walter; Vollhardt, Dieter
- Physical Review B, Vol. 37, Issue 13

##
Correlation of Electrons in a Narrow $s$ Band

journal, March 1965

- Gutzwiller, Martin C.
- Physical Review, Vol. 137, Issue 6A

##
Explicit approximate relation between reduced two- and one-particle density matrices

journal, November 1984

- Müller, A. M. K.
- Physics Letters A, Vol. 105, Issue 9

##
Kinetic-Energy Density-Functional Theory on a Lattice

journal, June 2018

- Theophilou, Iris; Buchholz, Florian; Eich, F. G.
- Journal of Chemical Theory and Computation, Vol. 14, Issue 8