Finite-temperature many-body perturbation theory for electrons: Algebraic recursive definitions, second-quantized derivation, linked-diagram theorem, general-order algorithms, and grand canonical and canonical ensembles

Hirata, So

doi:10.1063/5.0061384

Title: Finite-temperature many-body perturbation theory for electrons: Algebraic recursive definitions, second-quantized derivation, linked-diagram theorem, general-order algorithms, and grand canonical and canonical ensembles

Journal Article · 07 September 2021 · Journal of Chemical Physics

DOI: https://doi.org/10.1063/5.0061384 · OSTI ID:1818887

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Univ. of Illinois at Urbana-Champaign, IL (United States); University of Illinois at Urbana-Champaign

A comprehensive and detailed account is presented for the finite-temperature many-body perturbation theory for electrons that expands in power series all thermodynamic functions on an equal footing. Algebraic recursions in the style of the Rayleigh–Schrödinger perturbation theory are derived for the grand potential, chemical potential, internal energy, and entropy in the grand canonical ensemble and for the Helmholtz energy, internal energy, and entropy in the canonical ensemble, leading to their sum-over-states analytical formulas at any arbitrary order. For the grand canonical ensemble, these sum-over-states formulas are systematically transformed to sum-over-orbitals reduced analytical formulas by the quantum-field-theoretical techniques of normal-ordered second quantization and Feynman diagrams extended to finite temperature. It is found that the perturbation corrections to energies entering the recursions have to be treated as a nondiagonal matrix, whose off-diagonal elements are generally nonzero within a subspace spanned by degenerate Slater determinants. They give rise to a unique set of linked diagrams—renormalization diagrams—whose resolvent lines are displaced upward, which are distinct from the well-known anomalous diagrams of which one or more resolvent lines are erased. A linked-diagram theorem is introduced that proves the size-consistency of the finite-temperature many-body perturbation theory at any order. General-order algorithms implementing the recursions establish the convergence of the perturbation series toward the finite-temperature full-configuration-interaction limit unless the series diverges. As a result, the normal-ordered Hamiltonian at finite temperature sheds light on the relationship between the finite-temperature Hartree–Fock and first-order many-body perturbation theories.

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Research Organization:: Univ. of Illinois at Urbana-Champaign, IL (United States)

Sponsoring Organization:: USDOE Office of Science (SC), Basic Energy Sciences (BES). Chemical Sciences, Geosciences & Biosciences Division

Grant/Contract Number:: SC0006028

OSTI ID:: 1818887

Journal Information:: Journal of Chemical Physics, Journal Name: Journal of Chemical Physics Journal Issue: 9 Vol. 155; ISSN 0021-9606

Publisher:: American Institute of Physics (AIP)Copyright Statement

Country of Publication:: United States

Language:: English

References (101)

On the Brillouin-zone integrations in second-order many-body perturbation calculations for extended systems of one-dimensional periodicity: Second-Order Many-Body Perturbation Calculations Shimazaki, Tomomi; Hirata, So International Journal of Quantum Chemistry, Vol. 109, Issue 13 https://doi.org/10.1002/qua.22176	journal	April 2009
The linked-diagram expansion of the ground state of a many-electron system: A time-independent derivation Manne, Rolf International Journal of Quantum Chemistry, Vol. 12, Issue S11 https://doi.org/10.1002/qua.560120822	journal	January 1977
Thermodynamic limit and size-consistent design Hirata, So Theoretical Chemistry Accounts, Vol. 129, Issue 6 https://doi.org/10.1007/s00214-011-0954-4	journal	June 2011
On the mutual exclusion of variationality and size consistency Hirata, So; Grabowski, Ireneusz Theoretical Chemistry Accounts, Vol. 133, Issue 3 https://doi.org/10.1007/s00214-013-1440-y	journal	January 2014
Finite-temperature full configuration interaction Kou, Zhuangfei; Hirata, So Theoretical Chemistry Accounts, Vol. 133, Issue 6 https://doi.org/10.1007/s00214-014-1487-4	journal	April 2014
Stability of the thermal Hartree-Fock approximation Mermin, N. David Annals of Physics, Vol. 21, Issue 1 https://doi.org/10.1016/0003-4916(63)90226-4	journal	January 1963
Reduced partitioning technique for configuration interaction calculations using Padé approximants and inner-projections Brändas, E. J.; Bartlett, R. J. Chemical Physics Letters, Vol. 8, Issue 2 https://doi.org/10.1016/0009-2614(71)80001-5	journal	January 1971
Is fifth-order MBPT enough? Laidig, William D.; Fitzgerald, George; Bartlett, Rodney J. Chemical Physics Letters, Vol. 113, Issue 2 https://doi.org/10.1016/0009-2614(85)80934-9	journal	January 1985
The calculation of higher-order energies in the many-body perturbation theory series Knowles, P. J.; Somasundram, K.; Handy, N. C. Chemical Physics Letters, Vol. 113, Issue 1 https://doi.org/10.1016/0009-2614(85)85002-8	journal	January 1985
The expectation value coupled-cluster method and analytical energy derivatives Bartlett, Rodney J.; Noga, Jozef Chemical Physics Letters, Vol. 150, Issue 1-2 https://doi.org/10.1016/0009-2614(88)80392-0	journal	September 1988
Un développement du potentiel de gibbs d'un système quantique composé d'un grand nombre de particules Bloch, Claude; De Dominicis, Cyrano Nuclear Physics, Vol. 7 https://doi.org/10.1016/0029-5582(58)90285-2	journal	June 1958
Many-body basis for the optical model Frantz, Lee M.; Mills, Robert L. Nuclear Physics, Vol. 15 https://doi.org/10.1016/0029-5582(60)90278-9	journal	February 1960
Formulation de la me´canique statistique en termes de nombres d'occupation (I) Balian, Roger; Bloch, Claude; De Dominicis, Cyrano Nuclear Physics, Vol. 25 https://doi.org/10.1016/0029-5582(61)90183-3	journal	May 1961
Numerical evidence invalidating finite-temperature many-body perturbation theory Jha, Punit K.; Hirata, So Annual Reports in Computational Chemistry https://doi.org/10.1016/bs.arcc.2019.08.002	book	January 2019
Converging finite-temperature many-body perturbation theory in the grand canonical ensemble that conserves the average number of electrons Hirata, So; Jha, Punit K. Annual Reports in Computational Chemistry https://doi.org/10.1016/bs.arcc.2019.08.003	book	January 2019
Finite-temperature second-order many-body perturbation theory revisited Santra, Robin; Schirmer, Jochen Chemical Physics, Vol. 482 https://doi.org/10.1016/j.chemphys.2016.08.001	journal	January 2017
High-order coupled-cluster calculations through connected octuple excitations Hirata, So; Bartlett, Rodney J. Chemical Physics Letters, Vol. 321, Issue 3-4 https://doi.org/10.1016/s0009-2614(00)00387-0	journal	April 2000
High-order determinantal equation-of-motion coupled-cluster calculations for electronic excited states Hirata, So; Nooijen, Marcel; Bartlett, Rodney J. Chemical Physics Letters, Vol. 326, Issue 3-4 https://doi.org/10.1016/s0009-2614(00)00772-7	journal	August 2000
High-order determinantal equation-of-motion coupled-cluster calculations for ionized and electron-attached states Hirata, So; Nooijen, Marcel; Bartlett, Rodney J. Chemical Physics Letters, Vol. 328, Issue 4-6 https://doi.org/10.1016/s0009-2614(00)00965-9	journal	October 2000
A non-perturbative cumulant expansion method for the grand partition function of quantum systems Mandal, Sheikh Hannan; Ghosh, Rathindranath; Mukherjee, Debashis Chemical Physics Letters, Vol. 335, Issue 3-4 https://doi.org/10.1016/s0009-2614(01)00026-4	journal	February 2001
Perturbation theory of large quantum systems Hugenholtz, N. M. Physica, Vol. 23, Issue 1-5 https://doi.org/10.1016/s0031-8914(57)92950-6	journal	January 1957
Many – Body Methods in Chemistry and Physics Shavitt, Isaiah; Bartlett, Rodney J. https://doi.org/10.1017/CBO9780511596834	book	January 2009
Unveiling the Finite Temperature Physics of Hydrogen Chains via Auxiliary Field Quantum Monte Carlo Liu, Yuan; Shen, Tong; Zhang, Hang Journal of Chemical Theory and Computation, Vol. 16, Issue 7 https://doi.org/10.1021/acs.jctc.0c00288	journal	May 2020
General-Order Many-Body Green’s Function Method Hirata, So; Hermes, Matthew R.; Simons, Jack Journal of Chemical Theory and Computation, Vol. 11, Issue 4 https://doi.org/10.1021/acs.jctc.5b00005	journal	March 2015
Heat-Bath Configuration Interaction: An Efficient Selected Configuration Interaction Algorithm Inspired by Heat-Bath Sampling Holmes, Adam A.; Tubman, Norm M.; Umrigar, C. J. Journal of Chemical Theory and Computation, Vol. 12, Issue 8 https://doi.org/10.1021/acs.jctc.6b00407	journal	August 2016
Monte Carlo MP2 on Many Graphical Processing Units Doran, Alexander E.; Hirata, So Journal of Chemical Theory and Computation, Vol. 12, Issue 10 https://doi.org/10.1021/acs.jctc.6b00588	journal	September 2016
A Time-Dependent Formulation of Coupled-Cluster Theory for Many-Fermion Systems at Finite Temperature White, Alec F.; Chan, Garnet Kin-Lic Journal of Chemical Theory and Computation, Vol. 14, Issue 11 https://doi.org/10.1021/acs.jctc.8b00773	journal	September 2018
Monte Carlo Second- and Third-Order Many-Body Green’s Function Methods with Frequency-Dependent, Nondiagonal Self-Energy Doran, Alexander E.; Hirata, So Journal of Chemical Theory and Computation, Vol. 15, Issue 11 https://doi.org/10.1021/acs.jctc.9b00693	journal	October 2019
Thermofield Theory for Finite-Temperature Coupled Cluster Harsha, Gaurav; Henderson, Thomas M.; Scuseria, Gustavo E. Journal of Chemical Theory and Computation, Vol. 15, Issue 11 https://doi.org/10.1021/acs.jctc.9b00744	journal	September 2019
Efficient Implementation of Ab Initio Quantum Embedding in Periodic Systems: Density Matrix Embedding Theory Cui, Zhi-Hao; Zhu, Tianyu; Chan, Garnet Kin-Lic Journal of Chemical Theory and Computation, Vol. 16, Issue 1 https://doi.org/10.1021/acs.jctc.9b00933	journal	November 2019
On Pair Functions for Strong Correlations Ellis, Jason K.; Martin, Richard L.; Scuseria, Gustavo E. Journal of Chemical Theory and Computation, Vol. 9, Issue 7 https://doi.org/10.1021/ct400307d	journal	June 2013
Convergence Acceleration of Parallel Monte Carlo Second-Order Many-Body Perturbation Calculations Using Redundant Walkers Willow, Soohaeng Yoo; Hermes, Matthew R.; Kim, Kwang S. Journal of Chemical Theory and Computation, Vol. 9, Issue 10 https://doi.org/10.1021/ct400557z	journal	September 2013
Tensor Contraction Engine: Abstraction and Automated Parallel Implementation of Configuration-Interaction, Coupled-Cluster, and Many-Body Perturbation Theories Hirata, So The Journal of Physical Chemistry A, Vol. 107, Issue 46 https://doi.org/10.1021/jp034596z	journal	November 2003
Second-Order Many-Body Perturbation Theory: An Eternal Frontier Hirata, So; He, Xiao; Hermes, Matthew R. The Journal of Physical Chemistry A, Vol. 118, Issue 4 https://doi.org/10.1021/jp410587b	journal	December 2013
The initial implementation and applications of a general active space coupled cluster method Olsen, Jeppe The Journal of Chemical Physics, Vol. 113, Issue 17 https://doi.org/10.1063/1.1290005	journal	November 2000
Degenerate RS perturbation theory Hirschfelder, Joseph O.; Certain, Phillip R. The Journal of Chemical Physics, Vol. 60, Issue 3 https://doi.org/10.1063/1.1681123	journal	February 1974
Degenerate perturbation theory Klein, D. J. The Journal of Chemical Physics, Vol. 61, Issue 3 https://doi.org/10.1063/1.1682018	journal	August 1974
Stability Conditions for the Solutions of the Hartree—Fock Equations for Atomic and Molecular Systems. Application to the Pi‐Electron Model of Cyclic Polyenes Čížek, J.; Paldus, J. The Journal of Chemical Physics, Vol. 47, Issue 10 https://doi.org/10.1063/1.1701562	journal	November 1967
High-performance ab initio density matrix renormalization group method: Applicability to large-scale multireference problems for metal compounds Kurashige, Yuki; Yanai, Takeshi The Journal of Chemical Physics, Vol. 130, Issue 23 https://doi.org/10.1063/1.3152576	journal	June 2009
Logarithm second-order many-body perturbation method for extended systems Ohnishi, Yu-ya; Hirata, So The Journal of Chemical Physics, Vol. 133, Issue 3 https://doi.org/10.1063/1.3455717	journal	July 2010
Dynamical mean-field theory from a quantum chemical perspective Zgid, Dominika; Chan, Garnet Kin-Lic The Journal of Chemical Physics, Vol. 134, Issue 9 https://doi.org/10.1063/1.3556707	journal	March 2011
Breaking the carbon dimer: The challenges of multiple bond dissociation with full configuration interaction quantum Monte Carlo methods Booth, George H.; Cleland, Deidre; Thom, Alex J. W. The Journal of Chemical Physics, Vol. 135, Issue 8 https://doi.org/10.1063/1.3624383	journal	August 2011
Hybrid coupled-cluster and perturbation method for extended systems of one-dimensional periodicity Ohnishi, Yu-ya; Hirata, So The Journal of Chemical Physics, Vol. 135, Issue 9 https://doi.org/10.1063/1.3629843	journal	September 2011
Surprising cases of divergent behavior in Mo/ller–Plesset perturbation theory Olsen, Jeppe; Christiansen, Ove; Koch, Henrik The Journal of Chemical Physics, Vol. 105, Issue 12 https://doi.org/10.1063/1.472352	journal	September 1996
Stochastic evaluation of second-order many-body perturbation energies Willow, Soohaeng Yoo; Kim, Kwang S.; Hirata, So The Journal of Chemical Physics, Vol. 137, Issue 20 https://doi.org/10.1063/1.4768697	journal	November 2012
Stochastic evaluation of second-order Dyson self-energies Willow, Soohaeng Yoo; Kim, Kwang S.; Hirata, So The Journal of Chemical Physics, Vol. 138, Issue 16 https://doi.org/10.1063/1.4801862	journal	April 2013
Computing coupled-cluster wave functions with arbitrary excitations Kállay, Mihály; Surján, Péter R. The Journal of Chemical Physics, Vol. 113, Issue 4 https://doi.org/10.1063/1.481925	journal	July 2000
Finite-temperature second-order many-body perturbation and Hartree–Fock theories for one-dimensional solids: An application to Peierls and charge-density-wave transitions in conjugated polymers He, Xiao; Ryu, Shinsei; Hirata, So The Journal of Chemical Physics, Vol. 140, Issue 2 https://doi.org/10.1063/1.4859257	journal	January 2014
Stochastic, real-space, imaginary-time evaluation of third-order Feynman–Goldstone diagrams Willow, Soohaeng Yoo; Hirata, So The Journal of Chemical Physics, Vol. 140, Issue 2 https://doi.org/10.1063/1.4861561	journal	January 2014
Communication: Stochastic evaluation of explicitly correlated second-order many-body perturbation energy Willow, Soohaeng Yoo; Zhang, Jinmei; Valeev, Edward F. The Journal of Chemical Physics, Vol. 140, Issue 3 https://doi.org/10.1063/1.4862255	journal	January 2014
Singlet and triplet instability theorems Yamada, Tomonori; Hirata, So The Journal of Chemical Physics, Vol. 143, Issue 11 https://doi.org/10.1063/1.4929354	journal	September 2015
Seniority number description of potential energy surfaces: Symmetric dissociation of water, N ₂ , C ₂ , and Be ₂ Bytautas, Laimutis; Scuseria, Gustavo E.; Ruedenberg, Klaus The Journal of Chemical Physics, Vol. 143, Issue 9 https://doi.org/10.1063/1.4929904	journal	September 2015
Finite-temperature coupled-cluster, many-body perturbation, and restricted and unrestricted Hartree–Fock study on one-dimensional solids: Luttinger liquids, Peierls transitions, and spin- and charge-density waves Hermes, Matthew R.; Hirata, So The Journal of Chemical Physics, Vol. 143, Issue 10 https://doi.org/10.1063/1.4930024	journal	September 2015
A study of potential energy curves from the model space quantum Monte Carlo method Ohtsuka, Yuhki; Ten-no, Seiichiro The Journal of Chemical Physics, Vol. 143, Issue 21 https://doi.org/10.1063/1.4936412	journal	December 2015
Self-consistent second-order Green’s function perturbation theory for periodic systems Rusakov, Alexander A.; Zgid, Dominika The Journal of Chemical Physics, Vol. 144, Issue 5 https://doi.org/10.1063/1.4940900	journal	February 2016
Matrix product operators, matrix product states, and ab initio density matrix renormalization group algorithms Chan, Garnet Kin-Lic; Keselman, Anna; Nakatani, Naoki The Journal of Chemical Physics, Vol. 145, Issue 1 https://doi.org/10.1063/1.4955108	journal	July 2016
Monte Carlo explicitly correlated second-order many-body perturbation theory Johnson, Cole M.; Doran, Alexander E.; Zhang, Jinmei The Journal of Chemical Physics, Vol. 145, Issue 15 https://doi.org/10.1063/1.4964854	journal	October 2016
Exploring connections between statistical mechanics and Green’s functions for realistic systems: Temperature dependent electronic entropy and internal energy from a self-consistent second-order Green’s function Welden, Alicia Rae; Rusakov, Alexander A.; Zgid, Dominika The Journal of Chemical Physics, Vol. 145, Issue 20 https://doi.org/10.1063/1.4967449	journal	November 2016
Perspective: Explicitly correlated electronic structure theory for complex systems Grüneis, Andreas; Hirata, So; Ohnishi, Yu-ya The Journal of Chemical Physics, Vol. 146, Issue 8 https://doi.org/10.1063/1.4976974	journal	February 2017
One-particle many-body Green’s function theory: Algebraic recursive definitions, linked-diagram theorem, irreducible-diagram theorem, and general-order algorithms Hirata, So; Doran, Alexander E.; Knowles, Peter J. The Journal of Chemical Physics, Vol. 147, Issue 4 https://doi.org/10.1063/1.4994837	journal	July 2017
Monte Carlo explicitly correlated many-body Green’s function theory Johnson, Cole M.; Doran, Alexander E.; Ten-no, Seiichiro L. The Journal of Chemical Physics, Vol. 149, Issue 17 https://doi.org/10.1063/1.5054610	journal	November 2018
Thermofield theory for finite-temperature quantum chemistry Harsha, Gaurav; Henderson, Thomas M.; Scuseria, Gustavo E. The Journal of Chemical Physics, Vol. 150, Issue 15 https://doi.org/10.1063/1.5089560	journal	April 2019
The density matrix renormalization group in chemistry and molecular physics: Recent developments and new challenges Baiardi, Alberto; Reiher, Markus The Journal of Chemical Physics, Vol. 152, Issue 4 https://doi.org/10.1063/1.5129672	journal	January 2020
Finite-temperature many-body perturbation theory in the grand canonical ensemble Hirata, So; Jha, Punit K. The Journal of Chemical Physics, Vol. 153, Issue 1 https://doi.org/10.1063/5.0009679	journal	July 2020
Exploring Hilbert space on a budget: Novel benchmark set and performance metric for testing electronic structure methods in the regime of strong correlation Stair, Nicholas H.; Evangelista, Francesco A. The Journal of Chemical Physics, Vol. 153, Issue 10 https://doi.org/10.1063/5.0014928	journal	September 2020
Convergence acceleration of Monte Carlo many-body perturbation methods by direct sampling Doran, Alexander E.; Hirata, So The Journal of Chemical Physics, Vol. 153, Issue 10 https://doi.org/10.1063/5.0020583	journal	September 2020
Convergence acceleration of Monte Carlo many-body perturbation methods by using many control variates Doran, Alexander E.; Hirata, So The Journal of Chemical Physics, Vol. 153, Issue 9 https://doi.org/10.1063/5.0020584	journal	September 2020
Wave function methods for canonical ensemble thermal averages in correlated many-fermion systems Harsha, Gaurav; Henderson, Thomas M.; Scuseria, Gustavo E. The Journal of Chemical Physics, Vol. 153, Issue 12 https://doi.org/10.1063/5.0022702	journal	September 2020
A phaseless auxiliary-field quantum Monte Carlo perspective on the uniform electron gas at finite temperatures: Issues, observations, and benchmark study Lee, Joonho; Morales, Miguel A.; Malone, Fionn D. The Journal of Chemical Physics, Vol. 154, Issue 6 https://doi.org/10.1063/5.0041378	journal	February 2021
High-level coupled-cluster energetics by Monte Carlo sampling and moment expansions: Further details and comparisons Deustua, J. Emiliano; Shen, Jun; Piecuch, Piotr The Journal of Chemical Physics, Vol. 154, Issue 12 https://doi.org/10.1063/5.0045468	journal	March 2021
Stochastic evaluation of fourth-order many-body perturbation energies Doran, Alexander E.; Hirata, So The Journal of Chemical Physics, Vol. 154, Issue 13 https://doi.org/10.1063/5.0047798	journal	April 2021
LIII. Ionization in the solar chromosphere Saha, Megh Nad The London, Edinburgh, and Dublin Philosophical Magazine and Journal of Science, Vol. 40, Issue 238 https://doi.org/10.1080/14786441008636148	journal	October 1920
Mottness in high-temperature copper-oxide superconductors Phillips, Philip; Choy, Ting-Pong; Leigh, Robert G. Reports on Progress in Physics, Vol. 72, Issue 3 https://doi.org/10.1088/0034-4885/72/3/036501	journal	February 2009
Koopmans' theorem in the statistical Hartree–Fock theory Pain, Jean-Christophe Journal of Physics B: Atomic, Molecular and Optical Physics, Vol. 44, Issue 14 https://doi.org/10.1088/0953-4075/44/14/145001	journal	June 2011
On a Physical Theory of Stellar Spectra Saha, M. N. Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences, Vol. 99, Issue 697 https://doi.org/10.1098/rspa.1921.0029	journal	May 1921
Derivation of the Brueckner many-body theory Goldstone, Jeffrey Proceedings of the Royal Society of London. Series A. Mathematical and Physical Sciences, Vol. 239, Issue 1217, p. 267-279 https://doi.org/10.1098/rspa.1957.0037	journal	February 1957
Note on an Approximation Treatment for Many-Electron Systems Møller, Chr.; Plesset, M. S. Physical Review, Vol. 46, Issue 7 https://doi.org/10.1103/PhysRev.46.618	journal	October 1934
Many-Body Problem for Strongly Interacting Particles. II. Linked Cluster Expansion Brueckner, K. A. Physical Review, Vol. 100, Issue 1 https://doi.org/10.1103/physrev.100.36	journal	October 1955
Ground-State Energy of a Many-Fermion System. II Luttinger, J. M.; Ward, J. C. Physical Review, Vol. 118, Issue 5 https://doi.org/10.1103/physrev.118.1417	journal	June 1960
Ground-State Energy of a Many-Fermion System Kohn, W.; Luttinger, J. M. Physical Review, Vol. 118, Issue 1 https://doi.org/10.1103/physrev.118.41	journal	April 1960
Spin Density Waves in an Electron Gas Overhauser, A. W. Physical Review, Vol. 128, Issue 3 https://doi.org/10.1103/physrev.128.1437	journal	November 1962
Bound States in Quantum Field Theory Gell-Mann, Murray; Low, Francis Physical Review, Vol. 84, Issue 2 https://doi.org/10.1103/physrev.84.350	journal	October 1951
Low-temperature breakdown of many-body perturbation theory for thermodynamics Hirata, So Physical Review A, Vol. 103, Issue 1 https://doi.org/10.1103/physreva.103.012223	journal	January 2021
Finite-temperature density matrix embedding theory Sun, Chong; Ray, Ushnish; Cui, Zhi-Hao Physical Review B, Vol. 101, Issue 7 https://doi.org/10.1103/physrevb.101.075131	journal	February 2020
Fast second-order many-body perturbation method for extended systems Hirata, So; Shimazaki, Tomomi Physical Review B, Vol. 80, Issue 8 https://doi.org/10.1103/physrevb.80.085118	journal	August 2009
Brueckner-Goldstone quantum Monte Carlo for correlation energies and quasiparticle energy bands of one-dimensional solids Willow, Soohaeng Yoo; Kim, Kwang S.; Hirata, So Physical Review B, Vol. 90, Issue 20 https://doi.org/10.1103/physrevb.90.201110	journal	November 2014
Finite-temperature auxiliary-field quantum Monte Carlo: Self-consistent constraint and systematic approach to low temperatures He, Yuan-Yao; Qin, Mingpu; Shi, Hao Physical Review B, Vol. 99, Issue 4 https://doi.org/10.1103/physrevb.99.045108	journal	January 2019
Finite-temperature many-body perturbation theory in the canonical ensemble Jha, Punit K.; Hirata, So Physical Review E, Vol. 101, Issue 2 https://doi.org/10.1103/physreve.101.022106	journal	February 2020
Systematic nonperturbative approach for thermal averages in quantum many-body systems: The thermal-cluster-cumulant method Sanyal, G.; Mandal, S. H.; Guha, S. Physical Review E, Vol. 48, Issue 5 https://doi.org/10.1103/physreve.48.3373	journal	November 1993
Accurate Exchange-Correlation Energies for the Warm Dense Electron Gas Malone, Fionn D.; Blunt, N. S.; Brown, Ethan W. Physical Review Letters, Vol. 117, Issue 11 https://doi.org/10.1103/physrevlett.117.115701	journal	September 2016
Giant Spin Density Waves Overhauser, A. W. Physical Review Letters, Vol. 4, Issue 9 https://doi.org/10.1103/physrevlett.4.462	journal	May 1960
Solitons in Polyacetylene Su, W. P.; Schrieffer, J. R.; Heeger, A. J. Physical Review Letters, Vol. 42, Issue 25 https://doi.org/10.1103/physrevlett.42.1698	journal	June 1979
‘‘Luttinger-liquid’’ behavior of the normal metallic state of the 2D Hubbard model Anderson, P. W. Physical Review Letters, Vol. 64, Issue 15 https://doi.org/10.1103/physrevlett.64.1839	journal	April 1990
Theory of noninteracting fermions and bosons in the canonical ensemble Barghathi, Hatem; Yu, Jiangyong; Del Maestro, Adrian Physical Review Research, Vol. 2, Issue 4 https://doi.org/10.1103/physrevresearch.2.043206	journal	November 2020
Direct Comparison of Many-Body Methods for Realistic Electronic Hamiltonians Williams, Kiel T.; Yao, Yuan; Li, Jia Physical Review X, Vol. 10, Issue 1 https://doi.org/10.1103/physrevx.10.011041	journal	February 2020
Towards the Solution of the Many-Electron Problem in Real Materials: Equation of State of the Hydrogen Chain with State-of-the-Art Many-Body Methods Motta, Mario; Ceperley, David M.; Chan, Garnet Kin-Lic Physical Review X, Vol. 7, Issue 3 https://doi.org/10.1103/physrevx.7.031059	journal	September 2017
Solitons in conducting polymers Heeger, A. J.; Kivelson, S.; Schrieffer, J. R. Reviews of Modern Physics, Vol. 60, Issue 3 https://doi.org/10.1103/revmodphys.60.781	journal	July 1988
Doping a Mott insulator: Physics of high-temperature superconductivity Lee, Patrick A.; Nagaosa, Naoto; Wen, Xiao-Gang Reviews of Modern Physics, Vol. 78, Issue 1 https://doi.org/10.1103/revmodphys.78.17	journal	January 2006
A New Approach to Quantum-Statistical Mechanics Matsubara, Takeo Progress of Theoretical Physics, Vol. 14, Issue 4 https://doi.org/10.1143/ptp.14.351	journal	October 1955
Many-Body Perturbation Theory and Coupled Cluster Theory for Electron Correlation in Molecules Bartlett, R. J. Annual Review of Physical Chemistry, Vol. 32, Issue 1 https://doi.org/10.1146/annurev.pc.32.100181.002043	journal	October 1981
An Identity for the Sum of Multinomial Coefficients Kao, R. C.; Zetterberg, L. H. The American Mathematical Monthly, Vol. 64, Issue 2 https://doi.org/10.2307/2310388	journal	February 1957

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Title: Finite-temperature many-body perturbation theory for electrons: Algebraic recursive definitions, second-quantized derivation, linked-diagram theorem, general-order algorithms, and grand canonical and canonical ensembles

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