General solution to the Kohn–Luttinger nonconvergence problem

Hirata, So

doi:10.1016/j.cplett.2022.139668

General solution to the Kohn–Luttinger nonconvergence problem

Journal Article · Mon May 02 00:00:00 EDT 2022 · Chemical Physics Letters

DOI:https://doi.org/10.1016/j.cplett.2022.139668· OSTI ID:1866594

Hirata, So ^[1]

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

A simple, but general solution is proposed for the Kohn–Luttinger problem, i.e., the nonconvergence of the finite-temperature many-body perturbation theory with its zero-temperature counterpart as temperature is lowered to zero under some circumstances. How this nonconvergence can be avoided by altering the reference wave function is illustrated numerically by using up to the fifth order of the perturbation theory.

View Accepted Manuscript (DOE)

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

Sponsoring Organization:: Scalable Predictive Methods for Excitations and Correlated Phenomena (SPEC); USDOE Office of Science (SC), Basic Energy Sciences (BES); USDOE Office of Science (SC), Basic Energy Sciences (BES). Chemical Sciences, Geosciences & Biosciences Division

Grant/Contract Number:: SC0006028

OSTI ID:: 1866594

Alternate ID(s):: OSTI ID: 1866860

Journal Information:: Chemical Physics Letters, Journal Name: Chemical Physics Letters Vol. 800; ISSN 0009-2614

Publisher:: ElsevierCopyright Statement

Country of Publication:: United States

Language:: English

References (19)

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
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
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
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
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
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
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
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 The Journal of Chemical Physics, Vol. 155, Issue 9 https://doi.org/10.1063/5.0061384	journal	September 2021
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
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
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 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
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
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

Similar Records

On the Kohn-Luttinger conundrum

Journal Article · Tue May 28 00:00:00 EDT 2013 · Journal of Chemical Physics · OSTI ID:22118538

Low-temperature breakdown of many-body perturbation theory for thermodynamics

Journal Article · Mon Jan 25 19:00:00 EST 2021 · Physical Review A · OSTI ID:1762416

Related Subjects

74 ATOMIC AND MOLECULAR PHYSICS

General solution to the Kohn–Luttinger nonconvergence problem

Citation Formats

References (19)

Similar Records

Related Subjects