Wave function methods for canonical ensemble thermal averages in correlated many-fermion systems

Harsha, Gaurav; Henderson, Thomas M.; Scuseria, Gustavo E.

doi:10.1063/5.0022702

Title: Wave function methods for canonical ensemble thermal averages in correlated many-fermion systems

Journal Article · Tue Sep 29 00:00:00 EDT 2020 · Journal of Chemical Physics

DOI:https://doi.org/10.1063/5.0022702· OSTI ID:1774553

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Rice Univ., Houston, TX (United States)

We present a wave function representation for the canonical ensemble thermal density matrix by projecting the thermofield double state against the desired number of particles. Furthermore, the resulting canonical thermal state obeys an imaginary-time evolution equation. Starting with the mean-field approximation, where the canonical thermal state becomes an antisymmetrized geminal power (AGP) wave function, we explore two different schemes to add correlation: by number-projecting a correlated grand-canonical thermal state and by adding correlation to the number-projected mean-field state. As benchmark examples, we use number-projected configuration interaction and an AGP-based perturbation theory to study the hydrogen molecule in a minimal basis and the six-site Hubbard model.

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Research Organization:: Rice Univ., Houston, TX (United States)

Sponsoring Organization:: USDOE Office of Science (SC), Basic Energy Sciences (BES); Welch Foundation

Grant/Contract Number:: FG02-09ER16053; SC0001474

OSTI ID:: 1774553

Alternate ID(s):: OSTI ID: 1668438

Journal Information:: Journal of Chemical Physics, Vol. 153, Issue 12; ISSN 0021-9606

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

Country of Publication:: United States

Language:: English

References (53)

Particle-number projected Bogoliubov-coupled-cluster theory: Application to the pairing Hamiltonian Qiu, Y.; Henderson, T. M.; Duguet, T. Physical Review C, Vol. 99, Issue 4 https://doi.org/10.1103/physrevc.99.044301	journal	April 2019
Projected coupled cluster theory Qiu, Yiheng; Henderson, Thomas M.; Zhao, Jinmo The Journal of Chemical Physics, Vol. 147, Issue 6 https://doi.org/10.1063/1.4991020	journal	August 2017
Calculations of canonical averages from the grand canonical ensemble Kosov, D. S.; Gelin, M. F.; Vdovin, A. I. Physical Review E, Vol. 77, Issue 2 https://doi.org/10.1103/physreve.77.021120	journal	February 2008
Symmetry broken and restored coupled-cluster theory: I. Rotational symmetry and angular momentum Duguet, T. Journal of Physics G: Nuclear and Particle Physics, Vol. 42, Issue 2 https://doi.org/10.1088/0954-3899/42/2/025107	journal	December 2014
P y SCF: the Python-based simulations of chemistry framework : The PySCF program Sun, Qiming; Berkelbach, Timothy C.; Blunt, Nick S. Wiley Interdisciplinary Reviews: Computational Molecular Science, Vol. 8, Issue 1 https://doi.org/10.1002/wcms.1340	journal	September 2017
Efficient evaluation of AGP reduced density matrices Khamoshi, Armin; Henderson, Thomas M.; Scuseria, Gustavo E. The Journal of Chemical Physics, Vol. 151, Issue 18 https://doi.org/10.1063/1.5127850	journal	November 2019
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
Algorithm 937: MINRES-QLP for symmetric and Hermitian linear equations and least-squares problems Choi, Sou-Cheng T.; Saunders, Michael A. ACM Transactions on Mathematical Software, Vol. 40, Issue 2 https://doi.org/10.1145/2527267	journal	February 2014
Real-time density-matrix coupled-cluster approach for closed and open systems at finite temperature Shushkov, Philip; Miller, Thomas F. The Journal of Chemical Physics, Vol. 151, Issue 13 https://doi.org/10.1063/1.5121749	journal	October 2019
Time-Dependent Coupled Cluster Theory on the Keldysh Contour for Nonequilibrium Systems White, Alec F.; Chan, Garnet Kin-Lic Journal of Chemical Theory and Computation, Vol. 15, Issue 11 https://doi.org/10.1021/acs.jctc.9b00750	journal	October 2019
Combining symmetry collective states with coupled-cluster theory: Lessons from the Agassi model Hamiltonian Hermes, Matthew R.; Dukelsky, Jorge; Scuseria, Gustavo E. Physical Review C, Vol. 95, Issue 6 https://doi.org/10.1103/physrevc.95.064306	journal	June 2017
Time-Dependent Density Matrix Renormalization Group Algorithms for Nearly Exact Absorption and Fluorescence Spectra of Molecular Aggregates at Both Zero and Finite Temperature Ren, Jiajun; Shuai, Zhigang; Kin-Lic Chan, Garnet Journal of Chemical Theory and Computation, Vol. 14, Issue 10 https://doi.org/10.1021/acs.jctc.8b00628	journal	August 2018
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
Small Superconducting Grain in the Canonical Ensemble Mastellone, A.; Falci, G.; Fazio, Rosario Physical Review Letters, Vol. 80, Issue 20 https://doi.org/10.1103/physrevlett.80.4542	journal	May 1998
Topology by dissipation in atomic quantum wires Diehl, Sebastian; Rico, Enrique; Baranov, Mikhail A. Nature Physics, Vol. 7, Issue 12 https://doi.org/10.1038/nphys2106	journal	October 2011
Finite-Temperature Variational Monte Carlo Method for Strongly Correlated Electron Systems Takai, Kensaku; Ido, Kota; Misawa, Takahiro Journal of the Physical Society of Japan, Vol. 85, Issue 3 https://doi.org/10.7566/jpsj.85.034601	journal	March 2016
Using Density Matrix Quantum Monte Carlo for Calculating Exact-on-Average Energies for ab Initio Hamiltonians in a Finite Basis Set Petras, Hayley R.; Ramadugu, Sai Kumar; Malone, Fionn D. Journal of Chemical Theory and Computation, Vol. 16, Issue 2 https://doi.org/10.1021/acs.jctc.9b01080	journal	January 2020
Geminal-based configuration interaction Henderson, Thomas M.; Scuseria, Gustavo E. The Journal of Chemical Physics, Vol. 151, Issue 5 https://doi.org/10.1063/1.5116715	journal	August 2019
Finite Temperature Coupled Cluster Theories for Extended Systems Hummel, Felix Journal of Chemical Theory and Computation, Vol. 14, Issue 12 https://doi.org/10.1021/acs.jctc.8b00793	journal	October 2018
A derivation of the pairing-correlation method Bayman, B. F. Nuclear Physics, Vol. 15 https://doi.org/10.1016/0029-5582(60)90279-0	journal	February 1960
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
Perspective: Ultracold molecules and the dawn of cold controlled chemistry Balakrishnan, N. The Journal of Chemical Physics, Vol. 145, Issue 15 https://doi.org/10.1063/1.4964096	journal	October 2016
Path Integral Monte Carlo Calculation of the Deuterium Hugoniot Militzer, B.; Ceperley, D. M. Physical Review Letters, Vol. 85, Issue 9 https://doi.org/10.1103/physrevlett.85.1890	journal	August 2000
Thermal averaging in quantum many-body systems: a non-perturbative thermal cluster cumulant approach Sanyal, Goutam; Mandal, Seikh Hannan; Mukherjee, Debashis Chemical Physics Letters, Vol. 192, Issue 1 https://doi.org/10.1016/0009-2614(92)85427-c	journal	April 1992
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
Variational ansatz-based quantum simulation of imaginary time evolution McArdle, Sam; Jones, Tyson; Endo, Suguru npj Quantum Information, Vol. 5, Issue 1 https://doi.org/10.1038/s41534-019-0187-2	journal	September 2019
Effects of particle-number conservation on heat capacity of nuclei Esashika, K.; Nakada, H.; Tanabe, K. Physical Review C, Vol. 72, Issue 4 https://doi.org/10.1103/physrevc.72.044303	journal	October 2005
New Bardeen-Cooper-Schrieffer-type theory at finite temperature with particle-number conservation Nakada, H.; Tanabe, K. Physical Review C, Vol. 74, Issue 6 https://doi.org/10.1103/physrevc.74.061301	journal	December 2006
Symmetry broken and restored coupled-cluster theory: II. Global gauge symmetry and particle number Duguet, T.; Signoracci, A. Journal of Physics G: Nuclear and Particle Physics, Vol. 44, Issue 1 https://doi.org/10.1088/0954-3899/44/1/015103	journal	December 2016
Merging symmetry projection methods with coupled cluster theory: Lessons from the Lipkin model Hamiltonian Wahlen-Strothman, Jacob M.; Henderson, Thomas M.; Hermes, Matthew R. The Journal of Chemical Physics, Vol. 146, Issue 5 https://doi.org/10.1063/1.4974989	journal	February 2017
Communication: Configuration interaction combined with spin-projection for strongly correlated molecular electronic structures Tsuchimochi, Takashi; Ten-no, Seiichiro The Journal of Chemical Physics, Vol. 144, Issue 1 https://doi.org/10.1063/1.4939585	journal	January 2016
Ab Initio Finite Temperature Auxiliary Field Quantum Monte Carlo Liu, Yuan; Cho, Minsik; Rubenstein, Brenda Journal of Chemical Theory and Computation, Vol. 14, Issue 9 https://doi.org/10.1021/acs.jctc.8b00569	journal	August 2018
Heisenberg and interaction representations in thermo field dynamics Evans, T. S.; Hardman, I.; Umezawa, H. Journal of Mathematical Physics, Vol. 33, Issue 1 https://doi.org/10.1063/1.529915	journal	January 1992
Interiors of Giant Planets Inside and Outside the Solar System Guillot, T. Science, Vol. 286, Issue 5437 https://doi.org/10.1126/science.286.5437.72	journal	October 1999
Finite temperature quantum embedding theories for correlated systems Zgid, Dominika; Gull, Emanuel New Journal of Physics, Vol. 19, Issue 2 https://doi.org/10.1088/1367-2630/aa5d34	journal	February 2017
Methods of Quantum Field Theory in Condensed Matter Physics: New Perspectives, Extensions and Applications Umezawa, Hiroomi Progress of Theoretical Physics Supplement, Vol. 80 https://doi.org/10.1143/ptps.80.26	journal	January 1984
MINRES-QLP: A Krylov Subspace Method for Indefinite or Singular Symmetric Systems Choi, Sou-Cheng T.; Paige, Christopher C.; Saunders, Michael A. SIAM Journal on Scientific Computing, Vol. 33, Issue 4 https://doi.org/10.1137/100787921	journal	January 2011
Structure of Fermion Density Matrices. II. Antisymmetrized Geminal Powers Coleman, A. J. Journal of Mathematical Physics, Vol. 6, Issue 9 https://doi.org/10.1063/1.1704794	journal	September 1965
Determining eigenstates and thermal states on a quantum computer using quantum imaginary time evolution Motta, Mario; Sun, Chong; Tan, Adrian T. K. Nature Physics, Vol. 16, Issue 2 https://doi.org/10.1038/s41567-019-0704-4	journal	November 2019
Minimally entangled typical thermal state algorithms Stoudenmire, E. M.; White, Steven R. New Journal of Physics, Vol. 12, Issue 5 https://doi.org/10.1088/1367-2630/12/5/055026	journal	May 2010
The Collective Model of Nuclear Motion Peierls, R. E.; Yoccoz, J. Proceedings of the Physical Society. Section A, Vol. 70, Issue 5 https://doi.org/10.1088/0370-1298/70/5/309	journal	May 1957
Functional methods in thermofield dynamics: A real-time perturbation theory for quantum statistical mechanics Semenoff, G. W.; Umezawa, H. Nuclear Physics B, Vol. 220, Issue 2 https://doi.org/10.1016/0550-3213(83)90223-7	journal	June 1983
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
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
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
Geminal Replacement Models Based on AGP Dutta, Rishab; Henderson, Thomas M.; Scuseria, Gustavo E. Journal of Chemical Theory and Computation https://doi.org/10.1021/acs.jctc.0c00807	journal	September 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
Cold molecules: Progress in quantum engineering of chemistry and quantum matter Bohn, John L.; Rey, Ana Maria; Ye, Jun Science, Vol. 357, Issue 6355 https://doi.org/10.1126/science.aam6299	journal	September 2017
Some consequences of the thermal Hartree-Fock approximation at zero temperature Sokoloff, J. Annals of Physics, Vol. 45, Issue 2 https://doi.org/10.1016/0003-4916(67)90122-4	journal	November 1967
Quantum canonical ensemble: A projection operator approach Magnus, Wim; Lemmens, Lucien; Brosens, Fons Physica A: Statistical Mechanics and its Applications, Vol. 482 https://doi.org/10.1016/j.physa.2017.04.069	journal	September 2017
Quantum number projection at finite temperature via thermofield dynamics Tanabe, K.; Nakada, H. Physical Review C, Vol. 71, Issue 2 https://doi.org/10.1103/physrevc.71.024314	journal	February 2005
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
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

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Title: Wave function methods for canonical ensemble thermal averages in correlated many-fermion systems

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