Exchange-correlation contributions to thermodynamic properties of the homogeneous electron gas from a cumulant Green's function approach

Kas, J. J.; Blanton, T. D.; Rehr, J. J.

doi:10.1103/physrevb.100.195144

Title: Exchange-correlation contributions to thermodynamic properties of the homogeneous electron gas from a cumulant Green's function approach

Journal Article · Tue Nov 26 00:00:00 EST 2019 · Physical Review B

DOI:https://doi.org/10.1103/physrevb.100.195144· OSTI ID:1800947

Kas, J. J. ^[1]; Blanton, T. D. ^[1];

^[1]

Univ. of Washington, Seattle, WA (United States)

Thermodynamic properties of the interacting homogeneous electron gas are calculated using a finite-temperature cumulant Green's function approach over a broad range of densities and temperatures up to the warm dense matter regime $$T ~ T_F$$, where $$T_F$$ is the Fermi degeneracy temperature. These properties can be separated into independent particle and exchange-correlation contributions, and our focus here is on the latter. In this work our approach is based on the Galitskii-Migdal-Koltun and electron number sum rules from the finite temperature many-body Green's function formalism, together with an extension of the cumulant Green's function to finite temperature. Previously this approach yielded exchange-correlation energies and potentials in good agreement with quantum Monte-Carlo calculations. Here the method is extended for various thermodynamic quantities including the chemical potential, total energy, Helmholtz free-energy, electronic equation of state, specific heat, and isothermal compressibility, which optionally include spin dependence. We find that the exchange-correlation contributions are weakly varying at low temperature but exhibit significant temperature dependence in the WDM regime, as well as a crossover from exchange- to correlation-dominated behavior. In contrast to the $T = 0^+$ limit, we also find that renormalization effects are largely but not completely suppressed at finite temperature. Comparisons with other approaches at various levels of approximation are also discussed.

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Research Organization:: Univ. of Washington, Seattle, WA (United States)

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

Grant/Contract Number:: FG02-97ER45623

OSTI ID:: 1800947

Journal Information:: Physical Review B, Vol. 100, Issue 19; ISSN 2469-9950

Publisher:: American Physical Society (APS)Copyright Statement

Country of Publication:: United States

Language:: English

References (57)

Progress in the study of warm dense matter Koenig, M.; Benuzzi-Mounaix, A.; Ravasio, A. Plasma Physics and Controlled Fusion, Vol. 47, Issue 12B https://doi.org/10.1088/0741-3335/47/12B/S31	journal	November 2005
Spectral fingerprints of electron-plasmon coupling Caruso, Fabio; Giustino, Feliciano Physical Review B, Vol. 92, Issue 4 https://doi.org/10.1103/PhysRevB.92.045123	journal	July 2015
Exchange and correlation potentials for finite temperature quantum calculations at intermediate degeneracies Dharma-wardana, M. W. C.; Taylor, R. Journal of Physics C: Solid State Physics, Vol. 14, Issue 5 https://doi.org/10.1088/0022-3719/14/5/011	journal	February 1981
The importance of finite-temperature exchange-correlation for warm dense matter calculations Karasiev, Valentin V.; Calderín, Lázaro; Trickey, S. B. arXiv https://doi.org/10.48550/arxiv.1601.04543	text	January 2016
Many-Particle Physics Dowker, J. S. Physics Bulletin, Vol. 33, Issue 3 https://doi.org/10.1088/0031-9112/33/3/038	journal	March 1982
Quantum Monte Carlo study of the three-dimensional spin-polarized homogeneous electron gas Spink, G. G.; Needs, R. J.; Drummond, N. D. Physical Review B, Vol. 88, Issue 8 https://doi.org/10.1103/PhysRevB.88.085121	journal	August 2013
Finite temperature Green's function approach for excited state and thermodynamic properties of cool to warm dense matter Kas, J. J.; Rehr, J. J. arXiv https://doi.org/10.48550/arxiv.1708.04126	text	January 2017
Path-Integral Monte Carlo Simulation of the Warm Dense Homogeneous Electron Gas Brown, Ethan W.; Clark, Bryan K.; DuBois, Jonathan L. Physical Review Letters, Vol. 110, Issue 14 https://doi.org/10.1103/PhysRevLett.110.146405	journal	April 2013
Dielectric response of quantum plasmas in thermal equilibrium Arista, Néstor R.; Brandt, Werner Physical Review A, Vol. 29, Issue 3 https://doi.org/10.1103/PhysRevA.29.1471	journal	March 1984
Coupled Electron-Phonon System Engelsberg, S.; Schrieffer, J. R. Physical Review, Vol. 131, Issue 3 https://doi.org/10.1103/PhysRev.131.993	journal	August 1963
Exact conditions on the temperature dependence of density functionals Burke, Kieron; Smith, Justin C.; Grabowski, Paul E. arXiv https://doi.org/10.48550/arxiv.1511.02194	text	January 2015
Satellite structures in the spectral functions of the two-dimensional electron gas in semiconductor quantum wells: A $G W$ plus cumulant study Lischner, Johannes; Vigil-Fowler, Derek; Louie, Steven G. Physical Review B, Vol. 89, Issue 12 https://doi.org/10.1103/PhysRevB.89.125430	journal	March 2014
Statistical Mechanics of High‐Temperature Quantum Plasmas Beyond the Ring Approximation DeWitt, Hugh E. Journal of Mathematical Physics, Vol. 7, Issue 4 https://doi.org/10.1063/1.1704974	journal	April 1966
Theory of Many-Particle Systems. I Martin, Paul C.; Schwinger, Julian Physical Review, Vol. 115, Issue 6 https://doi.org/10.1103/PhysRev.115.1342	journal	September 1959
Conservation Laws and Correlation Functions Baym, Gordon; Kadanoff, Leo P. Physical Review, Vol. 124, Issue 2 https://doi.org/10.1103/PhysRev.124.287	journal	October 1961
Band Structures of Plasmonic Polarons Caruso, Fabio; Lambert, Henry; Giustino, Feliciano Physical Review Letters, Vol. 114, Issue 14 https://doi.org/10.1103/PhysRevLett.114.146404	journal	April 2015
Effective mass of quasiparticles from thermodynamics Eich, F. G.; Holzmann, Markus; Vignale, G. arXiv https://doi.org/10.48550/arxiv.1704.04076	text	January 2017
Real-time cumulant approach for charge-transfer satellites in x-ray photoemission spectra Kas, J. J.; Vila, F. D.; Rehr, J. J. Physical Review B, Vol. 91, Issue 12 https://doi.org/10.1103/PhysRevB.91.121112	journal	March 2015
Correlation energy and its temperature dependence Hong, Suklyun; Mahan, G. D. Physical Review B, Vol. 53, Issue 3 https://doi.org/10.1103/PhysRevB.53.1215	journal	January 1996
Electron-phonon interactions from first principles Giustino, Feliciano Reviews of Modern Physics, Vol. 89, Issue 1 https://doi.org/10.1103/RevModPhys.89.015003	journal	February 2017
Accurate Homogeneous Electron Gas Exchange-Correlation Free Energy for Local Spin-Density Calculations Karasiev, Valentin V.; Sjostrom, Travis; Dufty, James Physical Review Letters, Vol. 112, Issue 7 https://doi.org/10.1103/PhysRevLett.112.076403	journal	February 2014
Dense plasma X-ray scattering: Methods and applications Glenzer, S. H.; Lee, H. J.; Davis, P. High Energy Density Physics, Vol. 6, Issue 1 https://doi.org/10.1016/j.hedp.2009.09.003	journal	January 2010
Ab Initio Path Integral Monte Carlo Approach to the Static and Dynamic Density Response of the Uniform Electron Gas Groth, Simon; Dornheim, Tobias; Vorberger, Jan arXiv https://doi.org/10.48550/arxiv.1903.11970	text	January 2019
Self-Consistent Equations Including Exchange and Correlation Effects Kohn, W.; Sham, L. J. Physical Review, Vol. 140, Issue 4A, p. A1133-A1138 https://doi.org/10.1103/PhysRev.140.A1133	journal	November 1965
Finite-temperature quasiparticle self-consistent $GW$ approximation Faleev, Sergey V.; van Schilfgaarde, Mark; Kotani, Takao Physical Review B, Vol. 74, Issue 3 https://doi.org/10.1103/PhysRevB.74.033101	journal	July 2006
The Uniform Electron Gas at Warm Dense Matter Conditions Dornheim, Tobias; Groth, Simon; Bonitz, Michael arXiv https://doi.org/10.48550/arxiv.1801.05783	text	January 2018
Exact conditions on the temperature dependence of density functionals Burke, K.; Smith, J. C.; Grabowski, P. E. Physical Review B, Vol. 93, Issue 19 https://doi.org/10.1103/PhysRevB.93.195132	journal	May 2016
First-principles equation of state calculations of warm dense nitrogen Driver, K. P.; Militzer, B. Physical Review B, Vol. 93, Issue 6 https://doi.org/10.1103/PhysRevB.93.064101	journal	February 2016
On correlation effects in electron spectroscopies and the GW approximation Hedin, Lars Journal of Physics: Condensed Matter, Vol. 11, Issue 42 https://doi.org/10.1088/0953-8984/11/42/201	journal	October 1999
Singularities in the X-Ray Spectra of Metals Langreth, David C. Physical Review B, Vol. 1, Issue 2 https://doi.org/10.1103/PhysRevB.1.471	journal	January 1970
Quasiparticle excitation spectrum for nearly-free-electron metals Northrup, John E.; Hybertsen, Mark S.; Louie, Steven G. Physical Review B, Vol. 39, Issue 12 https://doi.org/10.1103/PhysRevB.39.8198	journal	April 1989
Electron Correlations at Metallic Densities Singwi, K. S.; Tosi, M. P.; Land, R. H. Physical Review, Vol. 176, Issue 2 https://doi.org/10.1103/PhysRev.176.589	journal	December 1968
Thermodynamics and Correlational Properties of Finite-Temperature Electron Liquids in the Singwi-Tosi-Land-Sjölander Approximation Tanaka, Shigenori; Ichimaru, Setsuo Journal of the Physical Society of Japan, Vol. 55, Issue 7 https://doi.org/10.1143/JPSJ.55.2278	journal	July 1986
Dynamical effects in electron spectroscopy Zhou, Jianqiang Sky; Kas, J. J.; Sponza, Lorenzo The Journal of Chemical Physics, Vol. 143, Issue 18 https://doi.org/10.1063/1.4934965	journal	November 2015
Importance of finite-temperature exchange correlation for warm dense matter calculations Karasiev, Valentin V.; Calderín, Lázaro; Trickey, S. B. Physical Review E, Vol. 93, Issue 6 https://doi.org/10.1103/PhysRevE.93.063207	journal	June 2016
Ab initio path integral Monte Carlo approach to the static and dynamic density response of the uniform electron gas Groth, S.; Dornheim, T.; Vorberger, J. Physical Review B, Vol. 99, Issue 23 https://doi.org/10.1103/PhysRevB.99.235122	journal	June 2019
Fermi Surface and Some Simple Equilibrium Properties of a System of Interacting Fermions Luttinger, J. M. Physical Review, Vol. 119, Issue 4 https://doi.org/10.1103/PhysRev.119.1153	journal	August 1960
Particle-hole cumulant approach for inelastic losses in x-ray spectra Kas, J. J.; Rehr, J. J.; Curtis, J. B. arXiv https://doi.org/10.48550/arxiv.1604.06829	text	January 2016
Status of free-energy representations for the homogeneous electron gas Karasiev, Valentin V.; Trickey, S. B.; Dufty, James W. Physical Review B, Vol. 99, Issue 19 https://doi.org/10.1103/PhysRevB.99.195134	journal	May 2019
Exchange and correlation in finite-temperature TDDFT Rehr, John J.; Kas, Joshua J. The European Physical Journal B, Vol. 91, Issue 7 https://doi.org/10.1140/epjb/e2018-90063-3	journal	July 2018
Theory of the temperature dependence of electronic band structures Allen, P. B.; Heine, V. Journal of Physics C: Solid State Physics, Vol. 9, Issue 12 https://doi.org/10.1088/0022-3719/9/12/013	journal	June 1976
Dynamic susceptibility of Fermi liquids at finite temperature Khanna, F. C.; Glyde, H. R. Canadian Journal of Physics, Vol. 54, Issue 6 https://doi.org/10.1139/p76-071	journal	March 1976
Band structures of plasmonic polarons Caruso, Fabio; Lambert, Henry; Giustino, Feliciano arXiv https://doi.org/10.48550/arxiv.1503.05778	text	January 2015
Inhomogeneous Electron Gas Hohenberg, P.; Kohn, W. Physical Review, Vol. 136, Issue 3B, p. B864-B871 https://doi.org/10.1103/PhysRev.136.B864	journal	November 1964
Spectral Fingerprints of Electron-Plasmon Coupling Caruso, Fabio; Giustino, Feliciano arXiv https://doi.org/10.48550/arxiv.1507.06911	text	January 2015
The uniform electron gas at warm dense matter conditions Dornheim, Tobias; Groth, Simon; Bonitz, Michael Physics Reports, Vol. 744 https://doi.org/10.1016/j.physrep.2018.04.001	journal	May 2018
Inhomogeneous Electron Gas Rajagopal, A. K.; Callaway, J. Physical Review B, Vol. 7, Issue 5 https://doi.org/10.1103/physrevb.7.1912	journal	March 1973
Effective mass of quasiparticles from thermodynamics Eich, F. G.; Holzmann, Markus; Vignale, G. Physical Review B, Vol. 96, Issue 3 https://doi.org/10.1103/PhysRevB.96.035132	journal	July 2017
Self-consistent ${GW}_{0}$ results for the electron gas: Fixed screened potential $W_{0}$ within the random-phase approximation von Barth, Ulf; Holm, Bengt Physical Review B, Vol. 54, Issue 12 https://doi.org/10.1103/PhysRevB.54.8411	journal	September 1996
Density-functional theory, finite-temperature classical maps, and their implications for foundational studies of quantum systems Dharma-wardana, M. W. C. Journal of Physics: Conference Series, Vol. 442 https://doi.org/10.1088/1742-6596/442/1/012030	journal	June 2013
Density functional for short-range correlation: Accuracy of the random-phase approximation for isoelectronic energy changes Yan, Zidan; Perdew, John P.; Kurth, Stefan Physical Review B, Vol. 61, Issue 24 https://doi.org/10.1103/PhysRevB.61.16430	journal	June 2000
Thermal Properties of the Inhomogeneous Electron Gas Mermin, N. David Physical Review, Vol. 137, Issue 5A https://doi.org/10.1103/PhysRev.137.A1441	journal	March 1965
Total Energies from $GW$ Calculations Holm, Bengt Physical Review Letters, Vol. 83, Issue 4 https://doi.org/10.1103/PhysRevLett.83.788	journal	July 1999
Many-Particle Physics Mahan, Gerald D. Physics of Solids and Liquids (PSLI) https://doi.org/10.1007/978-1-4757-5714-9	book	January 2000
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
Coulomb-hole and screened exchange in the electron self-energy at finite temperature Tan, Tun S.; Kas, J. J.; Rehr, J. J. Physical Review B, Vol. 98, Issue 11 https://doi.org/10.1103/PhysRevB.98.115125	journal	September 2018
Ab initio Exchange-Correlation Free Energy of the Uniform Electron Gas at Warm Dense Matter Conditions Groth, Simon; Dornheim, Tobias; Sjostrom, Travis arXiv https://doi.org/10.48550/arxiv.1703.08074	text	January 2017

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