1
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Rodríguez-Jiménez JA, Carreras A, Casanova D. Small-Occupation Density Functional Correlation Energy Correction to Wave Function Approximations. J Chem Theory Comput 2024. [PMID: 38227943 DOI: 10.1021/acs.jctc.3c01067] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/18/2024]
Abstract
In this work, we introduce a novel hybrid approach, termed WFT-soDFT, designed to seamlessly incorporate DFT correlation into wave function ansatzes. This is achieved through a partitioning of the orbital space, distinguishing between large and small natural occupation numbers associated with wave function theory (WFT) and DFT correlation, respectively. The method uses a novel criterion for partitioning the orbital space and mapping the electron density in natural orbitals with a small occupation with the correlation energy of fast electrons within the homogeneous electron gas. Central to our approach is the introduction of a separation parameter ν, the choice of the WFT approach, and the correlation functional. Here, we combine the RASCI wave function with hole and particle truncation with a local density correlation functional to only account for small-occupation correlation energy. We investigate the performance of the method in the study of small but challenging chemical systems, for which WFT-soDFT demonstrates notable improvements over pristine wave function calculations. These findings collectively highlight the potential of the WFT-soDFT approach as a computationally affordable strategy to improve the accuracy of WFT electronic structure calculations.
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Affiliation(s)
- José Aarón Rodríguez-Jiménez
- Donostia International Physics Center (DIPC), 20018 Donostia, Euskadi, Spain
- Polimero eta Material Aurreratuak: Fisika, Kimika eta Teknologia, Kimika Fakultatea, Euskal Herriko Unibertsitatea (UPV/EHU), 20018 Donostia, Euskadi, Spain
| | - Abel Carreras
- Multiverse Computing, 20008 Donostia, Euskadi, Spain
| | - David Casanova
- Donostia International Physics Center (DIPC), 20018 Donostia, Euskadi, Spain
- IKERBASQUE, Basque Foundation for Science, 48009 Bilbao, Euskadi, Spain
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2
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Holzmann M, Calcavecchia F, Ceperley DM, Olevano V. Static Self-Energy and Effective Mass of the Homogeneous Electron Gas from Quantum Monte Carlo Calculations. PHYSICAL REVIEW LETTERS 2023; 131:186501. [PMID: 37977649 DOI: 10.1103/physrevlett.131.186501] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 05/08/2023] [Accepted: 10/06/2023] [Indexed: 11/19/2023]
Abstract
We discuss the methodology of quantum Monte Carlo calculations of the effective mass based on the static self-energy Σ(k,0). We then use variational Monte Carlo calculations of Σ(k,0) of the homogeneous electron gas at various densities to obtain results very close to perturbative G_{0}W_{0} calculations for values of the density parameter 1≤r_{s}≤10. The obtained values for the effective mass are close to diagrammatic Monte Carlo results and disagree with previous quantum Monte Carlo calculations based on a heuristic mapping of excitation energies to those of an ideal gas.
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Affiliation(s)
| | | | - David M Ceperley
- University of Illinois Urbana-Champaign, Urbana, Illinois 61801, USA
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3
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Yuan S, Chang Y, Wagner LK. Quantification of electron correlation for approximate quantum calculations. J Chem Phys 2022; 157:194101. [DOI: 10.1063/5.0119260] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/17/2022] Open
Abstract
State-of-the-art many-body wave function techniques rely on heuristics to achieve high accuracy at an attainable computational cost to solve the many-body Schrödinger equation. By far, the most common property used to assess accuracy has been the total energy; however, total energies do not give a complete picture of electron correlation. In this work, we assess the von Neumann entropy of the one-particle reduced density matrix (1-RDM) to compare selected configuration interaction (CI), coupled cluster, variational Monte Carlo, and fixed-node diffusion Monte Carlo for benchmark hydrogen chains. A new algorithm, the circle reject method, is presented, which improves the efficiency of evaluating the von Neumann entropy using quantum Monte Carlo by several orders of magnitude. The von Neumann entropy of the 1-RDM and the eigenvalues of the 1-RDM are shown to distinguish between the dynamic correlation introduced by the Jastrow and the static correlation introduced by determinants with large weights, confirming some of the lore in the field concerning the difference between the selected CI and Slater–Jastrow wave functions.
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Affiliation(s)
- Shunyue Yuan
- Department of Physics, University of Illinois Urbana-Champaign, Champaign, Illinois 61801, USA
| | - Yueqing Chang
- Department of Physics, University of Illinois Urbana-Champaign, Champaign, Illinois 61801, USA
| | - Lucas K. Wagner
- Department of Physics, University of Illinois Urbana-Champaign, Champaign, Illinois 61801, USA
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4
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Weiler L, Mihm T, Shepherd JJ. Machine learning for a finite size correction in periodic coupled cluster theory calculations. J Chem Phys 2022; 156:204109. [DOI: 10.1063/5.0086580] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Abstract
We introduce a straightforward Gaussian process regression (GPR) model for the transition structure factor of metal periodic coupled cluster singles and doubles (CCSD) calculations. This is inspired by the method introduced by Liao and Gr\"uneis for interpolating over the transition structure factor to obtain a finite size correction for CCSD [J. Chem. Phys. 145, 141102 (2016)], and by our own prior work using the transition structure factor to efficiently converge CCSD for metals to the thermodynamic limit [Nat. Comput. Sci. 1, 801 (2021)]. In our CCSD-FS-GPR method to correct for finite size errors, we fit the structure factor to a 1D function in the momentum transfer, $G$.We then integrate over this function by projecting it onto a k-point mesh to obtain comparisons with extrapolated results. Results are shown for lithium, sodium, and the uniform electron gas.
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Affiliation(s)
| | - Tina Mihm
- Chemistry, University of Iowa, United States of America
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5
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Single-particle excitations in the uniform electron gas by diagrammatic Monte Carlo. Sci Rep 2022; 12:2294. [PMID: 35145153 PMCID: PMC8831554 DOI: 10.1038/s41598-022-06188-6] [Citation(s) in RCA: 2] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 02/04/2021] [Accepted: 01/24/2022] [Indexed: 11/30/2022] Open
Abstract
We calculate the single-particle excitation spectrum and the Landau liquid parameters for the archetypal model of solids, the three-dimensional uniform electron gas, with the variational diagrammatic Monte Carlo method, which gives numerically controlled results without systematic error. In the metallic range of density, we establish benchmark values for the wave-function renormalization factor Z, the effective mass \documentclass[12pt]{minimal}
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\begin{document}$$m^*/m$$\end{document}m∗/m, and the Landau parameters \documentclass[12pt]{minimal}
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\begin{document}$$F_0^a$$\end{document}F0a with unprecedented accuracy, and we resolve the long-standing puzzle of non-monotonic dependence of mass on density. We also exclude the possibility that experimentally measured large reduction of bandwidth in Na metal can originate from the charge and spin fluctuations contained in the model of the uniform electron gas.
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6
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Dornheim T, Vorberger J, Militzer B, Moldabekov ZA. Momentum distribution of the uniform electron gas at finite temperature: Effects of spin polarization. Phys Rev E 2021; 104:055206. [PMID: 34942706 DOI: 10.1103/physreve.104.055206] [Citation(s) in RCA: 4] [Impact Index Per Article: 1.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 06/03/2021] [Accepted: 10/25/2021] [Indexed: 11/07/2022]
Abstract
We carry out extensive direct path integral Monte Carlo (PIMC) simulations of the uniform electron gas (UEG) at finite temperature for different values of the spin-polarization ξ. This allows us to unambiguously quantify the impact of spin effects on the momentum distribution function n(k) and related properties. We find that interesting physical effects like the interaction-induced increase in the occupation of the zero-momentum state n(0) substantially depend on ξ. Our results further advance the current understanding of the UEG as a fundamental model system, and are of practical relevance for the description of transport properties of warm dense matter in an external magnetic field. All PIMC results are freely available online and can be used as a benchmark for the development of methods and applications.
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Affiliation(s)
- Tobias Dornheim
- Center for Advanced Systems Understanding (CASUS), D-02826 Görlitz, Germany.,Helmholtz-Zentrum Dresden-Rossendorf (HZDR), D-01328 Dresden, Germany
| | - Jan Vorberger
- Helmholtz-Zentrum Dresden-Rossendorf (HZDR), D-01328 Dresden, Germany
| | - Burkhard Militzer
- Department of Earth and Planetary Science, University of California, Berkeley, California 94720, USA.,Department of Astronomy, University of California, Berkeley, California 94720, USA
| | - Zhandos A Moldabekov
- Center for Advanced Systems Understanding (CASUS), D-02826 Görlitz, Germany.,Helmholtz-Zentrum Dresden-Rossendorf (HZDR), D-01328 Dresden, Germany
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7
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Azadi S, Drummond ND, Foulkes WMC. Quasiparticle Effective Mass of the Three-Dimensional Fermi Liquid by Quantum Monte Carlo. PHYSICAL REVIEW LETTERS 2021; 127:086401. [PMID: 34477398 DOI: 10.1103/physrevlett.127.086401] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 04/07/2021] [Accepted: 07/26/2021] [Indexed: 06/13/2023]
Abstract
According to Landau's Fermi liquid theory, the main properties of the quasiparticle excitations of an electron gas are embodied in the effective mass m^{*}, which determines the energy of a single quasiparticle, and the Landau interaction function, which indicates how the energy of a quasiparticle is modified by the presence of other quasiparticles. This simple paradigm underlies most of our current understanding of the physical and chemical behavior of metallic systems. The quasiparticle effective mass of the three-dimensional homogeneous electron gas has been the subject of theoretical controversy, and there is a lack of experimental data. In this Letter, we deploy diffusion Monte Carlo (DMC) methods to calculate m^{*} as a function of density for paramagnetic and ferromagnetic three-dimensional homogeneous electron gases. The DMC results indicate that m^{*} decreases when the density is reduced, especially in the ferromagnetic case. The DMC quasiparticle energy bands exclude the possibility of a reduction in the occupied bandwidth relative to that of the free-electron model at density parameter r_{s}=4, which corresponds to Na metal.
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Affiliation(s)
- Sam Azadi
- Department of Physics and the Thomas Young Centre for Theory and Simulation of Materials, South Kensington Campus, Imperial College London, London SW7 2AZ, United Kingdom
| | - N D Drummond
- Department of Physics, Lancaster University, Lancaster LA1 4YB, United Kingdom
| | - W M C Foulkes
- Department of Physics and the Thomas Young Centre for Theory and Simulation of Materials, South Kensington Campus, Imperial College London, London SW7 2AZ, United Kingdom
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8
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Hunger K, Schoof T, Dornheim T, Bonitz M, Filinov A. Momentum distribution function and short-range correlations of the warm dense electron gas: Ab initio quantum Monte Carlo results. Phys Rev E 2021; 103:053204. [PMID: 34134307 DOI: 10.1103/physreve.103.053204] [Citation(s) in RCA: 4] [Impact Index Per Article: 1.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 01/05/2021] [Accepted: 03/19/2021] [Indexed: 01/22/2023]
Abstract
In a classical plasma the momentum distribution, n(k), decays exponentially, for large k, and the same is observed for an ideal Fermi gas. However, when quantum and correlation effects are relevant simultaneously, an algebraic decay, n_{∞}(k)∼k^{-8} has been predicted. This is of relevance for cross sections and threshold processes in dense plasmas that depend on the number of energetic particles. Here we present extensive ab initio results for the momentum distribution of the nonideal uniform electron gas at warm dense matter conditions. Our results are based on first principle fermionic path integral Monte Carlo (CPIMC) simulations and clearly confirm the k^{-8} asymptotic. This asymptotic behavior is directly linked to short-range correlations which are analyzed via the on-top pair distribution function (on-top PDF), i.e., the PDF of electrons with opposite spin. We present extensive results for the density and temperature dependence of the on-top PDF and for the momentum distribution in the entire momentum range.
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Affiliation(s)
- Kai Hunger
- Institut für Theoretische Physik und Astrophysik, Christian-Albrechts-Universität zu Kiel, Leibnizstraße 15, 24098 Kiel, Germany
| | - Tim Schoof
- Institut für Theoretische Physik und Astrophysik, Christian-Albrechts-Universität zu Kiel, Leibnizstraße 15, 24098 Kiel, Germany.,Deutsches Elektronen Synchotron (DESY), Hamburg, Germany
| | - Tobias Dornheim
- Center for Advanced Systems Understanding (CASUS), D-02826 Görlitz, Germany.,Helmholtz-Zentrum Dresden-Rossendorf (HZDR), D-01328 Dresden, Germany
| | - Michael Bonitz
- Institut für Theoretische Physik und Astrophysik, Christian-Albrechts-Universität zu Kiel, Leibnizstraße 15, 24098 Kiel, Germany
| | - Alexey Filinov
- Institut für Theoretische Physik und Astrophysik, Christian-Albrechts-Universität zu Kiel, Leibnizstraße 15, 24098 Kiel, Germany.,Joint Institute for High Temperatures, Russian Academy of Sciences, Izhorskaya 13, Moscow 125412, Russia
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9
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Dornheim T, Vorberger J. Overcoming finite-size effects in electronic structure simulations at extreme conditions. J Chem Phys 2021; 154:144103. [DOI: 10.1063/5.0045634] [Citation(s) in RCA: 10] [Impact Index Per Article: 3.3] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Affiliation(s)
- Tobias Dornheim
- Center for Advanced Systems Understanding (CASUS), D-02826 Görlitz, Germany
- Helmholtz-Zentrum Dresden-Rossendorf (HZDR), D-01328 Dresden, Germany
| | - Jan Vorberger
- Helmholtz-Zentrum Dresden-Rossendorf (HZDR), D-01328 Dresden, Germany
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10
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Kent PRC, Annaberdiyev A, Benali A, Bennett MC, Landinez Borda EJ, Doak P, Hao H, Jordan KD, Krogel JT, Kylänpää I, Lee J, Luo Y, Malone FD, Melton CA, Mitas L, Morales MA, Neuscamman E, Reboredo FA, Rubenstein B, Saritas K, Upadhyay S, Wang G, Zhang S, Zhao L. QMCPACK: Advances in the development, efficiency, and application of auxiliary field and real-space variational and diffusion quantum Monte Carlo. J Chem Phys 2020; 152:174105. [DOI: 10.1063/5.0004860] [Citation(s) in RCA: 43] [Impact Index Per Article: 10.8] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/11/2022] Open
Affiliation(s)
- P. R. C. Kent
- Center for Nanophase Materials Sciences Division and Computational Sciences and Engineering Division, Oak Ridge National Laboratory, Oak Ridge, Tennessee 37831, USA
| | - Abdulgani Annaberdiyev
- Department of Physics, North Carolina State University, Raleigh, North Carolina 27695-8202, USA
| | - Anouar Benali
- Computational Science Division, Argonne National Laboratory, 9700 S. Cass Avenue, Lemont, Illinois 60439, USA
| | - M. Chandler Bennett
- Materials Science and Technology Division, Oak Ridge National Laboratory, Oak Ridge, Tennessee 37831, USA
| | - Edgar Josué Landinez Borda
- Quantum Simulations Group, Lawrence Livermore National Laboratory, 7000 East Avenue, Livermore, California 94551, USA
| | - Peter Doak
- Center for Nanophase Materials Sciences Division and Computational Sciences and Engineering Division, Oak Ridge National Laboratory, Oak Ridge, Tennessee 37831, USA
| | - Hongxia Hao
- Department of Chemistry, University of California, Berkeley, California 94720, USA
| | - Kenneth D. Jordan
- Department of Chemistry, University of Pittsburgh, Pittsburgh, Pennsylvania 15260, USA
| | - Jaron T. Krogel
- Materials Science and Technology Division, Oak Ridge National Laboratory, Oak Ridge, Tennessee 37831, USA
| | - Ilkka Kylänpää
- Computational Physics Laboratory, Tampere University, P.O. Box 692, 33014 Tampere, Finland
| | - Joonho Lee
- Department of Chemistry, Columbia University, New York, New York 10027, USA
| | - Ye Luo
- Computational Science Division, Argonne National Laboratory, 9700 S. Cass Avenue, Lemont, Illinois 60439, USA
| | - Fionn D. Malone
- Quantum Simulations Group, Lawrence Livermore National Laboratory, 7000 East Avenue, Livermore, California 94551, USA
| | - Cody A. Melton
- Sandia National Laboratories, Albuquerque, New Mexico 87123, USA
| | - Lubos Mitas
- Department of Physics, North Carolina State University, Raleigh, North Carolina 27695-8202, USA
| | - Miguel A. Morales
- Quantum Simulations Group, Lawrence Livermore National Laboratory, 7000 East Avenue, Livermore, California 94551, USA
| | - Eric Neuscamman
- Department of Chemistry, University of California, Berkeley, California 94720, USA
- Chemical Sciences Division, Lawrence Berkeley National Laboratory, Berkeley, California 94720, USA
| | - Fernando A. Reboredo
- Department of Chemistry, University of Pittsburgh, Pittsburgh, Pennsylvania 15260, USA
| | - Brenda Rubenstein
- Department of Chemistry, Brown University, Providence, Rhode Island 02912, USA
| | - Kayahan Saritas
- Department of Applied Physics, Yale University, New Haven, Connecticut 06520, USA
| | - Shiv Upadhyay
- Department of Chemistry, University of Pittsburgh, Pittsburgh, Pennsylvania 15260, USA
| | - Guangming Wang
- Department of Physics, North Carolina State University, Raleigh, North Carolina 27695-8202, USA
| | - Shuai Zhang
- Laboratory for Laser Energetics, University of Rochester, 250 E River Rd., Rochester, New York 14623, USA
| | - Luning Zhao
- Department of Chemistry, University of Washington, Seattle, Washington 98195, USA
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11
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Lee J, Malone FD, Morales MA. An auxiliary-Field quantum Monte Carlo perspective on the ground state of the dense uniform electron gas: An investigation with Hartree-Fock trial wavefunctions. J Chem Phys 2019. [DOI: 10.1063/1.5109572] [Citation(s) in RCA: 12] [Impact Index Per Article: 2.4] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Affiliation(s)
- Joonho Lee
- College of Chemistry, University of California, Berkeley, California 94720, USA
| | - Fionn D. Malone
- Quantum Simulations Group, Lawrence Livermore National Laboratory, 7000 East Avenue, Livermore, California 94551, USA
| | - Miguel A. Morales
- Quantum Simulations Group, Lawrence Livermore National Laboratory, 7000 East Avenue, Livermore, California 94551, USA
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12
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Pierleoni C, Rillo G, Ceperley DM, Holzmann M. Electron localization properties in high pressure hydrogen at the liquid-liquid phase transition by Coupled Electron-Ion Monte Carlo. ACTA ACUST UNITED AC 2018. [DOI: 10.1088/1742-6596/1136/1/012005] [Citation(s) in RCA: 6] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/12/2022]
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13
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Delle Site L. Simulation of Many-Electron Systems That Exchange Matter with the Environment. ADVANCED THEORY AND SIMULATIONS 2018. [DOI: 10.1002/adts.201800056] [Citation(s) in RCA: 8] [Impact Index Per Article: 1.3] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 12/16/2022]
Affiliation(s)
- Luigi Delle Site
- Institute for Mathematics; Freie Universität Berlin; D-14195 Berlin Germany
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14
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Schmidt M, Roy PN. Path integral molecular dynamic simulation of flexible molecular systems in their ground state: Application to the water dimer. J Chem Phys 2018; 148:124116. [DOI: 10.1063/1.5017532] [Citation(s) in RCA: 17] [Impact Index Per Article: 2.8] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Affiliation(s)
- Matthew Schmidt
- Department of Chemistry, University of Waterloo, Waterloo, Ontario N2L 3G1, Canada
| | - Pierre-Nicholas Roy
- Department of Chemistry, University of Waterloo, Waterloo, Ontario N2L 3G1, Canada
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15
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Pavlyukh Y. Padé resummation of many-body perturbation theories. Sci Rep 2017; 7:504. [PMID: 28356576 PMCID: PMC5428253 DOI: 10.1038/s41598-017-00355-w] [Citation(s) in RCA: 13] [Impact Index Per Article: 1.9] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 10/26/2016] [Accepted: 02/21/2017] [Indexed: 11/17/2022] Open
Abstract
In a typical scenario the diagrammatic many-body perturbation theory generates asymptotic series. Despite non-convergence, the asymptotic expansions are useful when truncated to a finite number of terms. This is the reason for the popularity of leading-order methods such as the GW approximation in condensed matter, molecular and atomic physics. Appropriate truncation order required for the accurate description of strongly correlated materials is, however, not known a priori. Here an efficient method based on the Padé approximation is introduced for the regularization of perturbative series allowing to perform higher-order self-consistent calculations and to make quantitative predictions on the convergence of many-body perturbation theories. The theory is extended towards excited states where the Wick theorem is not directly applicable. Focusing on the plasmon-assisted photoemission from graphene, we treat diagrammatically electrons coupled to the excited state plasmons and predict new spectral features that can be observed in the time-resolved measurements.
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Affiliation(s)
- Y Pavlyukh
- Department of Physics and Research Center OPTIMAS, University of Kaiserslautern, P.O. Box 3049, 67653, Kaiserslautern, Germany. .,Institut für Physik, Martin-Luther-Universität Halle-Wittenberg, 06120, Halle, Germany.
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16
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Pavlyukh Y, Uimonen AM, Stefanucci G, van Leeuwen R. Vertex Corrections for Positive-Definite Spectral Functions of Simple Metals. PHYSICAL REVIEW LETTERS 2016; 117:206402. [PMID: 27886474 DOI: 10.1103/physrevlett.117.206402] [Citation(s) in RCA: 8] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 07/14/2016] [Indexed: 06/06/2023]
Abstract
We present a systematic study of vertex corrections in a homogeneous electron gas at metallic densities. The vertex diagrams are built using a recently proposed positive-definite diagrammatic expansion for the spectral function. The vertex function not only provides corrections to the well known plasmon and particle-hole scatterings, but also gives rise to new physical processes such as the generation of two plasmon excitations or the decay of the one-particle state into a two-particle-one-hole state. By an efficient Monte Carlo momentum integration we are able to show that the additional scattering channels are responsible for a reduction of the bandwidth, the appearance of a secondary plasmon satellite below the Fermi level, and a substantial redistribution of spectral weights. The feasibility of the approach for first-principles band-structure calculations is also discussed.
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Affiliation(s)
- Y Pavlyukh
- Institut für Physik, Martin-Luther-Universität Halle-Wittenberg, 06120 Halle, Germany and Department of Physics and Research Center OPTIMAS, University of Kaiserslautern, P.O. Box 3049, 67653 Kaiserslautern, Germany
| | - A-M Uimonen
- Clarendon Laboratory, Department of Physics, University of Oxford, Parks Road, Oxford OX1 3PU, United Kingdom
| | - G Stefanucci
- Dipartimento di Fisica and European Theoretical Spectroscopy Facility (ETSF), Università di Roma Tor Vergata, Via della Ricerca Scientifica 1, 00133 Rome, Italy and INFN, Sezione di Roma Tor Vergata, Via della Ricerca Scientifica 1, 00133 Roma, Italy
| | - R van Leeuwen
- Department of Physics and European Theoretical Spectroscopy Facility (ETSF), Nanoscience Center, University of Jyväskylä, FI-40014 Jyväskylä, Finland
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17
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Wagner LK, Ceperley DM. Discovering correlated fermions using quantum Monte Carlo. REPORTS ON PROGRESS IN PHYSICS. PHYSICAL SOCIETY (GREAT BRITAIN) 2016; 79:094501. [PMID: 27518859 DOI: 10.1088/0034-4885/79/9/094501] [Citation(s) in RCA: 36] [Impact Index Per Article: 4.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/06/2023]
Abstract
It has become increasingly feasible to use quantum Monte Carlo (QMC) methods to study correlated fermion systems for realistic Hamiltonians. We give a summary of these techniques targeted at researchers in the field of correlated electrons, focusing on the fundamentals, capabilities, and current status of this technique. The QMC methods often offer the highest accuracy solutions available for systems in the continuum, and, since they address the many-body problem directly, the simulations can be analyzed to obtain insight into the nature of correlated quantum behavior.
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Affiliation(s)
- Lucas K Wagner
- Department of Physics, University of Illinois at Urbana-Champaign, Champaign, IL, USA
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18
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Cioslowski J. The Coulomb, exchange, and correlation components of the electron-electron repulsion in harmonium atoms. J Chem Phys 2015; 142:114105. [DOI: 10.1063/1.4914021] [Citation(s) in RCA: 5] [Impact Index Per Article: 0.6] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Affiliation(s)
- Jerzy Cioslowski
- Institute of Physics, University of Szczecin, Wielkopolska 15, 70-451 Szczecin, Poland and Max-Planck-Institut für Physik komplexer Systeme, Nöthnitzer Str. 38, D-01187 Dresden, Germany
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19
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Shepherd JJ, Henderson TM, Scuseria GE. Range-separated Brueckner coupled cluster doubles theory. PHYSICAL REVIEW LETTERS 2014; 112:133002. [PMID: 24745412 DOI: 10.1103/physrevlett.112.133002] [Citation(s) in RCA: 29] [Impact Index Per Article: 2.9] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 10/23/2013] [Indexed: 06/03/2023]
Abstract
We introduce a range-separation approximation to coupled cluster doubles (CCD) theory that successfully overcomes limitations of regular CCD when applied to the uniform electron gas. We combine the short-range ladder channel with the long-range ring channel in the presence of a Bruckner renormalized one-body interaction and obtain ground-state energies with an accuracy of 0.001 a.u./electron across a wide range of density regimes. Our scheme is particularly useful in the low-density and strongly correlated regimes, where regular CCD has serious drawbacks. Moreover, we cure the infamous overcorrelation of approaches based on ring diagrams (i.e., the particle-hole random phase approximation). Our energies are further shown to have appropriate basis set and thermodynamic limit convergence, and overall this scheme promises energetic properties for realistic periodic and extended systems which existing methods do not possess.
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Affiliation(s)
- James J Shepherd
- Department of Chemistry and Department of Physics and Astronomy, Rice University, Houston, Texas 77005-1892, USA
| | - Thomas M Henderson
- Department of Chemistry and Department of Physics and Astronomy, Rice University, Houston, Texas 77005-1892, USA
| | - Gustavo E Scuseria
- Department of Chemistry and Department of Physics and Astronomy, Rice University, Houston, Texas 77005-1892, USA
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Bruneval F, Gatti M. Quasiparticle Self-Consistent GW Method for the Spectral Properties of Complex Materials. Top Curr Chem (Cham) 2014; 347:99-135. [DOI: 10.1007/128_2013_460] [Citation(s) in RCA: 23] [Impact Index Per Article: 2.3] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/12/2022]
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Baguet L, Delyon F, Bernu B, Holzmann M. Hartree-Fock ground state phase diagram of jellium. PHYSICAL REVIEW LETTERS 2013; 111:166402. [PMID: 24182285 DOI: 10.1103/physrevlett.111.166402] [Citation(s) in RCA: 5] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 07/11/2013] [Indexed: 06/02/2023]
Abstract
We calculate the ground state phase diagram of the homogeneous electron gas in three dimensions within the Hartree-Fock approximation and show that broken symmetry states are energetically favored at any density against the homogeneous Fermi gas state with isotropic Fermi surface. At high density, we find metallic spin-unpolarized solutions where electronic charge and spin density form an incommensurate crystal having more crystal sites than electrons. For r(s)→0, our solutions approach pure spin-density waves, whereas the commensurate Wigner crystal is favored at lower densities, r(s)≳3.4. Decreasing the density, the system undergoes several structural phase transitions with different lattice symmetries. The polarization transition occurs around r(s)≈8.5.
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Affiliation(s)
- L Baguet
- LPTMC, UMR 7600 of CNRS, Université Pierre et Marie Curie, F-75252 Paris Cedex 05, France
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Boninsegni M, Moroni S. Population size bias in diffusion Monte Carlo. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2012; 86:056712. [PMID: 23214911 DOI: 10.1103/physreve.86.056712] [Citation(s) in RCA: 22] [Impact Index Per Article: 1.8] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Received: 09/08/2012] [Indexed: 06/01/2023]
Abstract
The size of the population of random walkers required to obtain converged estimates in diffusion Monte Carlo (DMC) increases dramatically with system size. We illustrate this by comparing ground state energies of small clusters of parahydrogen (up to 48 molecules) computed by DMC and path integral ground state (PIGS) techniques. We contend that the bias associated with a finite population of walkers is the most likely cause of quantitative numerical discrepancies between PIGS and DMC energy estimates reported in the literature, for this few-body Bose system. We discuss the viability of DMC as a general-purpose ground state technique, and argue that PIGS, and even finite temperature methods, enjoy more favorable scaling, and are therefore a superior option for systems of large size.
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Affiliation(s)
- Massimo Boninsegni
- Department of Physics, University of Alberta, Edmonton, Alberta, Canada T6G 2G7.
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Shepherd JJ, Booth GH, Alavi A. Investigation of the full configuration interaction quantum Monte Carlo method using homogeneous electron gas models. J Chem Phys 2012; 136:244101. [DOI: 10.1063/1.4720076] [Citation(s) in RCA: 76] [Impact Index Per Article: 6.3] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/14/2023] Open
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