1
|
Garioud R, Šimkovic F, Rossi R, Spada G, Schäfer T, Werner F, Ferrero M. Symmetry-Broken Perturbation Theory to Large Orders in Antiferromagnetic Phases. PHYSICAL REVIEW LETTERS 2024; 132:246505. [PMID: 38949372 DOI: 10.1103/physrevlett.132.246505] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 06/23/2023] [Revised: 03/12/2024] [Accepted: 05/07/2024] [Indexed: 07/02/2024]
Abstract
We introduce a spin-symmetry-broken extension of the connected determinant algorithm [Riccardo Rossi, Determinant diagrammatic Monte Carlo algorithm in the thermodynamic limit, Phys. Rev. Lett. 119, 045701 (2017).PRLTAO0031-900710.1103/PhysRevLett.119.045701]. The resulting systematic perturbative expansions around an antiferromagnetic state allow for numerically exact calculations directly inside a magnetically ordered phase. We show new precise results for the magnetic phase diagram and thermodynamics of the three-dimensional cubic Hubbard model at half-filling. With detailed computations of the order parameter in the low to intermediate-coupling regime, we establish the Néel phase boundary. The critical behavior in its vicinity is shown to be compatible with the O(3) Heisenberg universality class. By determining the evolution of the entropy with decreasing temperature through the phase transition we identify the different physical regimes at U/t=4. We provide quantitative results for several thermodynamic quantities deep inside the antiferromagnetic dome up to large interaction strengths and investigate the crossover between the Slater and Heisenberg regimes.
Collapse
Affiliation(s)
| | | | | | - Gabriele Spada
- Laboratoire Kastler Brossel, École Normale Supérieure - Université PSL, CNRS, Sorbonne Université, Collège de France, 75005 Paris, France
- Pitaevskii BEC Center, CNR-INO and Dipartimento di Fisica, Universitá di Trento, I-38123, Trento, Italy
| | | | | | | |
Collapse
|
2
|
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.
Collapse
Affiliation(s)
| | | | - David M Ceperley
- University of Illinois Urbana-Champaign, Urbana, Illinois 61801, USA
| | | |
Collapse
|
3
|
Dornheim T, Tolias P, Groth S, Moldabekov ZA, Vorberger J, Hirshberg B. Fermionic physics from ab initio path integral Monte Carlo simulations of fictitious identical particles. J Chem Phys 2023; 159:164113. [PMID: 37888764 DOI: 10.1063/5.0171930] [Citation(s) in RCA: 1] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 08/11/2023] [Accepted: 10/06/2023] [Indexed: 10/28/2023] Open
Abstract
The ab initio path integral Monte Carlo (PIMC) method is one of the most successful methods in statistical physics, quantum chemistry and related fields, but its application to quantum degenerate Fermi systems is severely hampered by an exponential computational bottleneck: the notorious fermion sign problem. Very recently, Xiong and Xiong [J. Chem. Phys. 157, 094112 (2022)] have suggested to partially circumvent the sign problem by carrying out simulations of fictitious systems guided by an interpolating continuous variable ξ ∈ [-1, 1], with the physical Fermi- and Bose-statistics corresponding to ξ = -1 and ξ = 1. It has been proposed that information about the fermionic limit might be obtained by calculations within the bosonic sector ξ > 0 combined with an extrapolation throughout the fermionic sector ξ < 0, essentially bypassing the sign problem. Here, we show how the inclusion of the artificial parameter ξ can be interpreted as an effective penalty on the formation of permutation cycles in the PIMC simulation. We demonstrate that the proposed extrapolation method breaks down for moderate to high quantum degeneracy. Instead, the method constitutes a valuable tool for the description of large Fermi-systems of weak quantum degeneracy. This is demonstrated for electrons in a 2D harmonic trap and for the uniform electron gas (UEG), where we find excellent agreement (∼0.5%) with exact configuration PIMC results in the high-density regime while attaining a speed-up exceeding 11 orders of magnitude. Finally, we extend the idea beyond the energy and analyze the radial density distribution (2D trap), as well as the static structure factor and imaginary-time density-density correlation function (UEG).
Collapse
Affiliation(s)
- Tobias Dornheim
- Center for Advanced Systems Understanding (CASUS), D-02826 Görlitz, Germany
- Helmholtz-Zentrum Dresden-Rossendorf (HZDR), D-01328 Dresden, Germany
| | - Panagiotis Tolias
- Space and Plasma Physics, Royal Institute of Technology (KTH), Stockholm SE-100 44, Sweden
| | - Simon Groth
- Christian-Albrechts-Universität zu Kiel, D-24098 Kiel, Germany
| | - Zhandos A Moldabekov
- 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
| | - Barak Hirshberg
- School of Chemistry, Tel Aviv University, Tel Aviv 6997801, Israel
- The Center for Computational Molecular and Materials Science, Tel Aviv University, Tel Aviv 6997801, Israel
| |
Collapse
|
4
|
Dornheim T, Böhme MP, Moldabekov ZA, Vorberger J. Electronic density response of warm dense hydrogen on the nanoscale. Phys Rev E 2023; 108:035204. [PMID: 37849144 DOI: 10.1103/physreve.108.035204] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 06/09/2023] [Accepted: 08/11/2023] [Indexed: 10/19/2023]
Abstract
The properties of hydrogen at warm dense matter (WDM) conditions are of high importance for the understanding of astrophysical objects and technological applications such as inertial confinement fusion. In this work, we present extensive ab initio path integral Monte Carlo results for the electronic properties in the Coulomb potential of a fixed ionic configuration. This gives us unique insights into the complex interplay between the electronic localization around the protons with their density response to an external harmonic perturbation. We find qualitative agreement between our simulation data and a heuristic model based on the assumption of a local uniform electron gas model, but important trends are not captured by this simplification. In addition to being interesting in their own right, we are convinced that our results will be of high value for future projects, such as the rigorous benchmarking of approximate theories for the simulation of WDM, most notably density functional theory.
Collapse
Affiliation(s)
- Tobias Dornheim
- Center for Advanced Systems Understanding (CASUS), D-02826 Görlitz, Germany
- Helmholtz-Zentrum Dresden-Rossendorf (HZDR), D-01328 Dresden, Germany
| | - Maximilian P Böhme
- Center for Advanced Systems Understanding (CASUS), D-02826 Görlitz, Germany
- Helmholtz-Zentrum Dresden-Rossendorf (HZDR), D-01328 Dresden, Germany
- Technische Universität Dresden, D-01062 Dresden, Germany
| | - Zhandos A Moldabekov
- 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
| |
Collapse
|
5
|
Moldabekov ZA, Lokamani M, Vorberger J, Cangi A, Dornheim T. Assessing the accuracy of hybrid exchange-correlation functionals for the density response of warm dense electrons. J Chem Phys 2023; 158:094105. [PMID: 36889956 DOI: 10.1063/5.0135729] [Citation(s) in RCA: 2] [Impact Index Per Article: 2.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 02/05/2023] Open
Abstract
We assess the accuracy of common hybrid exchange-correlation (XC) functionals (PBE0, PBE0-1/3, HSE06, HSE03, and B3LYP) within the Kohn-Sham density functional theory for the harmonically perturbed electron gas at parameters relevant for the challenging conditions of the warm dense matter. Generated by laser-induced compression and heating in the laboratory, the warm dense matter is a state of matter that also occurs in white dwarfs and planetary interiors. We consider both weak and strong degrees of density inhomogeneity induced by the external field at various wavenumbers. We perform an error analysis by comparing with the exact quantum Monte Carlo results. In the case of a weak perturbation, we report the static linear density response function and the static XC kernel at a metallic density for both the degenerate ground-state limit and for partial degeneracy at the electronic Fermi temperature. Overall, we observe an improvement in the density response when the PBE0, PBE0-1/3, HSE06, and HSE03 functionals are used, compared with the previously reported results for the PBE, PBEsol, local-density approximation, and AM05 functionals; B3LYP, on the other hand, does not perform well for the considered system. Additionally, the PBE0, PBE0-1/3, HSE06, and HSE03 functionals are more accurate for the density response properties than SCAN in the regime of partial degeneracy.
Collapse
Affiliation(s)
- Zhandos A Moldabekov
- Center for Advanced Systems Understanding (CASUS), Helmholtz-Zentrum Dresden-Rossendorf (HZDR), D-02826 Görlitz, Germany
| | - Mani Lokamani
- Information Services and Computing, Helmholtz-Zentrum Dresden-Rossendorf (HZDR), D-01328 Dresden, Germany
| | - Jan Vorberger
- Insitute of Radiation Physics, Helmholtz-Zentrum Dresden-Rossendorf (HZDR), D-01328 Dresden, Germany
| | - Attila Cangi
- Center for Advanced Systems Understanding (CASUS), Helmholtz-Zentrum Dresden-Rossendorf (HZDR), D-02826 Görlitz, Germany
| | - Tobias Dornheim
- Center for Advanced Systems Understanding (CASUS), Helmholtz-Zentrum Dresden-Rossendorf (HZDR), D-02826 Görlitz, Germany
| |
Collapse
|
6
|
LeBlanc JPF, Chen K, Haule K, Prokof'ev NV, Tupitsyn IS. Dynamic Response of an Electron Gas: Towards the Exact Exchange-Correlation Kernel. PHYSICAL REVIEW LETTERS 2022; 129:246401. [PMID: 36563239 DOI: 10.1103/physrevlett.129.246401] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 04/27/2022] [Revised: 09/19/2022] [Accepted: 11/07/2022] [Indexed: 06/17/2023]
Abstract
Precise calculations of dynamics in the homogeneous electron gas (jellium model) are of fundamental importance for design and characterization of new materials. We introduce a diagrammatic Monte Carlo technique based on algorithmic Matsubara integration that allows us to compute frequency and momentum resolved finite temperature response directly in the real frequency domain using a series of connected Feynman diagrams. The data for charge response at moderate electron density are used to extract the frequency dependence of the exchange-correlation kernel at finite momenta and temperature. These results are as important for development of the time-dependent density functional theory for materials dynamics as ground state energies are for the density functional theory.
Collapse
Affiliation(s)
- James P F LeBlanc
- Department of Physics and Physical Oceanography, Memorial University of Newfoundland, St. John's, Newfoundland & Labrador, Canada A1B 3X7
| | - Kun Chen
- Center for Computational Quantum Physics, Flatiron Institute, 162 Fifth Avenue, New York, New York 1001, USA
| | - Kristjan Haule
- Department of Physics and Astronomy, Rutgers University, Piscataway, New Jersey 08854, USA
| | - Nikolay V Prokof'ev
- Department of Physics, University of Massachusetts, Amherst, Massachusetts 01003, USA
| | - Igor S Tupitsyn
- Department of Physics, University of Massachusetts, Amherst, Massachusetts 01003, USA
| |
Collapse
|
7
|
Lenihan C, Kim AJ, Šimkovic F, Kozik E. Evaluating Second-Order Phase Transitions with Diagrammatic Monte Carlo: Néel Transition in the Doped Three-Dimensional Hubbard Model. PHYSICAL REVIEW LETTERS 2022; 129:107202. [PMID: 36112452 DOI: 10.1103/physrevlett.129.107202] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 12/31/2021] [Accepted: 07/25/2022] [Indexed: 06/15/2023]
Abstract
Diagrammatic Monte Carlo-the technique for the numerically exact summation of all Feynman diagrams to high orders-offers a unique unbiased probe of continuous phase transitions. Being formulated directly in the thermodynamic limit, the diagrammatic series is bound to diverge and is not resummable at the transition due to the nonanalyticity of physical observables. This enables the detection of the transition with controlled error bars from an analysis of the series coefficients alone, avoiding the challenge of evaluating physical observables near the transition. We demonstrate this technique by the example of the Néel transition in the 3D Hubbard model. At half filling and higher temperatures, the method matches the accuracy of state-of-the-art finite-size techniques, but surpasses it at low temperatures and allows us to map the phase diagram in the doped regime, where finite-size techniques struggle from the fermion sign problem. At low temperatures and sufficient doping, the transition to an incommensurate spin density wave state is observed.
Collapse
Affiliation(s)
- Connor Lenihan
- Department of Physics, King's College London, Strand, London WC2R 2LS, United Kingdom
| | - Aaram J Kim
- Department of Physics, King's College London, Strand, London WC2R 2LS, United Kingdom
- Department of Physics, University of Fribourg, Chemin du Musée 3, 1700 Fribourg, Switzerland
| | - Fedor Šimkovic
- Department of Physics, King's College London, Strand, London WC2R 2LS, United Kingdom
- CPHT, CNRS, École Polytechnique, Institut Polytechnique de Paris, Route de Saclay, 91128 Palaiseau, France
- Collège de France, 11 place Marcelin Berthelot, 75005 Paris, France
| | - Evgeny Kozik
- Department of Physics, King's College London, Strand, London WC2R 2LS, United Kingdom
| |
Collapse
|
8
|
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}
\usepackage{amsmath}
\usepackage{wasysym}
\usepackage{amsfonts}
\usepackage{amssymb}
\usepackage{amsbsy}
\usepackage{mathrsfs}
\usepackage{upgreek}
\setlength{\oddsidemargin}{-69pt}
\begin{document}$$m^*/m$$\end{document}m∗/m, and the Landau parameters \documentclass[12pt]{minimal}
\usepackage{amsmath}
\usepackage{wasysym}
\usepackage{amsfonts}
\usepackage{amssymb}
\usepackage{amsbsy}
\usepackage{mathrsfs}
\usepackage{upgreek}
\setlength{\oddsidemargin}{-69pt}
\begin{document}$$F_0^s$$\end{document}F0s and \documentclass[12pt]{minimal}
\usepackage{amsmath}
\usepackage{wasysym}
\usepackage{amsfonts}
\usepackage{amssymb}
\usepackage{amsbsy}
\usepackage{mathrsfs}
\usepackage{upgreek}
\setlength{\oddsidemargin}{-69pt}
\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.
Collapse
|
9
|
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.
Collapse
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
| |
Collapse
|
10
|
Tupitsyn IS, Tsvelik AM, Konik RM, Prokof'ev NV. Real-Frequency Response Functions at Finite Temperature. PHYSICAL REVIEW LETTERS 2021; 127:026403. [PMID: 34296932 DOI: 10.1103/physrevlett.127.026403] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 03/02/2021] [Accepted: 06/17/2021] [Indexed: 06/13/2023]
Abstract
Building on previous developments [A. Taheridehkordi, S. H. Curnoe, and J. P. F. LeBlanc, Phys. Rev. B 99, 035120 (2019); PRBMDO2469-995010.1103/PhysRevB.99.035120A. Taheridehkordi, S. H. Curnoe, and J. P. F. LeBlancPhys. Rev. B101, 125109 (2020); PRBMDO2469-995010.1103/PhysRevB.101.125109A. Taheridehkordi, S. H. Curnoe, and J. P. F. LeBlancPhys. Rev. B102, 045115 (2020)PRBMDO2469-995010.1103/PhysRevB.102.045115, B. Holm and U. von Barth, Phys. Rev. B 57, 2108 (1998)PRBMDO0163-182910.1103/PhysRevB.57.2108, J. Vičičević and M. Ferrero, Phys. Rev. B 101, 075113 (2020)PRBMDO2469-995010.1103/PhysRevB.101.075113], we show that the diagrammatic Monte Carlo technique allows us to compute finite-temperature response functions directly on the real-frequency axis within any field-theoretical formulation of the interacting fermion problem. There are no limitations on the type and nature of the system's action or whether partial summation and self-consistent treatment of certain diagram classes are used. In particular, by eliminating the need for numerical analytic continuation from a Matsubara representation, our scheme allows us to study spectral densities of arbitrary complexity with controlled accuracy in models with frequency-dependent effective interactions. For illustrative purposes we consider the problem of the plasmon linewidth in a homogeneous electron gas (jellium).
Collapse
Affiliation(s)
- I S Tupitsyn
- Department of Physics, University of Massachusetts, Amherst, Massachusetts 01003, USA
| | - A M Tsvelik
- Condensed Matter Physics and Materials Science Division, Brookhaven National Laboratory, Upton, New York 11973-5000, USA
| | - R M Konik
- Condensed Matter Physics and Materials Science Division, Brookhaven National Laboratory, Upton, New York 11973-5000, USA
| | - N V Prokof'ev
- Department of Physics, University of Massachusetts, Amherst, Massachusetts 01003, USA
| |
Collapse
|
11
|
Kim AJ, Prokof'ev NV, Svistunov BV, Kozik E. Homotopic Action: A Pathway to Convergent Diagrammatic Theories. PHYSICAL REVIEW LETTERS 2021; 126:257001. [PMID: 34241517 DOI: 10.1103/physrevlett.126.257001] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 10/11/2020] [Revised: 04/12/2021] [Accepted: 05/20/2021] [Indexed: 06/13/2023]
Abstract
The major obstacle preventing Feynman diagrammatic expansions from accurately solving many-fermion systems in strongly correlated regimes is the series slow convergence or divergence problem. Several techniques have been proposed to address this issue: series resummation by conformal mapping, changing the nature of the starting point of the expansion by shifted action tools, and applying the homotopy analysis method to the Dyson-Schwinger equation. They emerge as dissimilar mathematical procedures aimed at different aspects of the problem. The proposed homotopic action offers a universal and systematic framework for unifying the existing-and generating new-methods and ideas to formulate a physical system in terms of a convergent diagrammatic series. It eliminates the need for resummation, allows one to introduce effective interactions, enables a controlled ultraviolet regularization of continuous-space theories, and reduces the intrinsic polynomial complexity of the diagrammatic Monte Carlo method. We illustrate this approach by an application to the Hubbard model.
Collapse
Affiliation(s)
- Aaram J Kim
- Department of Physics, Kings College London, Strand, London WC2R 2LS, United Kingdom
| | - Nikolay V Prokof'ev
- Department of Physics, University of Massachusetts, Amherst, Massachusetts 01003, USA
| | - Boris V Svistunov
- Department of Physics, University of Massachusetts, Amherst, Massachusetts 01003, USA
- National Research Center Kurchatov Institute, 123182 Moscow, Russia
- Wilczek Quantum Center, School of Physics and Astronomy and T. D. Lee Institute, Shanghai Jiao Tong University, Shanghai 200240, China
| | - Evgeny Kozik
- Department of Physics, Kings College London, Strand, London WC2R 2LS, United Kingdom
| |
Collapse
|
12
|
Rossi R, Šimkovic F, Ferrero M. Renormalized perturbation theory at large expansion orders. ACTA ACUST UNITED AC 2020. [DOI: 10.1209/0295-5075/132/11001] [Citation(s) in RCA: 11] [Impact Index Per Article: 2.8] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/20/2022]
|
13
|
Maček M, Dumitrescu PT, Bertrand C, Triggs B, Parcollet O, Waintal X. Quantum Quasi-Monte Carlo Technique for Many-Body Perturbative Expansions. PHYSICAL REVIEW LETTERS 2020; 125:047702. [PMID: 32794809 DOI: 10.1103/physrevlett.125.047702] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.8] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 03/21/2020] [Revised: 05/08/2020] [Accepted: 06/04/2020] [Indexed: 06/11/2023]
Abstract
High order perturbation theory has seen an unexpected recent revival for controlled calculations of quantum many-body systems, even at strong coupling. We adapt integration methods using low-discrepancy sequences to this problem. They greatly outperform state-of-the-art diagrammatic Monte Carlo simulations. In practical applications, we show speed-ups of several orders of magnitude with scaling as fast as 1/N in sample number N; parametrically faster than 1/sqrt[N] in Monte Carlo simulations. We illustrate our technique with a solution of the Kondo ridge in quantum dots, where it allows large parameter sweeps.
Collapse
Affiliation(s)
- Marjan Maček
- Université Grenoble Alpes, CEA, IRIG-PHELIQS, 38000 Grenoble, France
| | - Philipp T Dumitrescu
- Center for Computational Quantum Physics, Flatiron Institute, 162 5th Avenue, New York, New York 10010, USA
| | - Corentin Bertrand
- Center for Computational Quantum Physics, Flatiron Institute, 162 5th Avenue, New York, New York 10010, USA
| | - Bill Triggs
- Laboratoire Jean Kuntzmann, Université Grenoble Alpes, CNRS, 38401 Grenoble, France
| | - Olivier Parcollet
- Center for Computational Quantum Physics, Flatiron Institute, 162 5th Avenue, New York, New York 10010, USA
- Université Paris-Saclay, CNRS, CEA, Institut de physique théorique, 91191 Gif-sur-Yvette, France
| | - Xavier Waintal
- Université Grenoble Alpes, CEA, IRIG-PHELIQS, 38000 Grenoble, France
| |
Collapse
|