Path integral Monte Carlo simulation of degenerate electrons: Permutation-cycle properties

Dornheim, Tobias; Groth, Simon; Filinov, A.; Bönitz, M.

doi:10.1063/1.5093171

Cited by 68 publications

(61 citation statements)

References 82 publications

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“…While being an important mile stone, these data have been obtained on the basis of the uncontrolled fixed node approximation [116], which has recently been revealed to be surprisingly inaccurate with systematic errors in the exchange-correlation energy exceeding 10%, at high density and low temperature [54]. This unsatisfactory situation has sparked a surge of new developments in the field of fermionic QMC simulations at finite temperature [55,[117][118][119][120][121][122][123][124]. In particular, Groth, Dornheim, and co-workers have introduced a combination of two complementary QMC methods-permutation blocking PIMC (PB-PIMC) and configuration PIMC (CPIMC)-that allows for a highly accurate description of the UEG over a broad parameter range without the fixed node approximation.…”

Section: A Summary Of Ab Initio Static Resultsmentioning

confidence: 99%

Ab initio simulation of warm dense matter

et al. 2020

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Warm dense matter (WDM) -an exotic state of highly compressed matter -has attracted high interest in recent years in astrophysics and for dense laboratory systems. At the same time, this state is extremely difficult to treat theoretically. This is due to the simultaneous appearance of quantum degeneracy, Coulomb correlations and thermal effects, as well as the overlap of plasma and condensed phases. Recent breakthroughs are due to the successful application of density functional theory (DFT) methods which, however, often lack the necessary accuracy and predictive capability for WDM applications. The situation has changed with the availability of the first ab initio data for the exchange-correlation free energy of the warm dense uniform electron gas (UEG) that were obtained by quantum Monte Carlo (QMC) simulations, for recent reviews, see Dornheim et al., Phys. Plasmas 24, 056303 (2017) and Phys. Rep. 744, 1-86 (2018). In the present article we review recent further progress in QMC simulations of the warm dense UEG: namely, ab initio results for the static local field correction G(q) and for the dynamic structure factor S(q, ω). These data are of key relevance for the comparison with x-ray scattering experiments at free electron laser facilities and for the improvement of theoretical models.In the second part of this paper we discuss simulations of WDM out of equilibrium. The theoretical approaches include Born-Oppenheimer molecular dynamics, quantum kinetic theory, timedependent DFT and hydrodynamics. Here we analyze strengths and limitations of these methods and argue that progress in WDM simulations will require a suitable combination of all methods. A particular role might be played by quantum hydrodynamics, and we concentrate on problems, recent progress, and possible improvements of this method.

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Section: A Summary Of Ab Initio Static Resultsmentioning

confidence: 99%

Ab initio simulation of warm dense matter

et al. 2020

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“…6, we investigate the probability to find a particle involved in a permutation cycle of length l, P (l)l, see Ref. [88] for a topical introduction and extensive discussion. Panel (a) shows simulation results for N = 6 noninteracting fermions in a 2D harmonic confinement at β = 0.3 (red squares), β = 1 (blue crosses), and β = 5 (green circles).…”

Section: B Temperature Dependencementioning

confidence: 99%

Fermion sign problem in path integral Monte Carlo simulations: Quantum dots, ultracold atoms, and warm dense matter

2019

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The ab initio thermodynamic simulation of correlated Fermi systems is of central importance for many applications, such as warm dense matter, electrons in quantum dots, and ultracold atoms. Unfortunately, path integral Monte Carlo (PIMC) simulations of fermions are severely restricted by the notorious fermion sign problem (FSP). In this work, we present a hands-on discussion of the FSP and investigate in detail its manifestation with respect to temperature, system size, interactionstrength and -type, and the dimensionality of the system. Moreover, we analyze the probability distribution of fermionic expectation values, which can be non-Gaussian and fat-tailed when the FSP is severe. As a practical application, we consider electrons and dipolar atoms in a harmonic confinement, and the uniform electron gas in the warm dense matter regime. In addition, we provide extensive PIMC data, which can be used as a reference for the development of new methods and as a benchmark for approximations.

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“…As a direct evaluation of (R a , R b , ) is not possible, one performs a Trotter decomposition [58] , and the final result for the partition function Z is given as the sum over all closed paths of particle coordinates in the imaginary time ∈ [0, ]; see refs. [41,55] for details. We note that this formulation in the imaginary time is particularly convenient in the context of the present work as it allows for a straightforward computation of imaginary-time correlation functions, such as the density autocorrelation function…”

Section: Path Integral Monte Carlomentioning

confidence: 99%

Ab initio results for the plasmon dispersion and damping of the warm dense electron gas

Hamann

Vorberger

Dornheim

et al. 2020

Contributions to Plasma Physics

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Warm dense matter (WDM) is an exotic state on the border between condensed matter and dense plasmas. Important occurrences of WDM include dense astrophysical objects, matter in the core of our Earth, and matter produced in strong compression experiments. As of late, x‐ray Thomson scattering has become an advanced tool to diagnose WDM. The interpretation of the data requires model input for the dynamic structure factor S(q, ω) and the plasmon dispersion ω(q). Recently, the first ab initio results for S(q, ω) of the homogeneous warm dense electron gas were obtained from path integral Monte Carlo simulations (Dornheim et al., Phys. Rev. Lett., 121, 255001, 2018). Here, we analyse the effects of correlations and finite temperature on the dynamic dielectric function and the plasmon dispersion. Our results for the plasmon dispersion and damping differ significantly from the random‐phase approximation and from earlier models of the correlated electron gas. Moreover, we show when commonly used weak damping approximations break down and how the method of complex zeroes of the dielectric function can solve this problem for WDM conditions.

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Path integral Monte Carlo simulation of degenerate electrons: Permutation-cycle properties

Cited by 68 publications

References 82 publications

Ab initio simulation of warm dense matter

Ab initio simulation of warm dense matter

Fermion sign problem in path integral Monte Carlo simulations: Quantum dots, ultracold atoms, and warm dense matter

Ab initio results for the plasmon dispersion and damping of the warm dense electron gas

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