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

Dornheim, Tobias

doi:10.1103/physreve.100.023307

Cited by 123 publications

(177 citation statements)

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“…ii) the current validity domain of, e.g., the GDSMFBB parametrization to 0 ≤ r s ≤ 20 can be significantly extended by incorporating the recent ab initio PIMC results for the electron liquid regime (20 ≤ r s ≤ 100) by Dornheim et al [128]. iii) new ab intio QMC results at low temperature, θ ∼ 10 −1 , could help to more accurately resolve open thermodynamic questions like the effective mass enhancement [129], but are difficult to obtain due to the notorious fermion sign problem [130]. iv) Neural networks are known to be valuable as universal function approximators (see also Sec.…”

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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“…At θ = 0.5, the simulations are computationally expensive due to the fermion sign problem (we find an average sign of S ≈ 0.01, see Ref. [104] for an extensive discussion) and the statistical uncertainty is substantial for large q. Still, the neural net is capable to provide a prediction that is fully consistent with the benchmark data even in a regime where the training data are sparse.…”

Section: B Physical Behavior and Neural Net Representationmentioning

confidence: 91%

“…1. Here the main obstacle is given by the notorious fermion sign problem [104,105], which prevents PIMC simulations below half the Fermi temperature and limits the feasible system size to N = 14, . .…”

Section: Arxiv:190708473v1 [Physicsplasm-ph] 19 Jul 2019mentioning

confidence: 99%

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The static local field correction of the warm dense electron gas: An ab initio path integral Monte Carlo study and machine learning representation

Dornheim

Vorberger

Groth

et al. 2019

The Journal of Chemical Physics

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The study of matter at extreme densities and temperatures as they occur in astrophysical objects and state-of-the art experiments with high-intensity lasers is of high current interest for many applications. While no overarching theory for this regime exists, accurate data for the density response of correlated electrons to an external perturbation are of paramount importance. In this context, the key quantity is given by the local field correction (LFC), which provides a wave-vector resolved description of exchange-correlation effects. In this work, we present extensive new path integral Monte Carlo (PIMC) results for the static LFC of the uniform electron gas, which are subsequently used to train a fully connected deep neural network. This allows us to present a continuous representation of the LFC with respect to wave-vector, density, and temperature covering the entire warm dense matter regime. Both the PIMC data and neural-net results are available online. Moreover, we expect the presented combination of ab initio calculations with machinelearning methods to be a promising strategy for many applications.

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“…Moreover, it is straightforward to see that the sign exponentially decreases both with β and the system size N , which is the origin of the notorious fermion sign problem [104,105], see Ref. [106] for a topical review article. More specifically, the relative statistical uncertainty from a fermionic Monte Carlo calculation is inversely proportional to S [107],…”

Section: Path Integral Monte Carlomentioning

confidence: 99%

Ab initio path integral monte carlo simulation of the uniform electron gas in the high energy density regime

Dornheim

Moldabekov

Vorberger

et al. 2020

Plasma Phys. Control. Fusion

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The response of the uniform electron gas (UEG) to an external perturbation is of paramount importance for many applications. Recently, highly accurate results for the static density response function and the corresponding local field correction have been provided both for warm dense matter [J. Chem. Phys. 151, 194104 (2019)] and strongly coupled electron liquid [Phys. Rev. B 101, 045129 (2020)] conditions based on exact ab initio path integral Monte Carlo (PIMC) simulations. In the present work, we further complete our current description of the UEG by exploring the high energy density regime, which is relevant for, e.g., astrophysical applications and inertial confinement fusion experiments. To this end, we present extensive new PIMC results for the static density response in the range of 0.05 ≤ r s ≤ 0.5 and 0.85 ≤ θ ≤ 8. These data are subsequently used to benchmark the accuracy of the widely used random phase approximation and the dielectric theory by Singwi, Tosi, Land, and Sjölander (STLS). Moreover, we compare our results to configuration PIMC data where they are available and find perfect agreement with a relative accuracy of 0.001 − 0.01%. All PIMC data are available online.The Uniform Electron Gas in the High Density Regime 2 IntroductionThe uniform electron gas (UEG), also known as jellium or quantum one-component plasma, is defined as a system of Coulomb interacting electrons in a neutralizing homogeneous background and constitutes one of the most import model systems in physics and chemistry [1,2,3]. Having been introduced as a simple model description for conduction electrons in metals [4], the UEG exhibits a variety of interesting effects, such as Wigner crystallization [5,6,7] and a possible incipient excitonic mode which has been predicted to appear at low density [8,9,10,11].Moreover, the availability of highly accurate quantum Monte Carlo (QMC) data [12,13,14,15,16] at metallic densities and zero-temperature has sparked remarkable developments in many fields, most notably the hitherto unequaled success of density functional theory (DFT) regarding the description of real materials [17,18].Recently, the interest in matter under extreme conditions [19] has led to the need for analogous quantum Monte Carlo data at finite temperature. Of particular importance is the so-called warm dense matter (WDM) regime, which is defined by two characteristic parameters that are both of the order of one: i) the density parameter r s = r/a B (with r and a B being the average inter-particle distance and first Bohr radius) and ii) the reduced temperature θ = k B T /E F (with k B and E F being the Boltzmann constant and Fermi energy [1]), cf. Fig. 1 below. These conditions occur in astrophysical objects like giant planet interiors [20,21,22] and are expected to manifest on the pathway towards inertial confinement fusion [23]. Furthermore, WDM is nowadays routinely realized in large research facilities around the globe like the Linac Coherent Light Source (LCLS) [24], the National Ignition Facility (NIF) [25], and th...

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

Cited by 123 publications

References 112 publications

Ab initio simulation of warm dense matter

Ab initio simulation of warm dense matter

The static local field correction of the warm dense electron gas: An ab initio path integral Monte Carlo study and machine learning representation

Ab initio path integral monte carlo simulation of the uniform electron gas in the high energy density regime

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