Ethan Brown

Path-Integral Monte Carlo Simulation of the Warm Dense Homogeneous Electron Gas

We perform calculations of the 3D finite-temperature homogeneous electron gas in the warm-dense regime (r(s) ≡ (3/4πn)(1/3)a(0)(-1) = 1.0-40.0 and Θ ≡ T/T(F) = 0.0625-8.0) using restricted path-integral Monte Carlo simulations. Precise energies, pair correlation functions, and structure factors are obtained. For all densities, we find a significant discrepancy between the ground state parametrized local density approximation and our results around T(F). These results can be used as a benchmark for developing finite-temperature density functionals, as well as input for orbital-free density function theory formulations.

Exchange-correlation energy for the three-dimensional homogeneous electron gas at arbitrary temperature

0625]. In doing so, we construct a Pade approximant which collapses to Debye-H´ uckel theory¨inthe high-temperature, low-density limit.Likewise, the zero-temperature limitmatches the numerical results ofground-state quantum Monte Carlo, as well as analytical results in the high-density limit.DOI: 10.1103/PhysRevB.88.081102 PACS number(s): 71

Quantum Monte Carlo Techniques and Applications for Warm Dense Matter

The Quantum Monte Carlo (QMC) method is used to study physical problems which are analytically intractable due to many-body interactions and strong coupling strengths. This makes QMC a natural choice in the warm dense matter (WDM) regime where both the Coulomb coupling parameter \(\varGamma \equiv {e}^{2}/(r_{s}k_{B}T)\) and the electron degeneracy parameter Θ ≡ T∕T F are close to unity. As a truly first-principles simulation method, it affords superior accuracy while still maintaining reasonable scaling, emphasizing its role as a benchmark tool.Here we give an overview of QMC methods including diffusion MC, path integral MC, and coupled electron-ion MC. We then provide several examples of their use in the WDM regime, reviewing applications to the electron gas, hydrogen plasma, and first row elements. We conclude with a comparison of QMC to other existing methods, touching specifically on QMC’s range of applicability.

Overcoming the fermion sign problem in homogeneous systems

Explicit treatment of many-body Fermi statistics in path integral Monte Carlo (PIMC) results in exponentially scaling computational cost due to the near cancellation of contributions to observables from even and odd permutations. Through direct analysis of exchange statistics we find that individual exchange probabilities in homogeneous systems are, except for finite size effects, independent of the configuration of other permutations present. For two representative systems, 3-He and the homogeneous electron gas, we show that this allows the entire antisymmetrized density matrix to be generated from a simple model depending on only a few parameters obtainable directly from a standard PIMC simulation. The result is a polynomial scaling algorithm and up to a 10 order of magnitude increase in efficiency in measuring fermionic observables for the systems considered.

Quantum Monte Carlo techniques and applications for warm dense matter

The Quantum Monte Carlo (QMC) method is used to study physical problems which are analytically intractable due to many-body interactions and strong coupling strengths. This makes QMC a natural choice in the warm dense matter (WDM) regime where both the Coulomb coupling parameter Γ ≡ e/(rskBT ) and the electron degeneracy parameter Θ ≡ T/TF are close to unity. As a truly firstprinciples simulation method, it affords superior accuracy while still maintaining reasonable scaling, emphasizing its role as a benchmark tool. Here we give an overview of QMC methods including diffusion MC, path integral MC, and coupled electron-ion MC. We then provide several examples of their use in the WDM regime, reviewing applications to the electron gas, hydrogen plasma, and first row elements. We conclude with a comparison of QMC to other existing methods, touching specifically on QMC’s range of applicability. Ethan Brown Lawrence Livermore National Laboratory, 7000 East Ave., Livermore CA, 94550 and Department of Physics, University of Illinois Urbana-Champaign, 1110 W. Green St. , Urbana, IL 61801-3080, USA e-mail: brown122@illinois.edu Miguel A. Morales Lawrence Livermore National Laboratory, 7000 East Ave., Livermore CA, 94550 e-mail: moralessilva2@llnll.gov Carlo Pierleoni Dipartimento di Scienze Fisiche e Chimiche, Universita dell’Aquila and CNISM, UdR dell’Aquila, a V. Vetoio 10, Loc. Coppito, I-67100 L’Aquila, Italy e-mail: carlo.pierleoni@aquila.infn.it David Ceperley Department of Physics, University of Illinois Urbana-Champaign, 1110 W. Green St. , Urbana, IL 61801-3080, USA e-mail: ceperley@illinois.edu