Restricted configuration path integral Monte Carlo

TL;DR

This paper introduces restricted versions of configuration path integral Monte Carlo (CPIMC) to extend simulations of dense quantum plasmas into lower density regimes, overcoming the sign problem in certain parameter ranges.

Contribution

The authors develop two restricted CPIMC methods that mitigate the sign problem, enabling accurate simulations of the warm dense electron gas at lower densities than previously possible.

Findings

RCPIMC has no sign problem but less accuracy.

RCPIMC+ balances accuracy and feasibility.

Simulations reach density parameters up to r_s ~ 5.

Abstract

Quantum Monte Carlo belongs to the most accurate simulation techniques for quantum many-particle systems. However, for fermions, these simulations are hampered by the sign problem that prohibits simulations in the regime of strong degeneracy. The situation changed with the development of configuration path integral Monte Carlo (CPIMC) by Schoof \textit{et al.} [T. Schoof \textit{et al.}, Contrib. Plasma Phys. \textbf{51}, 687 (2011)] that allowed for the first \textit{ab initio} simulations for dense quantum plasmas. CPIMC also has a sign problem that occurs when the density is lowered, i.e. in a parameter range that is complementary to traditional QMC formulated in coordinate space. Thus, CPIMC simulations for the warm dense electron gas are limited to small values of the Brueckner parameter -- the ratio of the interparticle distance to the Bohr radius -- $r_s=\bar{r}/a_B \lesssim 1$. In order to reach the regime of stronger coupling (lower density) with CPIMC, here we investigate additional restrictions on the Monte Carlo procedure. In particular, we introduce two different versions of "restricted CPIMC" where certain sign changing Monte Carlo updates are being omitted. Interestingly, one of the methods (RCPIMC) has no sign problem at all, but it is less accurate than RCPIMC+ which neglects only a smaller class of the Monte Carlo steps. Here we report extensive simulations for the ferromagnetic uniform electron gas with which we investigate the properties and accuracy of RCPIMC and RCPIMC+. Further, we establish the parameter range in the density-temperature plane where these simulations are both feasible and accurate. The conclusion is that RCPIMC and RCPIMC+ work best at temperatures in the range of $\Theta \sim 0.1\dots 0.5$ allowing to reach density parameters up to $r_s \sim 3\dots 5$, thereby partially filling a gap left open by existing \textit{ab initio} QMC methods.