\emph{Ab initio} Quantum Monte Carlo simulation of the warm dense electron gas

TL;DR

This paper reviews recent advances in quantum Monte Carlo simulations of warm dense electron gas, highlighting breakthroughs that enable highly accurate thermodynamic results for this challenging state of matter.

Contribution

It provides an overview of recent quantum Monte Carlo methods that accurately simulate warm dense electron gas, including extrapolation techniques to the thermodynamic limit.

Findings

Exact simulations of finite electron systems are feasible without fixed node approximations.

Accurate extrapolation methods allow results to be extended to the thermodynamic limit.

Thermodynamic properties of warm dense electron gas are now known with about 0.1% accuracy.

Abstract

Warm dense matter is one of the most active frontiers in plasma physics due to its relevance for dense astrophysical objects as well as for novel laboratory experiments in which matter is being strongly compressed e.g. by high-power lasers. Its description is theoretically very challenging as it contains correlated quantum electrons at finite temperature---a system that cannot be accurately modeled by standard analytical or ground state approaches. Recently several breakthroughs have been achieved in the field of fermionic quantum Monte Carlo simulations. First, it was shown that exact simulations of a finite model system ($30 \dots 100$ electrons) is possible that avoid any simplifying approximations such as fixed nodes [Schoof {\em et al.}, Phys. Rev. Lett. {\bf 115}, 130402 (2015)]. Second, a novel way to accurately extrapolate these results to the thermodynamic limit was reported by Dornheim {\em et al.} [Phys. Rev. Lett. {\bf 117}, 156403 (2016)]. As a result, now thermodynamic results for the warm dense electron gas are available that have an unprecedented accuracy on the order of $0.1\%$. Here we present an overview on these results and discuss limitations and future directions.