Ab initio path integral Monte Carlo simulations of hydrogen snapshots at warm dense matter conditions

TL;DR

This paper presents an exact ab initio path integral Monte Carlo approach combined with DFT-MD snapshots to study warm dense hydrogen, providing benchmarks and insights into electronic properties without model assumptions.

Contribution

It introduces a novel combination of PIMC with fixed ion configurations from DFT-MD to accurately simulate warm dense hydrogen without nodal restrictions.

Findings

Demonstrates favorable convergence with pair approximation

Provides benchmark results for electronic properties of warm dense hydrogen

Analyzes the fermion sign problem in detail

Abstract

We combine ab initio path integral Monte Carlo (PIMC) simulations with fixed ion configurations from density functional theory molecular dynamics (DFT-MD) simulations to solve the electronic problem for hydrogen under warm dense matter conditions [M.B\"ohme et. al. Phys.Rev.Lett.(in print)]. The problem of path collapse due to the Coulomb attraction is avoided by utilizing the pair approximation, which is compared against the simpler Kelbg pair-potential. We find very favourable convergence behaviour towards the former. Since we do not impose any nodal restrictions, our PIMC simulations are afflicted with the notorious fermion sign problem, which we analyse in detail. While computationally demanding, our results constitute an exact benchmark for other methods and approximations such as DFT. Our set-up gives us the unique capability to study important properties of warm dense hydrogen such as the electronic static density response and exchange--correlation (XC) kernel without any model assumptions, which will be very valuable for a variety of applications such as the interpretation of experiments and the development of new XC functionals.