Ab initio path integral Monte Carlo approach to the momentum distribution of the uniform electron gas at finite temperature without fixed nodes

TL;DR

This paper introduces comprehensive ab initio path integral Monte Carlo simulations of the momentum distribution in the uniform electron gas at finite temperatures, revealing exchange-correlation effects and serving as benchmarks without fixed node constraints.

Contribution

The study provides the first extensive fixed-node free ab initio PIMC results for the momentum distribution of the warm dense electron gas across various densities and temperatures.

Findings

Exchange-correlation effects increase low-momentum states near Fermi temperature.

Quantum statistics significantly influence momentum distribution and off-diagonal density matrix.

Results serve as benchmark data for future theoretical and computational methods.

Abstract

We present extensive new \textit{ab intio} path integral Monte Carlo results for the momentum distribution function $n(\mathbf{k})$ of the uniform electron gas (UEG) in the warm dense matter (WDM) regime over a broad range of densities and temperatures. This allows us to study the nontrivial exchange--correlation induced increase of low-momentum states around the Fermi temperature, and to investigate its connection to the related lowering of the kinetic energy compared to the ideal Fermi gas. In addition, we investigate the impact of quantum statistics on both $n(\mathbf{k})$ and the off-diagonal density matrix in coordinate space, and find that it cannot be neglected even in the strongly coupled electron liquid regime. Our results were derived without any nodal constraints, and thus constitute a benchmark for other methods and approximations.