Path Integral Monte Carlo Calculation of the Momentum Distribution of the Homogeneous Electron Gas at Finite Temperature

TL;DR

This paper employs path integral Monte Carlo simulations to compute the momentum distribution of the homogeneous electron gas at finite temperature, addressing the fermionic sign problem and comparing results with theoretical predictions.

Contribution

It extends restricted path integral Monte Carlo methods to handle open paths in fermionic systems with a sign problem, enabling accurate momentum distribution calculations.

Findings

Significant deviations from free fermion results at strong correlation

Agreement with variational method predictions

Demonstration of extended PIMC method for fermionic open paths

Abstract

Path integral Monte Carlo (PIMC) simulations are used to calculate the momentum distribution of the homogeneous electron gas at finite temperature. This is done by calculating the off-diagonal elements of the real-space density matrix, represented in PIMC by open paths. It is demonstrated how the restricted path integral Monte Carlo methods can be extended in order to deal with open paths in fermionic systems where a sign problem is present. The computed momentum distribution shows significant deviations for strong correlation from free fermion results but agrees with predictions from variational methods.