Thermodynamic properties of the finite-temperature electron gas by the fermionic path integral Monte Carlo method

TL;DR

This paper introduces a new quantum path integral Monte Carlo method to accurately compute thermodynamic properties of the strongly coupled, degenerate uniform electron gas at finite temperatures, addressing the fermionic sign problem.

Contribution

The paper develops an improved ab initio Monte Carlo approach that incorporates Coulomb and exchange interactions, reducing the fermionic sign problem in simulations of the electron gas.

Findings

Good agreement with existing results at low temperatures

Accurate calculations of pair distribution functions and thermodynamic properties

Method effectively mitigates the fermionic sign problem

Abstract

The new {\em ab initio} quantum path integral Monte Carlo approach has been developed and applied for the entropy difference calculations for the strongly coupled degenerated uniform electron gas (UEG), a well--known model of simple metals. Calculations have been carried out at finite temperature in canonical ensemble over the wide density and temperature ranges. Obtained data may be crucial for density functional theory. Improvements of the developed approach include the Coulomb and exchange interaction of fermions in the basic Monte Carlo cell and its periodic images and the proper change of variables in the path integral measure. The developed approach shows good agreement with available results for fermions even at temperature four times less than the Fermi energy and practically doesn't suffer from the "fermionic sign problem", which takes place in standard path integral Monte Carlo simulations of degenerate fermionic systems. Presented results include pair distribution functions, isochors and isotherms of pressure, internal energy and entropy change in strongly coupled and degenerate UEG in a wide range of density and temperature.