Accelerated free energy estimation in ab initio path integral Monte Carlo simulations

TL;DR

This paper introduces a method to accelerate free energy calculations in ab initio path integral Monte Carlo simulations by using an intermediate reference system, significantly reducing computational cost and enabling large system analysis.

Contribution

The authors develop a novel approach combining an intermediate reference system and a $\xi$-extrapolation technique to speed up free energy estimation and mitigate the fermion sign problem.

Findings

Interaction evaluation up to 18 times faster than traditional methods.

Successful application to systems with 1000 electrons, achieving chemical accuracy.

Effective reduction of finite-size and statistical errors in large quantum systems.

Abstract

We present a methodology for accelerating the estimation of the free energy from path integral Monte Carlo simulations by considering an intermediate artificial reference system where interactions are inexpensive to evaluate numerically. Using the spherically averaged Ewald interaction as this intermediate reference system for the uniform electron gas, the interaction contribution for the free energy was evaluated up to 18 times faster than the Ewald-only method. Furthermore, a $\xi$-extrapolation technique was tested and applied to alleviate the fermion sign problem and to resolve the sign for large particle numbers. Combining these two techniques enabled the evaluation of the free energy for a system of 1000 electrons, where both finite-size and statistical errors are below chemical accuracy. The general procedure can be applied to systems relevant for planetary and inertial confinement fusion modeling with low to moderate levels of quantum degeneracy.