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

Recently, a method for computing the Helmholtz free energy in path integral Monte Carlo was introduced by including a Monte Carlo update which alters the coupling strength [1]. However, as the system sizes increases, additional intermediate steps in the coupling strength are needed to ergodically explore the phase space. We present a methodology for accelerating these free energy estimations 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 ξ-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.

[1] T. Dornheim, et al., Direct free energy calculation from ab initio path integral Monte Carlo simulations of warm dense matter. Phys. Rev. B, 111, L041114 (2025)