Reweighting scheme for the calculation of grand-canonical expectation values in quantum Monte Carlo simulations with a fermion sign problem

TL;DR

This paper introduces a reweighting scheme that enables calculation of grand-canonical expectation values in fermionic quantum Monte Carlo simulations despite the fermion sign problem, by leveraging canonical ensemble simulations.

Contribution

A simple reweighting method is proposed to access grandcanonical expectation values using canonical fermionic PIMC simulations, mitigating the fermion sign problem.

Findings

Effective in calculating grandcanonical properties of warm dense electron gas.

Reduces computational complexity associated with the fermion sign problem.

Applicable to systems relevant for astrophysics and fusion energy.

Abstract

Ab initio path integral Monte Carlo (PIMC) simulations constitute the gold standard for the estimation of a broad range of equilibrium properties of a host of interacting quantum many-body systems spanning conditions from ultracold atoms to warm dense quantum plasmas. A key practical limitation is given by the notorious fermion sign problem, which manifests as an exponential computational bottleneck with respect to system size and inverse temperature. In practice, the sign problem is particularly severe in the grandcanonical ensemble, where the bosonic and fermionic configuration spaces differ not only with respect to the symmetry of the thermal density matrix but, crucially, also with respect to the particle number distribution for a given chemical potential $\mu$ [T. Dornheim, J. Phys. A 54, 335001 (2021)]. Here, we present a simple reweighting scheme that basically allows one to retain access to grandcanonical expectation values at the cost of fermionic PIMC simulations in the canonical ensemble for the largest significant particle number in the fermionic sector. As a practical example, we consider the warm dense electron gas, which has attracted considerable recent attention due to its relevance, e.g., for the modeling of compact astrophysical objects and inertial fusion energy applications