A hybrid Monte Carlo approach to the entanglement entropy of interacting fermions

TL;DR

This paper introduces a hybrid Monte Carlo method that effectively computes entanglement entropy in interacting fermion systems without noise issues, improving upon existing techniques and applicable to various models.

Contribution

It combines free-fermion decomposition with hybrid Monte Carlo to overcome noise and sign problems in entanglement entropy calculations for interacting fermions.

Findings

No sign problem for tested cases

Accurate $S_2$ calculation for 1D Hubbard model

Consistent results with exact diagonalization

Abstract

The Monte Carlo calculation of R\'enyi entanglement entropies $S^{}_n$ of interacting fermions suffers from a well-known signal-to-noise problem, even for a large number of situations in which the infamous sign problem is absent. A few methods have been proposed to overcome this issue, such as ensemble switching and the use of auxiliary partition-function ratios. Here, we present an approach that builds on the recently proposed free-fermion decomposition method; it incorporates entanglement in the probability measure in a natural way; it takes advantage of the hybrid Monte Carlo algorithm (an essential tool in lattice quantum chromodynamics and other gauge theories with dynamical fermions); and it does not suffer from noise problems. This method displays no sign problem for the same cases as other approaches and is therefore useful for a wide variety of systems. As a proof of principle, we calculate $S_2^{}$ for the one-dimensional, half-filled Hubbard model and compare with results from exact diagonalization and the free-fermion decomposition method.