A Generic Solution of Fermion Sign Problem

TL;DR

This paper presents a comprehensive solution to the fermion sign problem in quantum Monte Carlo calculations by identifying a class of paths with positive weights, enabling exact computation of physical quantities.

Contribution

The paper introduces a novel Monte Carlo method that completely solves the fermion sign problem using a new path integral approach and mathematical proof.

Findings

Successfully applied to the 2D Hubbard model

Demonstrates exact calculation of physical quantities

Eliminates the fermion sign problem in simulations

Abstract

The fermion sign problem, the biggest obstacle in quantum Monte Carlo calculations, is completely solved in this paper. Here, we find a strategy, in which the contribution from those negative-weighted paths is thoroughly cancelled or replaced by some positive-weighted paths. The crucial point lies on the Feynman path integral formula proposed in our group, which allows us to deeply analyze the Boltzmann weight of each path. Through mathematical proof, we demonstrate that physical quantities can be exactly calculated within a specific kind of paths, which have positive the Boltzmann weight. With this finding, a new Monte Carlo method is proposed, in which the fermion sign problem is absent. As an example, the current method is applied to the two-dimensional Hubbard model, and the results do manifest the correctness.