A sufficient condition for the absence of the sign problem in the fermionic quantum Monte-Carlo algorithm

TL;DR

This paper establishes a general condition based on time reversal symmetry that ensures the absence of the sign problem in fermionic quantum Monte-Carlo simulations, broadening the class of models that can be efficiently studied.

Contribution

It introduces a new criterion related to time reversal symmetry for sign problem elimination, applicable to a wider range of fermionic models in QMC simulations.

Findings

The algorithm applies to various strongly correlated models.

Many novel phases can be simulated without the sign problem.

The method is effective across different doping levels and lattice geometries.

Abstract

Quantum Monte-Carlo (QMC) simulations involving fermions have the notorious sign problem. Some well-known exceptions of the auxiliary field QMC algorithm rely on the factorizibility of the fermion determinant. Recently, a fermionic QMC algorithm [1] has been found in which the fermion determinant may not necessarily factorizable, but can instead be expressed as a product of complex conjugate pairs of eigenvalues, thus eliminating the sign problem for a much wider class of models. In this paper, we present general conditions for the applicability of this algorithm and point out that it is deeply related to the time reversal symmetry of the fermion matrix. We apply this method to various models of strongly correlated systems at all doping levels and lattice geometries, and show that many novel phases can be simulated without the sign problem.