Solving fermion sign problem in quantum Monte Carlo by Majorana representation

TL;DR

This paper introduces Majorana QMC, a novel quantum Monte Carlo method that employs Majorana fermion representation to eliminate the fermion sign problem in certain interacting fermion models, enabling efficient simulations.

Contribution

The paper presents the first auxiliary field QMC method that solves the fermion sign problem in spinless fermion models using Majorana representation.

Findings

Sign problem is eliminated in specific spinless fermion models

Efficient simulations at finite and zero temperatures achieved

Potential to extend to more complex fermionic systems

Abstract

In this paper, we discover a new quantum Monte Carlo (QMC) method to solve the fermion sign problem in interacting fermion models by employing Majorana representation of complex fermions. We call it "Majorana QMC" (MQMC). Especially, MQMC is fermion sign free in simulating a class of spinless fermion models on bipartite lattices at half filling and with arbitrary range of (unfrustrated) interactions. To the best of our knowledge, MQMC is the first auxiliary field QMC method to solve fermion sign problem in spinless (more generally, odd number of species) fermion models. MQMC simulations can be performed efficiently both at finite and zero temperatures. We believe that MQMC could pave a new avenue to solve fermion sign problem in more generic fermionic models.