Majorana-time-reversal symmetries: a fundamental principle for sign-problem-free quantum Monte Carlo simulations

TL;DR

This paper introduces Majorana-time-reversal symmetries as a unifying principle to identify and classify models in quantum Monte Carlo simulations that are free of the fermion sign problem, enabling more efficient studies of complex quantum systems.

Contribution

It rigorously classifies Majorana-bilinear operators based on MTR symmetries, identifying two fundamental sign-problem-free classes: the Majorana class and the Kramers class.

Findings

Identified two fundamental sign-problem-free classes: Majorana and Kramers.

Provided examples of models in the Majorana class, including topological superconductors.

Established a unifying symmetry principle for sign-problem-free QMC simulations.

Abstract

A fundamental open issue in physics is whether and how the fermion sign problem in quantum Monte Carlo (QMC) simulations can be solved generically. Here, we show that Majorana-time-reversal (MTR) symmetries can provide a unifying principle to solve the fermion sign problem in interacting fermionic models. By systematically classifying Majorana-bilinear operators according to the anti-commuting MTR symmetries they respect, we rigorously proved that there are two and only two fundamental symmetry classes which are sign-problem-free and which we call the "Majorana class" and "Kramers class", respectively. Novel sign-problem-free models in the Majorana class include interacting topological superconductors and interacting models of charge-4e superconductors. We believe that our MTR unifying principle could shed new light on sign-problem-free QMC simulation on strongly correlated systems and interacting topological matters.