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

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.