title: Majorana-Time-Reversal Symmetries: A Fundamental Principle for Sign-Problem-Free Quantum Monte Carlo 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 anticommuting MTR symmetries they respect, we rigorously prove 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.
authors.affiliation: Institute for Advanced Study, Tsinghua University, Beijing 100084, China.
authors.forename: Zi-Xiang
authors.initials: ZX
authors.lastname: Li
authors.affiliation: Institute for Advanced Study, Tsinghua University, Beijing 100084, China.
authors.forename: Yi-Fan
authors.initials: YF
authors.lastname: Jiang
authors.affiliation: Institute for Advanced Study, Tsinghua University, Beijing 100084, China.
authors.forename: Hong
authors.initials: H
authors.lastname: Yao