title: Majorana Positivity and the Fermion Sign Problem of Quantum Monte Carlo Simulations.
abstract: The sign problem is a major obstacle in quantum Monte Carlo simulations for many-body fermion systems. We examine this problem with a new perspective based on the Majorana reflection positivity and Majorana Kramers positivity. Two sufficient conditions are proven for the absence of the fermion sign problem. Our proof provides a unified description for all the interacting lattice fermion models previously known to be free of the sign problem based on the auxiliary field quantum Monte Carlo method. It also allows us to identify a number of new sign-problem-free interacting fermion models including, but not limited to, lattice fermion models with repulsive interactions but without particle-hole symmetry, and interacting topological insulators with spin-flip terms.
authors.affiliation: Institute of Physics, Chinese Academy of Sciences, P.O. Box 603, Beijing 100190, China.
authors.forename: Z C
authors.initials: ZC
authors.lastname: Wei
authors.affiliation: Department of Physics, University of California, San Diego, California 92093, USA.
authors.forename: Congjun
authors.initials: C
authors.lastname: Wu
authors.affiliation: Princeton Center for Theoretical Science, Princeton University, Princeton, New Jersey 08544, USA.
authors.forename: Yi
authors.initials: Y
authors.lastname: Li
authors.affiliation: Department of Physics, The College of William and Mary, Williamsburg, Virginia 23187, USA.
authors.forename: Shiwei
authors.initials: S
authors.lastname: Zhang
authors.affiliation: Institute of Physics, Chinese Academy of Sciences, P.O. Box 603, Beijing 100190, China.|Collaborative Innovation Center of Quantum Matter, Beijing 100190, China.
authors.forename: T
authors.initials: T
authors.lastname: Xiang