title: Split Orthogonal Group: A Guiding Principle for Sign-Problem-Free Fermionic Simulations.
abstract: We present a guiding principle for designing fermionic Hamiltonians and quantum Monte Carlo (QMC) methods that are free from the infamous sign problem by exploiting the Lie groups and Lie algebras that appear naturally in the Monte Carlo weight of fermionic QMC simulations. Specifically, rigorous mathematical constraints on the determinants involving matrices that lie in the split orthogonal group provide a guideline for sign-free simulations of fermionic models on bipartite lattices. This guiding principle not only unifies the recent solutions of the sign problem based on the continuous-time quantum Monte Carlo methods and the Majorana representation, but also suggests new efficient algorithms to simulate physical systems that were previously prohibitive because of the sign problem.
authors.affiliation: Theoretische Physik, ETH Zurich, 8093 Zurich, Switzerland.
authors.forename: Lei
authors.initials: L
authors.lastname: Wang
authors.affiliation: Theoretische Physik, ETH Zurich, 8093 Zurich, Switzerland.
authors.forename: Ye-Hua
authors.initials: YH
authors.lastname: Liu
authors.affiliation: Theoretische Physik, ETH Zurich, 8093 Zurich, Switzerland.
authors.forename: Mauro
authors.initials: M
authors.lastname: Iazzi
authors.affiliation: Theoretische Physik, ETH Zurich, 8093 Zurich, Switzerland.
authors.forename: Matthias
authors.initials: M
authors.lastname: Troyer
authors.affiliation: Alfréd Rényi Institute of Mathematics, Reáltanoda utca 13-15., Budapest H-1053, Hungary.
authors.forename: Gergely
authors.initials: G
authors.lastname: Harcos