Semigroup approach to the sign problem in quantum Monte Carlo simulations

Abstract

We propose a framework based on the concept of the semigroup to understand the fermion sign problem. By using properties of contraction semigroups, we obtain sufficient conditions for quantum lattice fermion models to be sign-problem-free. Many previous results can be considered as special cases of our new results. As a direct application of our new results, we construct a class of sign-problem-free fermion lattice models, which cannot be understood by previous frameworks. This framework also provides an interesting aspect in understanding related quantum many-body systems. We establish a series of inequalities for all the sign-problem-free fermion lattice models that satisfy our sufficient conditions.

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Cited by in corpus (3)

• Complex Langevin and other approaches to the sign problem in quantum many-body physics
• Electronic and phononic properties of a two dimensional electron gas coupled to dipolar phonons via small-momentum-transfer scattering
• Addressing the Infinite Variance Problem in Fermionic Monte Carlo Simulations: Retrospective Error Remediation and the Exact Bridge Link Method