Document Type

Article

Publication Date

January 2015

Abstract

The sign problem is the fundamental limitation to quantum Monte Carlo simulations of the statistical mechanics of interacting fermions. Determinant quantum Monte Carlo (DQMC) is one of the leading methods to study lattice fermions, such as the Hubbard Hamiltonian, which describe strongly correlated phenomena including magnetism, metal-insulator transitions, and possibly exotic superconductivity. Here, we provide a comprehensive dataset on the geometry dependence of the DQMC sign problem for different densities, interaction strengths, temperatures, and spatial lattice sizes. We supplement these data with several observations concerning general trends in the data, including the dependence on spatial volume and how this can be probed by examining decoupled clusters, the scaling of the sign in the vicinity of a particle-hole symmetric point, and the correlation between the total sign and the signs for the individual spin species.

Comments

This article originally appeared in Physical Review B, volume 92, issue 4, 2015, published by the American Physical Society. ©2015 American Physical Society. The article can also be found online at this link.
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