Geometry Dependence of the Sign Problem

TL;DR

This paper provides a comprehensive dataset and analysis of how the sign problem in determinant quantum Monte Carlo depends on lattice geometry, density, interaction strength, temperature, and size, revealing key trends and correlations.

Contribution

It offers the first extensive dataset on geometry dependence of the sign problem in DQMC, including analysis of volume effects, particle-hole symmetry, and spin sign correlations.

Findings

Sign problem varies with lattice geometry and parameters.

Decoupled clusters help probe volume dependence.

Sign correlations exist between total and spin-specific signs.

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 models 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 this 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.