Geometry Dependence of the Sign Problem

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.

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• Determinant Quantum Monte Carlo Study of Exhaustion in the Periodic Anderson Model
• Tendencies of enhanced electronic nematicity in the Hubbard model and a comparison with Raman scattering on high-temperature superconductors
• Fundamental invariants of many-body Hilbert space
• Sampling and the complexity of nature