Flexible class of exact Hubbard-Stratonovich transformations

We consider a class of Hubbard-Stratonovich transformations suitable for treating Hubbard interactions in the context of quantum Monte Carlo simulations. A tunable parameter p allows us to continuously vary from a discrete Ising auxiliary field (p = infinity) to a compact auxiliary field that couples to electrons sinusoidally (p = 0). In tests on the single-band square and triangular Hubbard models, we find that the severity of the sign problem decreases systematically with increasing p. Selecting p finite, however, enables continuous sampling methods such as the Langevin or Hamiltonian Monte Carlo methods. We explore the tradeoffs between various simulation methods through numerical benchmarks.

Automated summary

In this study, a class of Hubbard-Stratonovich transformations suitable for quantum Monte Carlo simulations of Hubbard interactions is considered. A tunable parameter p allows for a continuous variation from a discrete Ising auxiliary field (p = infinity) to a compact auxiliary field that couples to electrons sinusoidally (p = 0). Testing on the single-band square and triangular Hubbard models shows that the severity of the sign problem decreases systematically with increasing p. However, selecting a finite p enables continuous sampling methods such as Langevin or Hamiltonian Monte Carlo. The tradeoffs between various simulation methods are explored through numerical benchmarks.