Flexible class of exact Hubbard-Stratonovich transformations

Abstract

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 = ∞) 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 like the Langevin or Hamiltonian Monte Carlo methods. We explore the tradeoffs between various simulation methods through numerical benchmarks.

SmoQyDQMC.jl: A flexible implementation of determinant quantum Monte Carlo for Hubbard and electron-phonon interactions

“…At this point, the only term in the Hamiltonian that is not quadratic in Fermion creation and annihilation operators is Vhub . This term can be rendered quadratic using the discrete Ising Hubbard-Stratonovich (HS) transformation [104,105] (or other variants [106][107][108])…”