A flexible class of exact Hubbard-Stratonovich transformations

TL;DR

This paper introduces a flexible family of Hubbard-Stratonovich transformations with a tunable parameter, reducing the sign problem in quantum Monte Carlo simulations and enabling continuous sampling methods.

Contribution

It presents a new class of transformations that interpolate between discrete and sinusoidal auxiliary fields, improving simulation efficiency and flexibility.

Findings

Sign problem severity decreases with increasing parameter p

Finite p allows use of continuous sampling methods

Numerical benchmarks compare different simulation tradeoffs

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 ($p=\infty$) to a compact auxiliary field that couples to electrons sinusoidally ($p=0$). In tests on the single-band Hubbard model, 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.