A discrete Hubbard-Stratonovich decomposition for general, fermionic two-body interactions

TL;DR

The paper introduces a discrete decomposition method for two-body operators, enabling an alternative to the Hubbard-Stratonovich transformation in quantum Monte Carlo simulations, demonstrated on the Hubbard model and nuclear pairing Hamiltonian.

Contribution

It presents a novel discrete decomposition scheme for two-body operators, expanding the toolkit for auxiliary-field quantum Monte Carlo methods.

Findings

Equivalent to Hirsch's discrete Hubbard-Stratonovich transformation for the Hubbard model

Applicable to nuclear pairing Hamiltonian

Provides a new approach for two-body operator decomposition

Abstract

A scheme is presented to decompose the exponential of a two-body operator in a discrete sum over exponentials of one-body operators. This discrete decomposition can be used instead of the Hubbard-Stratonovich transformation in auxiliary-field quantum Monte-Carlo methods. As an illustration, the decomposition is applied to the Hubbard model, where it is equivalent to the discrete Hubbard-Stratonovich transformation introduced by Hirsch, and to the nuclear pairing Hamiltonian.