# Sampling General N-Body Interactions with Auxiliary Fields

## TL;DR

This paper introduces a versatile auxiliary field transformation that enables non-perturbative sampling of complex N-body contact interactions in lattice quantum Monte Carlo simulations, with controllable interaction strengths.

## Contribution

The authors develop a novel auxiliary field transformation that generates all N-body contact terms and allows for their controlled, non-perturbative sampling in quantum Monte Carlo methods.

## Key findings

- Reproduces exact solutions for a two-site quantum problem
- Provides a controllable way to generate N-body interactions
- Enables non-perturbative sampling of higher-order contact interactions

## Abstract

We present a general auxiliary field transformation which generates effective interactions containing all possible N-body contact terms. The strength of the induced terms can analytically be described in terms of general coefficients associated with the transformation and thus are controllable. This transformation provides a novel way for sampling 3- and 4-body (and higher) contact interactions non-perturbatively in lattice quantum monte-carlo simulations. We show that our method reproduces the exact solution for a two-site quantum mechanical problem.