A new way to deal with fermions in Monte Carlo simulations

TL;DR

This paper introduces an exact, nonlocal Monte Carlo algorithm for simulating theories with dynamical fermions, aiming to improve computational efficiency in such complex quantum field theories.

Contribution

It presents a novel finite step-size algorithm based on solving a specific equation involving the fermionic operator, enhancing simulation speed for fermionic theories.

Findings

First test conducted on SU(3) QCD with fermionic action.

Algorithm shows potential for accelerating fermionic simulations.

Provides a new approach for handling Grassmann variables in Monte Carlo methods.

Abstract

An exact, nonlocal, finite step-size algorithm for Monte Carlo simulation of theories with dynamical fermions is proposed. The algorithm is based on obtaining the new configuration U' from the old one U by solving the equation $ M(U') \eta = \omega M(U) \eta$, where $M$ is fermionic operator, $\eta$ is random Gaussian vector, and $\omega$ is random real number close to unity. This algorithm can be used for the acceleration of current simulations in theories with Grassmann variables. A first test was done for SU(3) QCD with purely fermionic term in the action.