The Factorization Method for Simulating Systems With a Complex Action

TL;DR

This paper introduces a factorization method for Monte Carlo simulations of systems with complex actions, effectively addressing the overlap problem and demonstrating its application in finite density QCD models.

Contribution

It presents a general Monte Carlo approach for complex action systems and applies it to finite density QCD, revealing non-commutativity of certain limits.

Findings

Successfully applied to random matrix theory of finite density QCD

Identified non-commutativity of limits $$ and $N$ in the model

Provides a potential solution to the overlap problem in complex systems

Abstract

We propose a method for Monte Carlo simulations of systems with a complex action. The method has the advantages of being in principle applicable to any such system and provides a solution to the overlap problem. We apply it in random matrix theory of finite density QCD where we compare with analytic results. In this model we find non--commutativity of the limits $\mu\to 0$ and $N\to\infty$ which could be of relevance in QCD at finite density.