The factorization method for systems with a complex action -a test in Random Matrix Theory for finite density QCD-

TL;DR

This paper tests a new factorization method for systems with complex actions, successfully reproducing exact results in a Random Matrix Theory model of finite density QCD and shedding light on phase transition mechanisms.

Contribution

It introduces and validates a novel factorization approach that overcomes the overlap problem in complex action systems, demonstrated through a finite density QCD model.

Findings

Successfully reproduces exact quark number density results

Extracts thermodynamic limit in large system sizes

Provides insight into phase transition induced by imaginary action

Abstract

Monte Carlo simulations of systems with a complex action are known to be extremely difficult. A new approach to this problem based on a factorization property of distribution functions of observables has been proposed recently. The method can be applied to any system with a complex action, and it eliminates the so-called overlap problem completely. We test the new approach in a Random Matrix Theory for finite density QCD, where we are able to reproduce the exact results for the quark number density. The achieved system size is large enough to extract the thermodynamic limit. Our results provide a clear understanding of how the expected first order phase transition is induced by the imaginary part of the action.