Towards an Effective Importance Sampling in Monte Carlo Simulations of a System with a Complex Action

TL;DR

This paper proposes an improved importance sampling technique for Monte Carlo simulations of systems with complex actions, effectively addressing the sign problem by using constrained observables correlated with the phase.

Contribution

It introduces a factorization method with optimized constraints on observables to mitigate the sign problem in Monte Carlo simulations of complex systems.

Findings

Method successfully applied to a matrix model with a strong sign problem

Results consistent with analytic Gaussian Expansion Method calculations

Enhanced sampling efficiency in the presence of a complex action

Abstract

The sign problem is a notorious problem, which occurs in Monte Carlo simulations of a system with a partition function whose integrand is not positive. One way to simulate such a system is to use the factorization method where one enforces sampling in the part of the configuration space which gives important contribution to the partition function. This is accomplished by using constraints on some observables chosen appropriately and minimizing the free energy associated with their joint distribution functions. These observables are maximally correlated with the complex phase. Observables not in this set essentially decouple from the phase and can be calculated without the sign problem in the corresponding "microcanonical" ensemble. These ideas are applied on a simple matrix model with very strong sign problem and the results are found to be consistent with analytic calculations using the Gaussian Expansion Method.