Finite-Density Monte Carlo Calculations on Sign-Optimized Manifolds

TL;DR

This paper introduces a technique that deforms the path integral domain to a complex manifold to mitigate the sign problem in Monte Carlo simulations, demonstrated on the 1+1D Thirring model, improving efficiency and parameter range.

Contribution

The paper proposes a novel manifold deformation method that optimizes the average sign, enabling more efficient Monte Carlo simulations of field theories with sign problems.

Findings

Successfully applied to 1+1D Thirring model with Wilson fermions

Achieves higher chemical potential $$ than previous methods

Reduces computational time significantly

Abstract

We present a general technique for addressing sign problems that arise in Monte Carlo simulations of field theories. This method deforms the domain of the path integral to a manifold in complex field space that maximizes the average sign (therefore reducing the sign problem) within a parameterized family of manifolds. We presents results for the $1+1$ dimensional Thirring model with Wilson fermions on lattice sizes up to $40\times 10$. This method reaches higher $\mu$ then previous techniques while substantially decreasing the computational time required.