Sign problem and Monte Carlo calculations beyond Lefschetz thimbles

TL;DR

This paper introduces a novel approach to Monte Carlo simulations for theories with severe sign problems by exploring complex manifolds that interpolate between tangent spaces and Lefschetz thimbles, improving solvability.

Contribution

It proposes a family of complex manifolds for Monte Carlo integration that interpolate between tangent spaces and Lefschetz thimbles, addressing sign problems more effectively.

Findings

Successfully applied to a 0+1 dimensional fermion model

Solved cases where Lefschetz thimbles approach was ineffective

Demonstrated reduced sign problem severity on the new manifolds

Abstract

We point out that Monte Carlo simulations of theories with severe sign problems can be profitably performed over manifolds in complex space different from the one with fixed imaginary part of the action. We describe a family of such manifolds that interpolate between the tangent space at one critical point, where the sign problem is milder compared to the real plane but in some cases still severe, and the union of relevant thimbles, where the sign problem is mild but a multimodal distribution function complicates the Monte Carlo sampling. We exemplify this approach using a simple 0 + 1 dimensional fermion model previously used on sign problem studies and show that it can solve the model for some parameter values where a solution using Lefshetz thimbles was elusive.