Beyond Thimbles: Sign-Optimized Manifolds for Finite Density

TL;DR

This paper introduces a new method for selecting optimal complex manifolds to mitigate the sign problem in finite density field theories, demonstrated on the 3D Thirring model and compared to Lefschetz thimbles.

Contribution

It proposes a sign-optimized manifold selection technique that maximizes average phase, improving over traditional Lefschetz thimbles in finite density simulations.

Findings

Method effectively reduces sign problem in 3D Thirring model

Outperforms direct integration on Lefschetz thimbles in heavy-dense limit

Demonstrates potential for broader application in finite density quantum field theories

Abstract

The sign problem of relativistic field theories at finite fermion chemical potential has been approached by deforming the domain of integration into complex field space. We present a method for selecting a deformed manifold of integration which is a local maximum of the average phase, and demonstrate this method on the three-dimensional Thirring model. Finally, we compare the performance of this method, in the heavy-dense limit, to direct integration on the Lefschetz thimbles.