Finite Density $QED_{1+1}$ Near Lefschetz Thimbles

TL;DR

This paper explores applying the Lefschetz thimble method to finite-density $QED_{1+1}$, demonstrating it can reduce the sign problem and produce correct results more efficiently than traditional techniques.

Contribution

It discusses conceptual challenges of using generalized thimble methods in gauge theories and shows successful application to finite-density $QED_{1+1}$ with improved efficiency.

Findings

Generalized thimble method yields correct results for $QED_{1+1}$ at finite density.

The method reduces computational effort compared to standard approaches.

Conceptual issues in applying thimble methods to gauge theories are addressed.

Abstract

One strategy for reducing the sign problem in finite-density field theories is to deform the path integral contour from real to complex fields. If the deformed manifold is the appropriate combination of Lefschetz thimbles -- or somewhat close to them -- the sign problem is alleviated. Gauge theories lack a well-defined thimble decomposition, and therefore it is unclear how to carry out a generalized thimble method. In this paper we discuss some of the conceptual issues involved by applying this method to $QED_{1+1}$ at finite density, showing that the generalized thimble method yields correct results with less computational effort than standard methods.