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

Understand

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.