Reweighting Lefschetz Thimbles

TL;DR

This paper introduces a reweighting method to compute relative weights of Lefschetz thimbles, proposes parametrization techniques, and explores combining thimble methods with Complex Langevin evolution, tested on toy models.

Contribution

It presents a novel reweighting approach for thimble weight calculation and new parametrization recipes, enhancing Lefschetz thimble simulations.

Findings

Reweighting successfully computes relative thimble weights.

Parametrization methods facilitate thimble identification.

Combining thimble methods with Complex Langevin shows promise.

Abstract

One of the main challenges in simulations on Lefschetz thimbles is the computation of the relative weights of contributing thimbles. In this paper we propose a solution to that problem by means of computing those weights using a reweighting procedure. Besides we present recipes for finding parametrizations of thimbles and anti-thimbles for a given theory. Moreover, we study some approaches to combine the Lefschetz thimble method with the Complex Langevin evolution. Our numerical investigations are carried out by using toy models among which we consider a one-site z^4 model as well as a U(1) one-link model.