On the Lefschetz thimbles structure of the Thirring model

TL;DR

This paper explores the complex structure of Lefschetz thimbles in the Thirring model to address the sign problem, emphasizing the importance of multi-thimble contributions for accurate results.

Contribution

It presents preliminary methods for reconstructing full results from multiple thimble simulations in the Thirring model, advancing multi-thimble integration techniques.

Findings

Single thimble approximation is insufficient for full accuracy.

Multi-thimble contributions are essential for correct results.

Preliminary results show promise in reconstructing full theory from multiple thimbles.

Abstract

The complexification of field variables is an elegant approach to attack the sign problem. In one approach one integrates on Lefschetz thimbles: over them, the imaginary part of the action stays constant and can be factored out of the integrals so that on each thimble the sign problem disappears. However, for systems in which more than one thimble contribute one is faced with the challenging task of collecting contributions coming from multiple thimbles. The Thirring model is a nice playground to test multi-thimble integration techniques; even in a low dimensional theory, the thimble structure can be rich. It has been shown since a few years that collecting the contribution of the dominant thimble is not enough to capture the full content of the theory. We report preliminary results on reconstructing the complete results from multiple thimble simulations.