Anatomy of a strong residual sign problem on the thimbles

TL;DR

The paper analyzes how a residual sign problem arises in thimble integration for complex actions, especially when phase interactions cause exponential suppression, affecting the accuracy of phase factor calculations.

Contribution

It identifies the conditions under which a strong residual sign problem occurs in thimble methods for complex actions, highlighting the impact of phase interactions.

Findings

Residual sign problem can be strong when phase interactions align unfavorably.

The sign problem causes exponential suppression of the average phase factor.

Sensitivity to phase distribution parameters affects computational accuracy.

Abstract

Using a simple Gaussian-like Ansatz for the phase distribution of a theory with a complex action, we show how the thimble integration for the average phase factor can be plagued by a strong residual sign problem when the phase of the complex integration measure conspires with the constant phase of the integrand along the thimble. This strong sign problem prohibits the accurate computation of the average phase factor when it becomes exponentially small, and causes a strong sensitivity to the parameters describing the phase distribution.