Work

Is it worth the effort to find Lefschetz thimbles? Integration contours with numerically optimal signal-to-noise ratios in simple fermionic toy models

Year: 2025

Type: article

Abstract: We perform a detailed analysis of the fermionic sign problem in a series of one-dimensional integrals, that are achieved as extreme (one-site) limits of genuine physics models. Altogether we studied a Hubbard-like, a Gross-Neveu-like, a Thirring-like, and a Chern-Simons-like integral. We compare the Lefschetz-thimble structure for these integrals with contours obtained with the holomorphic flow equations at different flow times and with numerically optimized continuous integration contours, defined by a maximal value of the expectation values of the phases. With the holomorphic flow equation, we perform the large flow-time limit, so that the average phase corresponds to its value on the thimbles. In all of these integrals we observe that the convergence to this value is not monotonic, meaning that there is an optimal flow time where the sign problem is weaker than it is on the thimbles. Furthermore, we find that for all of these toy models, numerical optimization can find continuous contours on which the sign problem is considerably weaker than it is both on the thimbles and at flowed integration contours at the optimal flow time.

Source: Physical review. D/Physical review. D.

DOI: 10.1103/fywf-77b4

Authors: Attila Pásztor, Dávid Pesznyák

Institutions: Eötvös Loránd University, Pennsylvania State University, HUN-REN Wigner Research Centre for Physics

Language: English

Topic: Theoretical and Computational Physics

Subfield: Condensed Matter Physics

Field: Physics and Astronomy

Domain: Physical Sciences

Open Access status: hybrid