Worldvolume tempered Lefschetz thimble method and its error estimation

TL;DR

The paper introduces the worldvolume tempered Lefschetz thimble method (WV-TLTM), an improved algorithm for solving the sign problem in complex systems, reducing computational costs and avoiding ergodicity issues, demonstrated on a chiral random matrix model.

Contribution

The paper proposes WV-TLTM, a novel algorithm that enhances the tempered Lefschetz thimble method by eliminating Jacobian calculations, improving efficiency and stability in sign problem simulations.

Findings

Successfully applied to the Stephanov model.

Reduces computational cost compared to previous methods.

Avoids ergodicity problems inherent in other approaches.

Abstract

The worldvolume tempered Lefschetz thimble method (WV-TLTM) is an algorithm towards solving the sign problem, where hybrid Monte Carlo updates are performed on a continuous accumulation of flowed surfaces foliated by the anti-holomorphic gradient flow (the worldvolume of integration surface). Sharing the advantage with the original tempered Lefschetz thimble method (TLTM) that the sign problem is resolved without introducing the ergodicity problem, the new algorithm is expected to significantly reduce the computational cost, because it eliminates the need to compute the Jacobian of the flow in generating a configuration. We demonstrate the effectiveness of the WV-TLTM with its successful application to the Stephanov model (a chiral random matrix model), for which the complex Langevin method is known to suffer from a serious wrong convergence problem. We also discuss the statistical analysis method for the WV-TLTM.