Worldvolume approach to the tempered Lefschetz thimble method

TL;DR

The paper introduces a novel Hybrid Monte Carlo algorithm that operates on a continuum set of integration surfaces to address the sign problem, improving upon the tempered Lefschetz thimble method by reducing computational complexity and demonstrating effectiveness on a challenging model.

Contribution

It extends the tempered Lefschetz thimble method by developing a worldvolume approach that avoids Jacobian calculations, enhancing efficiency in solving sign and multimodal problems.

Findings

Successfully applied to a chiral random matrix model

Avoids Jacobian computation during configuration generation

Addresses sign and multimodal problems simultaneously

Abstract

As a solution towards the numerical sign problem, we propose a novel Hybrid Monte Carlo algorithm, in which molecular dynamics is performed on a continuum set of integration surfaces foliated by the antiholomorphic gradient flow ("the worldvolume of an integration surface"). This is an extension of the tempered Lefschetz thimble method (TLTM), and solves the sign and multimodal problems simultaneously as the original TLTM does. Furthermore, in this new algorithm, one no longer needs to compute the Jacobian of the gradient flow in generating a configuration, and only needs to evaluate its phase upon measurement. To demonstrate that this algorithm works correctly, we apply the algorithm to a chiral random matrix model, for which the complex Langevin method is known not to work.