Worldvolume approach to the tempered Lefschetz thimble method

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.

Automated summary

The novel hybrid Monte Carlo algorithm proposed in this study extends the tempered Lefschetz thimble method by performing molecular dynamics on a continuum set of integration surfaces foliated by the antiholomorphic gradient flow. This algorithm solves the sign and multimodal problems simultaneously without the need to compute the Jacobian of the gradient flow during configuration generation.