Computing real-time quantum path integrals on Sewed, almost-Lefschetz thimbles

TL;DR

This paper introduces a numerical method for computing real-time quantum path integrals using Monte-Carlo sampling on near-Lefschetz thimbles, offering an alternative to existing techniques and tested in quantum mechanics.

Contribution

It develops a set of tools based on Lefschetz thimble methods, including coordinate parameterization and local deformation, to improve real-time path integral computations.

Findings

Effective numerical integration along radial coordinates

Identification of pitfalls and benefits in quantum mechanics applications

Benchmarking shows improved efficiency over traditional methods

Abstract

We present a method to compute real-time path integrals numerically, by Monte-Carlo sampling on near-Lefschetz thimbles. We present a collection of tools based on the Lefschetz thimble methods, which together provide an alternative to existing methods such as the Generalised thimble. These involve a convenient coordinate parameterization of the thimble, direct numerical integration along a radial coordinate into an effective path integral weight and locally deforming the Lefschetz thimble using its Gaussian (non-interacting theory) counterpart in a region about the critical point. We apply this to quantum mechanics, identify possible pitfalls and benefits, and benchmark its efficiency.