Hamilton dynamics for the Lefschetz thimble integration akin to the complex Langevin method
High Energy Physics - Theory
2015-11-19 v2 High Energy Physics - Lattice
Abstract
The Lefschetz thimble method, i.e., the integration along the steepest descent cycles, is an idea to evade the sign problem by complexifying the theory. We discuss that such steepest descent cycles can be identified as ground-state wave-functions of a supersymmetric Hamilton dynamics, which is described with a framework akin to the complex Langevin method. We numerically construct the wave-functions on a grid using a toy model and confirm their well-localized behavior.
Cite
@article{arxiv.1507.07351,
title = {Hamilton dynamics for the Lefschetz thimble integration akin to the complex Langevin method},
author = {Kenji Fukushima and Yuya Tanizaki},
journal= {arXiv preprint arXiv:1507.07351},
year = {2015}
}
Comments
11 pages, 4 figures; (v2) Secs. 2 and 4 are improved, Fig. 4 is added, References are updated