English

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.

Keywords

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

R2 v1 2026-06-22T10:19:16.912Z