Complex saddle points and the sign problem in complex Langevin simulation
Abstract
We show that complex Langevin simulation converges to a wrong result, by relating it to the Lefschetz-thimble path integral, when the path-integral weight has different phases among dominant complex saddle points. Equilibrium solution of the complex Langevin equation forms local distributions around complex saddle points. Its ensemble average approximately becomes a direct sum of the average in each local distribution, where relative phases among them are dropped. We propose that by taking these phases into account through reweighting, we can solve the wrong convergence problem. However, this prescription may lead to a recurrence of the sign problem in the complex Langevin method for quantum many-body systems.
Keywords
Cite
@article{arxiv.1511.02437,
title = {Complex saddle points and the sign problem in complex Langevin simulation},
author = {Tomoya Hayata and Yoshimasa Hidaka and Yuya Tanizaki},
journal= {arXiv preprint arXiv:1511.02437},
year = {2017}
}
Comments
6 pages, 5 figures. v2: Commet added. Figures corrected v3: Accepted version