Complex saddle points and the sign problem in complex Langevin simulation

Hayata, Tomoya  (RIKEN Center for Emergent Matter Science (CEMS), Wako, Saitama, 351-0198, Japan) ; Hidaka, Yoshimasa (Theoretical Research Division, Nishina Center, RIKEN, Wako, Saitama, 351-0198, Japan) ; Tanizaki, Yuya  (RIKEN BNL Research Center, Brookhaven National Laboratory, Upton, NY, 11973, USA)

03 August 2016

Abstract: We show that complex Langevin simulation converges to a wrong result within the semiclassical analysis, 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.

Published in: Nuclear Physics B (2016)
Published by: Elsevier
DOI: 10.1016/j.nuclphysb.2016.07.031
License: CC-BY-3.0

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