Complex saddle points and the sign problem in complex Langevin simulation

Tomoya Hayata, Yoshimasa Hidaka, Yuya Tanizaki

Research output: Contribution to journalArticlepeer-review

26 Citations (Scopus)


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.

Original languageEnglish
Pages (from-to)94-105
Number of pages12
JournalNuclear Physics B
Publication statusPublished - 2016 Oct 1
Externally publishedYes

ASJC Scopus subject areas

  • Nuclear and High Energy Physics


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