Lefschetz-thimble analysis of the sign problem in one-site fermion model

Yuya Tanizaki, Yoshimasa Hidaka, Tomoya Hayata

Research output: Contribution to journalArticlepeer-review

65 Citations (Scopus)


The Lefschetz-thimble approach to path integrals is applied to a one-site model of electrons, i.e., the one-site Hubbard model. Since the one-site Hubbard model shows a non-analytic behavior at the zero temperature and its path integral expression has the sign problem, this toy model is a good testing ground for an idea or a technique to attack the sign problem. Semiclassical analysis using complex saddle points unveils the significance of interference among multiple Lefschetz thimbles to reproduce the non-analytic behavior by using the path integral. If the number of Lefschetz thimbles is insufficient, we found not only large discrepancies from the exact result, but also thermodynamic instabilities. Analyzing such singular behaviors semiclassically, we propose a criterion to identify the necessary number of Lefschetz thimbles. We argue that this interference of multiple saddle points is a key issue to understand the sign problem of the finite-density quantum chromodynamics.

Original languageEnglish
Article number033002
JournalNew Journal of Physics
Issue number3
Publication statusPublished - 2016 Mar 1
Externally publishedYes


  • Lee-Yang zeros
  • Lefschetz thimbles
  • semiclassical analysis
  • sign problem

ASJC Scopus subject areas

  • Physics and Astronomy(all)


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