### 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.

Original language | English |
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Pages (from-to) | 94-105 |

Number of pages | 12 |

Journal | Nuclear Physics B |

Volume | 911 |

DOIs | |

Publication status | Published - 2016 Oct 1 |

Externally published | Yes |

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### ASJC Scopus subject areas

- Nuclear and High Energy Physics

### Cite this

*Nuclear Physics B*,

*911*, 94-105. https://doi.org/10.1016/j.nuclphysb.2016.07.031

**Complex saddle points and the sign problem in complex Langevin simulation.** / Hayata, Tomoya; Hidaka, Yoshimasa; Tanizaki, Yuya.

Research output: Contribution to journal › Article

*Nuclear Physics B*, vol. 911, pp. 94-105. https://doi.org/10.1016/j.nuclphysb.2016.07.031

}

TY - JOUR

T1 - Complex saddle points and the sign problem in complex Langevin simulation

AU - Hayata, Tomoya

AU - Hidaka, Yoshimasa

AU - Tanizaki, Yuya

PY - 2016/10/1

Y1 - 2016/10/1

N2 - 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.

AB - 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.

UR - http://www.scopus.com/inward/record.url?scp=84982787949&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=84982787949&partnerID=8YFLogxK

U2 - 10.1016/j.nuclphysb.2016.07.031

DO - 10.1016/j.nuclphysb.2016.07.031

M3 - Article

AN - SCOPUS:84982787949

VL - 911

SP - 94

EP - 105

JO - Nuclear Physics B

JF - Nuclear Physics B

SN - 0550-3213

ER -