### Abstract

The sign problem of finite-density QCD at the zero temperature becomes very severe if the quark chemical potential exceeds half of the pion mass. In order to understand its property, we consider the sign problem of the one-site fermion model appearing in its path-integral expression by using the Lefschetz-thimble method. We show that the original integration cycle becomes decomposed into multiple Lefschetz thimbles at a certain value of the fermion chemical potential, which would correspond to half of the pion mass of finite-density QCD. This triggers a fictitious phase transition on each Lefschetz thimble, and the interference of complex phases among them plays an important role for the correct description of the system. We also show that the complex Langevin method does not work in this situation.

Original language | English |
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Journal | Proceedings of Science |

Volume | Part F128557 |

Publication status | Published - 2016 Jan 1 |

Externally published | Yes |

Event | 34th Annual International Symposium on Lattice Field Theory, LATTICE 2016 - Southampton, United Kingdom Duration: 2016 Jul 24 → 2016 Jul 30 |

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### ASJC Scopus subject areas

- General

### Cite this

*Proceedings of Science*,

*Part F128557*.

**Lefschetz-thimble approach to the Silver Blaze problem of one-site fermion model.** / Tanizaki, Yuya; Hidaka, Yoshimasa; Hayata, Tomoya.

Research output: Contribution to journal › Conference article

*Proceedings of Science*, vol. Part F128557.

}

TY - JOUR

T1 - Lefschetz-thimble approach to the Silver Blaze problem of one-site fermion model

AU - Tanizaki, Yuya

AU - Hidaka, Yoshimasa

AU - Hayata, Tomoya

PY - 2016/1/1

Y1 - 2016/1/1

N2 - The sign problem of finite-density QCD at the zero temperature becomes very severe if the quark chemical potential exceeds half of the pion mass. In order to understand its property, we consider the sign problem of the one-site fermion model appearing in its path-integral expression by using the Lefschetz-thimble method. We show that the original integration cycle becomes decomposed into multiple Lefschetz thimbles at a certain value of the fermion chemical potential, which would correspond to half of the pion mass of finite-density QCD. This triggers a fictitious phase transition on each Lefschetz thimble, and the interference of complex phases among them plays an important role for the correct description of the system. We also show that the complex Langevin method does not work in this situation.

AB - The sign problem of finite-density QCD at the zero temperature becomes very severe if the quark chemical potential exceeds half of the pion mass. In order to understand its property, we consider the sign problem of the one-site fermion model appearing in its path-integral expression by using the Lefschetz-thimble method. We show that the original integration cycle becomes decomposed into multiple Lefschetz thimbles at a certain value of the fermion chemical potential, which would correspond to half of the pion mass of finite-density QCD. This triggers a fictitious phase transition on each Lefschetz thimble, and the interference of complex phases among them plays an important role for the correct description of the system. We also show that the complex Langevin method does not work in this situation.

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M3 - Conference article

AN - SCOPUS:85025827865

VL - Part F128557

JO - Proceedings of Science

JF - Proceedings of Science

SN - 1824-8039

ER -