Evading the sign problem in the mean-field approximation through Lefschetz-thimble path integral

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Evading the sign problem in the mean-field approximation through Lefschetz-thimble path integral

Yuya Tanizaki, Hiromichi Nishimura, and Kouji Kashiwa

Phys. Rev. D 91, 101701(R) – Published 27 May 2015

Abstract

The fermion sign problem appearing in the mean-field approximation is considered, and the systematic computational scheme of the free energy is devised by using the Lefschetz-thimble method. We show that the Lefschetz-thimble method respects the reflection symmetry, which makes physical quantities manifestly real at any order of approximations using complex saddle points. The formula is demonstrated through the Airy integral as an example, and its application to the Polyakov-loop effective model of dense QCD is discussed in detail.

Received 15 April 2015

DOI:https://doi.org/10.1103/PhysRevD.91.101701

Authors & Affiliations

Yuya Tanizaki^1,2,*, Hiromichi Nishimura^3,†, and Kouji Kashiwa^4,‡

¹Department of Physics, The University of Tokyo, Bunkyo-ku, Tokyo 113-0033, Japan
²Theoretical Research Division, Nishina Center, RIKEN, Wako, Saitama 351-0198, Japan
³Faculty of Physics, Bielefeld University, D-33615 Bielefeld, Germany
⁴Yukawa Institute for Theoretical Physics, Kyoto University, Kyoto 606-8502, Japan

^*yuya.tanizaki@riken.jp
^†nishimura@physik.uni-bielefeld.de
^‡kouji.kashiwa@yukawa.kyoto-u.ac.jp

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Issue

Vol. 91, Iss. 10 — 15 May 2015

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Physical Review D

covering particles, fields, gravitation, and cosmology