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Journal of High Energy Physics

, Volume 2015, Issue 12, pp 1–17 | Cite as

Monte Carlo study of Lefschetz thimble structure in one-dimensional Thirring model at finite density

  • Hirotsugu Fujii
  • Syo KamataEmail author
  • Yoshio Kikukawa
Open Access
Regular Article - Theoretical Physics

Abstract

We consider the one-dimensional massive Thirring model formulated on the lattice with staggered fermions and an auxiliary compact vector (link) field, which is exactly solvable and shows a phase transition with increasing the chemical potential of fermion number: the crossover at a finite temperature and the first order transition at zero temperature. We complexify its path-integration on Lefschetz thimbles and examine its phase transition by hybrid Monte Carlo simulations on the single dominant thimble. We observe a discrepancy between the numerical and exact results in the crossover region for small inverse coupling β and/or large lattice size L, while they are in good agreement in the lower and higher density regions. We also observe that the discrepancy persists in the continuum limit to keep the temperature finite and it becomes more significant toward the low-temperature limit. This numerical result is consistent with our analytical study of the model and implies that the contributions of subdominant thimbles should be summed up in order to reproduce the first order transition in the low-temperature limit.

Keywords

Lattice Integrable Models Lattice Quantum Field Theory Phase Diagram of QCD 

Notes

Open Access

This article is distributed under the terms of the Creative Commons Attribution License (CC-BY 4.0), which permits any use, distribution and reproduction in any medium, provided the original author(s) and source are credited.

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Authors and Affiliations

  1. 1.Institute of PhysicsUniversity of TokyoTokyoJapan
  2. 2.Department of PhysicsRikkyo UniversityTokyoJapan

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