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Complex Langevin simulation of a random matrix model at nonzero chemical potential

  • J. Bloch
  • J. Glesaaen
  • J. J. M. Verbaarschot
  • S. ZafeiropoulosEmail author
Open Access
Regular Article - Theoretical Physics

Abstract

In this paper we test the complex Langevin algorithm for numerical simulations of a random matrix model of QCD with a first order phase transition to a phase of finite baryon density. We observe that a naive implementation of the algorithm leads to phase quenched results, which were also derived analytically in this article. We test several fixes for the convergence issues of the algorithm, in particular the method of gauge cooling, the shifted representation, the deformation technique and reweighted complex Langevin, but only the latter method reproduces the correct analytical results in the region where the quark mass is inside the domain of the eigenvalues. In order to shed more light on the issues of the methods we also apply them to a similar random matrix model with a milder sign problem and no phase transition, and in that case gauge cooling solves the convergence problems as was shown before in the literature.

Keywords

Lattice QCD Lattice Quantum Field Theory Matrix Models 

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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Copyright information

© The Author(s) 2018

Authors and Affiliations

  • J. Bloch
    • 1
  • J. Glesaaen
    • 2
  • J. J. M. Verbaarschot
    • 3
  • S. Zafeiropoulos
    • 4
    • 5
    • 6
    Email author
  1. 1.Institute for Theoretical PhysicsUniversity of RegensburgRegensburgGermany
  2. 2.Department of PhysicsSwansea UniversitySwanseaU.K.
  3. 3.Department of Physics and AstronomyStony Brook UniversityStony BrookU.S.A.
  4. 4.Institute for Theoretical PhysicsHeidelberg UniversityHeidelbergGermany
  5. 5.Department of PhysicsThe College of William & MaryWilliamsburgU.S.A.
  6. 6.Thomas Jefferson National Accelerator FacilityNewport NewsU.S.A.

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