Complex Langevin dynamics and zeroes of the fermion determinant

  • Gert Aarts
  • Erhard Seiler
  • Dénes Sexty
  • Ion-Olimpiu Stamatescu
Open Access
Regular Article - Theoretical Physics

Abstract

QCD at nonzero baryon chemical potential suffers from the sign problem, due to the complex quark determinant. Complex Langevin dynamics can provide a solution, provided certain conditions are met. One of these conditions, holomorphicity of the Langevin drift, is absent in QCD since zeroes of the determinant result in a meromorphic drift. We first derive how poles in the drift affect the formal justification of the approach and then explore the various possibilities in simple models. The lessons from these are subsequently applied to both heavy dense QCD and full QCD, and we find that the results obtained show a consistent picture. We conclude that with careful monitoring, the method can be justified a posteriori, even in the presence of meromorphicity.

Keywords

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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Copyright information

© The Author(s) 2017

Authors and Affiliations

  • Gert Aarts
    • 1
  • Erhard Seiler
    • 2
  • Dénes Sexty
    • 3
  • Ion-Olimpiu Stamatescu
    • 4
    • 5
  1. 1.Department of Physics, College of ScienceSwansea UniversitySwanseaU.K.
  2. 2.Max-Planck-Institut für Physik (Werner-Heisenberg-Institut)MünchenGermany
  3. 3.Bergische Universität WuppertalWuppertalGermany
  4. 4.Institut für Theoretische Physik, Universität HeidelbergHeidelbergGermany
  5. 5.FESTHeidelbergGermany

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