Complex Langevin: etiology and diagnostics of its main problem

  • Gert Aarts
  • Frank A. James
  • Erhard Seiler
  • Ion-Olimpiu Stamatescu
Regular Article - Theoretical Physics

Abstract

The complex Langevin method is a leading candidate for solving the so-called sign problem occurring in various physical situations. Its most vexing problem is that sometimes it produces ‘convergence to the wrong limit’. In this paper we carefully revisit the formal justification of the method, identifying points at which it may fail and derive a necessary and sufficient criterion for correctness. This criterion is, however, not practical, since its application requires checking an infinite tower of identities. We propose instead a practical test involving only a check of the first few of those identities; this raises the question of the ‘sensitivity’ of the test. This sensitivity as well as the general insights into the possible reasons of failure (the etiology) are then tested in two toy models where the correct answer is known. At least in those models the test works perfectly.

Keywords

High Energy Phys Boundary Term Equilibrium Measure Formal Argument Complex Noise 

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Copyright information

© Springer-Verlag / Società Italiana di Fisica 2011

Authors and Affiliations

  • Gert Aarts
    • 1
  • Frank A. James
    • 1
  • Erhard Seiler
    • 2
  • Ion-Olimpiu Stamatescu
    • 3
  1. 1.Department of PhysicsSwansea UniversitySwanseaUK
  2. 2.Max-Planck-Institut für Physik (Werner-Heisenberg-Institut)MünchenGermany
  3. 3.Institut für Theoretische PhysikUniversität Heidelberg and FESTHeidelbergGermany

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