Stability of complex Langevin dynamics in effective models

A bstract The sign problem at nonzero chemical potential prohibits the use of importance sampling in lattice simulations. Since complex Langevin dynamics does not rely on importance sampling, it provides a potential solution. Recently it was shown that complex Langevin dynamics fails in the disorder...

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Bibliographic Details
Published in:The journal of high energy physics 2013-03, Vol.2013 (3), p.1-29, Article 73
Main Authors: Aarts, Gert, James, Frank A., Pawlowski, Jan M., Seiler, Erhard, Sexty, Dénes, Stamatescu, Ion-Olimpiu
Format: Article
Language:English
Subjects:
Classical and Quantum Gravitation
Computer simulation
Dynamic tests
Dynamics
Elementary Particles
High energy physics
Importance sampling
Lattices
Phase diagrams
Physics
Physics and Astronomy
Quantum Field Theories
Quantum Field Theory
Quantum Physics
Relativity Theory
Stability
String Theory
Three dimensional models
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Summary:A bstract The sign problem at nonzero chemical potential prohibits the use of importance sampling in lattice simulations. Since complex Langevin dynamics does not rely on importance sampling, it provides a potential solution. Recently it was shown that complex Langevin dynamics fails in the disordered phase in the case of the three-dimensional XY model, while it appears to work in the entire phase diagram in the case of the three-dimensional SU(3) spin model. Here we analyse this difference and argue that it is due to the presence of the nontrivial Haar measure in the SU(3) case, which has a stabilizing effect on the complexified dynamics. The freedom to modify and stabilize the complex Langevin process is discussed in some detail.
ISSN:1029-8479
1029-8479
DOI:10.1007/JHEP03(2013)073