Testing the criterion for correct convergence in the complex Langevin method

Nagata, Keitaro (0000 0001 0659 9825, Center of Medical Information Science, Kochi Medical School, Kochi University, Kohasu, Oko-cho, Nankoku-shi, Kochi, 783-8505, Japan) (0000 0001 2155 959X, KEK Theory Center, High Energy Accelerator Research Organization, 1-1 Oho, Tsukuba, Ibaraki, 305-0801, Japan) ; Nishimura, Jun (0000 0001 2155 959X, KEK Theory Center, High Energy Accelerator Research Organization, 1-1 Oho, Tsukuba, Ibaraki, 305-0801, Japan) (0000 0004 1763 208X, Department of Particle and Nuclear Physics, School of High Energy Accelerator Science, Graduate University for Advanced Studies (SOKENDAI), 1-1 Oho, Tsukuba, Ibaraki, 305-0801, Japan) ; Shimasaki, Shinji (0000 0001 2155 959X, KEK Theory Center, High Energy Accelerator Research Organization, 1-1 Oho, Tsukuba, Ibaraki, 305-0801, Japan) (0000 0004 1936 9959, Research and Education Center for Natural Sciences, Keio University, Hiyoshi 4-1-1, Yokohama, Kanagawa, 223-8521, Japan)

09 May 2018

Abstract: Recently the complex Langevin method (CLM) has been attracting attention as a solution to the sign problem, which occurs in Monte Carlo calculations when the effective Boltzmann weight is not real positive. An undesirable feature of the method, however, was that it can happen in some parameter regions that the method yields wrong results even if the Langevin process reaches equilibrium without any problem. In our previous work, we proposed a practical criterion for correct convergence based on the probability distribution of the drift term that appears in the complex Langevin equation. Here we demonstrate the usefulness of this criterion in two solvable theories with many dynamical degrees of freedom, i.e., two-dimensional Yang-Mills theory with a complex coupling constant and the chiral Random Matrix Theory for finite density QCD, which were studied by the CLM before. Our criterion can indeed tell the parameter regions in which the CLM gives correct results.


Published in: JHEP 1805 (2018) 004
Published by: Springer/SISSA
DOI: 10.1007/JHEP05(2018)004
arXiv: 1802.01876
License: CC-BY-4.0



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