Testing the criterion for correct convergence in the complex Langevin method

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.

arXiv comment16 pages, 2 figures; (v2) reference and comment added; (v3) minor revision; (v4) final version published in JHEP

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• Dynamical stabilisation of complex Langevin simulations of QCD
• Complex Langevin calculations in finite density QCD at large $\mu /T$ with the deformation technique
• Complex Langevin calculations in QCD at finite density
• Complex Langevin analysis of the spontaneous breaking of 10D rotational symmetry in the Euclidean IKKT matrix model
• Stabilizing complex Langevin for real-time gauge theories with an anisotropic kernel
• Complex Langevin Simulations of Zero-dimensional Supersymmetric Quantum Field Theories
• Complex Langevin Dynamics in Large $N$ Unitary Matrix Models
• Complex Langevin study for polarons in an attractively interacting one-dimensional two-component Fermi gas
• Complex Langevin Dynamics and Supersymmetric Quantum Mechanics
• Towards sampling complex actions
• A lattice pairing-field approach to ultracold Fermi gases
• On the validity of the complex Langevin method near the deconfining phase transition in QCD at finite density
• Correctness criteria for complex Langevin
• Equation of state from complex Langevin simulations