Complex Langevin method applied to the 2D $SU(2)$ Yang-Mills theory

Abstract

The complex Langevin method in conjunction with the gauge cooling is applied to the two-dimensional lattice $SU(2)$ Yang-Mills theory that is analytically solvable. We obtain strong numerical evidence that at large Langevin time the expectation value of the plaquette variable converges, but to a wrong value when the complex phase of the gauge coupling is large.

10 pages, 7 figures, the final version to appear in Physical Review D

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• Complex Langevin calculations in finite density QCD at large $\mu /T$ with the deformation technique
• Reweighting complex Langevin trajectories
• Path optimization for $U(1)$ gauge theory with complexified parameters
• Exploring Complex-Langevin Methods for Finite-Density QCD
• Comparison of algorithms for solving the sign problem in the O(3) model in 1+1 dimensions at finite chemical potential
• A projected complex Langevin sampling method for bosons in the canonical and microcanonical ensembles
• Simulating gauge theories on Lefschetz thimbles
• Correctness criteria for complex Langevin