Complex Langevin simulation of a random matrix model at nonzero chemical potential
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In this paper we test the complex Langevin algorithm for numerical simulations of a random matrix model of QCD with a first order phase transition to a phase of finite baryon density. We observe that a naive implementation of the algorithm leads to phase quenched results, which were also derived analytically in this article. We test several fixes for the convergence issues of the algorithm, in particular the method of gauge cooling, the shifted representation, the deformation technique and reweighted complex Langevin, but only the latter method reproduces the correct analytical results in the region where the quark mass is inside the domain of the eigenvalues. In order to shed more light on the issues of the methods we also apply them to a similar random matrix model with a milder sign problem and no phase transition, and in that case gauge cooling solves the convergence problems as was shown before in the literature.
KeywordsLattice QCD Lattice Quantum Field Theory Matrix Models
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- J. Bloch, J. Glesaaen, O. Philipsen, J. Verbaarschot and S. Zafeiropoulos, Complex Langevin simulations of a finite density matrix model for QCD, in 12th Conference on Quark Confinement and the Hadron Spectrum (Confinement XII), Thessaloniki Greece, 28 August-4 September 2016 [EPJ Web Conf. 137 (2017) 07030] [arXiv:1612.04621] [INSPIRE].
- R. Brent, An algorithm with guaranteed convergence for finding a zero of a function, in Algorithms for minimization without derivatives, ch. 4, Prentice-Hall, Englewood Cliffs NJ U.S.A., (1973).Google Scholar