Abstract
We study the Stephanov model, which is an RMT model for QCD at finite density, using the Complex Langevin algorithm. Naive implementation of the algorithm shows convergence towards the phase quenched or quenched theory rather than to intended theory with dynamical quarks. A detailed analysis of this issue and a potential resolution of the failure of this algorithm are discussed. We study the effect of gauge cooling on the Dirac eigenvalue distribution and time evolution of the norm for various cooling norms, which were specifically designed to remove the pathologies of the complex Langevin evolution. The cooling is further supplemented with a shifted representation for the random matrices. Unfortunately, none of these modifications generate a substantial improvement on the complex Langevin evolution and the final results still do not agree with the analytical predictions.
Highlights
Many interesting physical systems have a complex action which impedes Monte Carlo simulations due to the notorious sign problem
Detailed studies have revealed that the criteria which were put forward in order to guarantee a correct result are not fulfilled in practice in many cases of interest such as cold and dense QCD close to the chiral limit
We study an Random Matrix Theory (RMT) model for QCD at finite density, proposed by Stephanov [5]
Summary
Many interesting physical systems have a complex action which impedes Monte Carlo simulations due to the notorious sign problem. An update of the current status can be found in [3] In this talk we discuss a Random Matrix Theory (RMT) model of QCD at nonzero baryon density, which has an exponentially hard sign problem, but serves as an excellent test bed for new algorithms since it can be solved analytically. This model is based on a model for QCD at nonzero nonzero temperature or imaginary chemical potential [4] and was extended to QCD at nonzero chemical potential by Stephanov in [5]. First results of our studies were presented in [14]
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