Abstract
We study a random matrix model for QCD at finite density via complex Langevin dynamics. This model has a phase transition to a phase with nonzero baryon density. We study the convergence of the algorithm as a function of the quark mass and the chemical potential and focus on two main observables: the baryon density and the chiral condensate. For simulations close to the chiral limit, the algorithm has wrong convergence properties when the quark mass is in the spectral domain of the Dirac operator. A possible solution of this problem is discussed.
Highlights
IntroductionBecause, stochastic quantization reproduces the results of path integral quantization in the case when the action is real [4], this is not necessarily the case when the action is complex
The study of the phase diagram of QCD in the temperature (T )-chemical potential (μ) plane is one of the biggest challenges in Quantum Chromodynamics
We study the convergence of the algorithm as a function of the quark mass and the chemical potential and focus on two main observables: the baryon density and the chiral condensate
Summary
Because, stochastic quantization reproduces the results of path integral quantization in the case when the action is real [4], this is not necessarily the case when the action is complex. The question to which the whole community would like to know the answer is if CL will work correctly close to the chiral limit in the confined phase This was, for example, recently investigated in two-dimensional strong-coupling QCD [9], where it was shown that CL leads to wrong results for small masses. In this contribution, we will address this question by studying a random matrix theory (RMT) model of QCD at nonzero chemical potential which has both a complex fermion determinant and a finite density phase transition. The model has a known analytic solution, which gives us a handle on the discretization errors otherwise appearing due to lattice artefacts
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