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Register a new userAnalytic Continuation in Two-color Finite Density QCD and Chiral Random Matrix Model
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Two-color finite density QCD is free from the sign problem, and it is thus regarded as a good model to check the validity of the analytic continuation method. We study the method in terms of the corresponding chiral random matrix model. It is found that at temperatures slightly higher than the pseudo critical temperature, the ratio type of extrapolated function works well in accordance with the results of the Monte Carlo simulations.
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The method of analytic continuation is one of the most powerful tools to circumvent the sign problem in lattice QCD. The present study is part of a larger project which, based on the investigation of QCD-like theories which are free of the sign problem, is aimed at testing the validity of the method of analytic continuation and at improving its predictivity, in view of its application to real QCD. We have shown that a considerable improvement can be achieved if suitable functions are used to interpolate data with imaginary chemical potential. We present results obtained in a theory free of the sign problem such as two-color QCD at finite chemical potential.
We compute individual distributions of low-lying eigenvalues of massive chiral random matrix ensembles by the Nystrom-type quadrature method for evaluating the Fredholm determinant and Pfaffian that represent the analytic continuation of the Janossy densities (conditional gap probabilities). A compact formula for individual eigenvalue distributions suited for precise numerical evaluation by the Nystrom-type method is obtained in an explicit form, and the $k^{rm{small th}}$ smallest eigenvalue distributions are numerically evaluated for chiral unitary and symplectic ensembles in the microscopic limit. As an application of our result, the low-lying Dirac spectra of the SU(2) lattice gauge theory with $N_F=8$ staggered flavors are fitted to the numerical prediction from the chiral symplectic ensemble, leading to a precise determination of the chiral condensateof a two-color QCD-like system in the future.
Complex nature of finite density QCD with heavy quarks in the strong coupling region is studied. For this purpose, we consider the effective potential as a function of Polyakov line, and study thermodynamic singularities and associated Stokes boundaries in the complex chemical potential plane. We also perform an explicit analytic continuation of the first order transition and crossover lines in the complex chemical potential plane.
The phase diagram of two-color QCD with a chiral chemical potential is studied on the lattice. The focus is on the confinement/deconfinement phase transition and the breaking/restoration of chiral symmetry. The simulations are carried out with dynamical staggered fermions without rooting. The dependence of the Polyakov loop, the chiral condensate and the corresponding susceptibilities on the chiral chemical potential and the temperature are presented.
We present the crossover line between the quark gluon plasma and the hadron gas phases for small real chemical potentials. First we determine the effect of imaginary values of the chemical potential on the transition temperature using lattice QCD simulations. Then we use various formulas to perform an analytic continuation to real values of the baryo-chemical potential. Our data set maintains strangeness neutrality to match the conditions of heavy ion physics. The systematic errors are under control up to $mu_Bapprox 300$ MeV. For the curvature of the transition line we find that there is an approximate agreement between values from three different observables: the chiral susceptibility, chiral condensate and strange quark susceptibility. The continuum extrapolation is based on $N_t=$ 10, 12 and 16 lattices. By combining the analysis for these three observables we find, for the curvature, the value $kappa = 0.0149 pm 0.0021$.
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