Lee-Yang zeros in lattice QCD for searching phase transition points

Abstract

We report Lee-Yang zeros behavior at finite temperature and density. The quark number densities, n , are calculated at the pure imaginary chemical potential iµ qI , where no sign problem occurs. Then, the canonical partition functions, Z C (n, T, V ), up to some maximal values of n are estimated through fitting theoretically motivated functions to n , which are used to compute the Lee-Yang zeros. We study the temperature dependence of the distributions of the Lee-Yang zeros around the pseudo-critical temperature region T /T c = 0.84 -1.35.In the distributions of the Lee-Yang zeros, we observe the Roberge-Weiss phase transition at T /T c ≥ 1.20. We discuss the dependence of the behaviors of Lee-Yang zeros on the maximal value of n, so that we can estimate a reliable infinite volume limit.

Search of QCD phase transition points in the canonical approach of the NJL model

“…In lattice QCD calculations, moreover, the integration method [14][15][16][17][18] is used to extract Z C for large n. In the integration method, Z GC (iµ I ) is evaluated from the number density,…”

“…Following Refs. [18,27], we choose N max so that the value of N max /V is approximately unchanged when V changes. Figure 2 indicates that the right edges of LYZs, which is defined by a position of min[Im(ξ)] in the first quadrant in the complex ξ plane, approach the expected CP as V increases.…”

“…Many methods have been proposed toward avoiding the sign problem. Meanwhile, a method called the canonical approach [4] has been recently developed rapidly with multiple-precision arithmetic [5][6][7][8][9][10][11][12][13][14][15][16][17][18]. In the canonical approach physical quantities are calculated at pure imaginary chemical potentials, in which the sign problem does not exist.…”

“…In Ref. [18], one of the present authors studied the socalled Lee-Yang zeros (LYZs), which are zeros of grand canonical partition functions as functions of the fugacity parameter. LYZs provide us with various information of phase transitions [19,20].…”

“…We show how the LYZs with finite degrees of freedom are smoothly extrapolated to those with infinite degrees of freedom. Moreover, we also study an additional approximation for the number density as a function of imaginary chemical potential which has been used in the lattice simulations [14][15][16][17][18]. Taking into account the two features, phase transition points are well determined from the data of finite degrees of freedom.…”