手征极限下带温度和化学势的两味道Wilson费米子QCD的相结构 吴良凯 罗向前 （教授） 中山大学 罗向前 教授

Outline Introduction Lattice formulation Lattice QCD with Imaginary Chemical Potential with Wilson Quarks Conclusion

Phase diagram of QCD at zero-density I. Introduction Phase diagram of QCD at zero-density Satz’s and Aoki’s talks

两味道QCD在手征极限下的相图 QGP 2SC Tricritical point Hadronic phase Four fermion model: Alford, Wilczek, et al., 2SC Tricritical point Hadronic phase

II. Lattice Formulation 味夸克的系统的配分函数为（带有化学势） 为纯规范场作用量， 为夸克作用量

纯规范场作用量 在格点上代换为 Wilson 作用量 with β=6/g2

利用 Wilson 费米子, 则费米子矩阵为： 在需要考虑化学势时，代换费米子作用量中时间方向的链， 引入化学势。

但是： 引入化学势后, 对SU(3) 费米子矩阵的行列式为复数， 使得Monte Carlo模拟不能进行。

连续的夸克作用量 在格点上代换为离散的夸克作用量 M 是离散的费米子矩阵

解决办法 a. Improved reweighting b. Imaginary chemical potential

Lattice QCD with Imaginary Chemical Potential With Wilson Quarks

The Phase diagram suggested by Roberge and Weiss First order

Some observables considered Polyakov loop Chiral condensate

Phase diagran suggested by MC study Z(3) transition, First order Deconfinement phase transition Nf=2 of KS fermions Nf=4 of KS fermions

First Results from two flavors of Wilson fermions The results above indicate that at higher T, there is Z(3) first order phase transition for QCD with Wilson quarks at imaginary chemical potential. First scan This direction Z(3) tranition Second scan in this direction, deconfinement transition

History and histogram at a =0.262

The phase of Polyakov loop changes with imaginary chemical potential at different coupling at kappa=0.16

The determination of chiral limit Determine the chiral limit through the axial vector Ward-Takahashi identity Y.Iwasaki, K.Kanaya,et al, Phys.Rev.Lett.67,1494(1991) On the lattice with

The average number of iteration for the fermionic matrix inversio Is enormously large at chiral limit in the confining phase Is of order several hundreds in the deconfining phase

From hot start cold start

Results from the scanning along the temperature axis, i.e. beta axis.

Critical beta as a function of imaginary chemical potential To obtain critical beta as a function of real chemical potential, replace by

Using the renormalization group equation and obtain

The finite size scaling of chiral condensate

The history and histogran of chiral condensate

Conclusion Second order Crossover First order L.G.Yaffe, B.Svetisky, Phys.Rev.D26,963(1982)

QCD Phase Diagram on the (T,μ) plane from lattice QCD Lagrangian Lattice QCD from Imaginary chemical potential method: de Forcrand, Lombardo, H. Chen, X.Q. Luo, Phys. Rev. D72 (2005) 034504 Multi-dimensional reweighting: Fodor and Katz, … Hamiltonian lattice QCD with Wilson quarks X.Q. Luo, Phys. Rev. D70（2004）091504　(Rapid Commun.) X.L. Yu, X.Q. Luo, hep-lat/0508032 CPPACS Bielefeld We are making efforts Hamiltonian lattice QCD: Greogry, Guo, Kroger, X.Q. Luo, Phys. Rev. D62 (2000) 054508. Y. Fang, X.Q. Luo, Phys. Rev. D69 (2004) 114501.

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