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
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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. I. Introduction. Phase diagram of QCD at zero-density. Satz’s and Aoki’s talks. - PowerPoint PPT PresentationTRANSCRIPT
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
Satz’s and Aoki’s talks
Phase diagram of QCD at zero-densityI. Introduction
两味道 QCD 在手征极限下的相图
Four fermion model: Alford, Wilczek, et al.,
QGP
2SC
Tricritical pointHadronic phase
II. Lattice Formulation
fN 味夸克的系统的配分函数为(带有化学势)
gf sN eU))[dU]Det(M(
fg ssedddUZ ]][][[
fsgs 为纯规范场作用量, 为夸克作用量
• 纯规范场作用量
with β=6/g2
• 在格点上代换为 Wilson 作用量
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)
5
5
† †5
† †5
( ) , ( 0)
( ) , ( 0)
M M
M M
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
III. Lattice QCD with Imaginary Chemical Potential With Wilson Quarks
The Phase diagram suggested by Roberge and Weiss
First order
Polyakov loop
Chiral condensate
1
0
( ) [ ( )]tN
tt
P x Tr U x
( )
1
1[ ][ ][ ]
1[ ] ( )( ( ))
G F
f G
S S
N S
t
dU d d eZ
dU M U DetM U eZVN
Some observables considered
Nf=2 of KS fermions
Nf=4 of KS fermions
Deconfinement phase transition
Phase diagran suggested by MC study
Z(3) transition, First order
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 Results from two flavors of Wilson fermions
Second scan in this direction, deconfinement transition
First scanThis directionZ(3) tranition
History and histogram at a I =0.262
The phase of Polyakov loop changes with imaginary chemical potential at different coupling at kappa=0.1
6
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 invN
invN Is enormously large at chiral limit in the confining phase
invN Is of order several hundreds in the deconfining phase
invN 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
)())(27(649.0)1(203.5 442IIc aOa
To obtain critical beta as a function of real chemical potential, replace I by Ii
)())(27(649.0)1(203.5 442IIc aOa
Using the renormalization group equation
and
obtain
The finite size scaling of chiral condensate
The history and histogran of chiral condensate
IV. Conclusion
Second order
Crossover First orderL.G.Yaffe, B.Svetisky, Phys.Rev.D26,963(1982)
QCD Phase Diagram on the (T,μ) plane
from lattice QCD
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
Hamiltonian lattice QCD: Greogry, Guo, Kroger, X.Q. Luo, Phys. Rev. D62 (2000) 054508.
Y. Fang, X.Q. Luo, Phys. Rev. D69 (2004) 114501.
Lagrangian Lattice QCD from Imaginary chemical potential method: de Forcrand, Lombardo, H. Chen, X.Q. Luo, Phys. Rev. D72 (2005) 034504
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