Finite temperature study of the axial U(1) symmetry on the lattice with overlap fermion formulation
Finite temperature study of the axial U(1) symmetry on the lattice with overlap fermion formulation
复制标题
DOI：
10.1103/physrevd.87.114514
复制
发表时间：
2013-04
影响因子：
5
通讯作者：
G. Cossu;S. Aoki;H. Fukaya;S. Hashimoto;T. Kaneko;H. Matsufuru;J. Noaki
中科院分区：
文献类型：
--
作者：
G. Cossu;S. Aoki;H. Fukaya;S. Hashimoto;T. Kaneko;H. Matsufuru;J. Noaki
我们利用晶格QCD模拟研究了双味QCD在有限温度相变附近和以上的轴向U(1)对称性。虽然量化总是破坏轴向U(1)对称性（即手性异常），但相关函数可以在高温阶段有效地恢复对称性。我们通过计算介子相关子和临界点附近的狄拉克算符谱密度，明确地研究了这种可能性。我们的数值模拟是在$16^3\ × 8$晶格上进行的，其中有两种由重叠费米子形式表示的动态夸克。该公式明确地实现了轴向异常引起的手性对称性及其破坏，这是研究有效恢复轴向U(1)对称性的先决条件。为了避免精确手性晶格费米子在规范位形空间中出现的不连续，模拟被限制在一个固定的拓扑扇区中。它引起有限体积效应，这是由一个基于$\ $-真空的傅里叶变换的公式很好地描述的。我们通过计算淬火理论中的拓扑磁化率，在有限温度下证实了这一公式。我们的两个flavor模拟显示介子相关子的简并和Dirac算子谱密度的间隙，这意味着轴向U(1)对称性在手性对称相中有效地恢复了。
We examine the axial U(1) symmetry near and above the finite temperature phase transition in two-flavor QCD using lattice QCD simulations. Although the axial U(1) symmetry is always violated by quantization, (i.e.) the chiral anomaly, the correlation functions may manifest effective restoration of the symmetry in the high temperature phase. We explicitly study this possibility by calculating the meson correlators as well as the Dirac operator spectral density near the critical point. Our numerical simulations are performed on a $16^3\times 8$ lattice with two flavors of dynamical quarks represented by the overlap fermion formalism. Chiral symmetry and its violation due to the axial anomaly is manifestly realized with this formulation, which is a prerequisite for the study of the effective restoration of the axial U(1) symmetry. In order to avoid discontinuity in the gauge configuration space, which occurs for the exactly chiral lattice fermions, the simulation is confined in a fixed topological sector. It induces finite volume effect, which is well described by a formula based on the Fourier transform from the $\theta$-vacua. We confirm this formula at finite temperature by calculating the topological susceptibility in the quenched theory. Our two flavor simulations show degeneracy of the meson correlators and a gap in the Dirac operator spectral density, which implies that the axial U(1) symmetry is effectively restored in the chirally symmetric phase.