论文标题
规范分区功能和中心对称性破坏有限密度晶格理论
Canonical partition function and center symmetry breaking in finite density lattice gauge theories
论文作者
论文摘要
我们通过专注于概率分布函数来研究晶格计理论在高温和高密度下的相变的性质，这代表了在热浴中实现一定密度的概率。概率分布函数是通过创建一个规范分区函数来固定大量分区函数的粒子数量的。但是，如果Z_3中心对称性对于理解SU（3）晶格仪理论的有限温度相变很重要，则保持在有限的晶格上，概率分布函数始终为零，除非粒子的数量为3的倍数。对于U（1）lattice Gauge理论，此问题更为严重。当粒子数为非零时，概率分布将变为零。此问题与问题基本相同，即使用有限体积计算时，Polyakov环的期望值总是为零。在这项研究中，我们提出了解决此问题的解决方案。我们还提出了一种避免符号问题的方法，这是使用中心对称性在有限密度下的重要问题。对于用大量费米子的U（1）晶格量规理论，实际上进行了数值模拟，我们证明，可以通过本研究中提出的方法计算有限密度的概率分布函数。此外，讨论了该方法在QCD中的应用。
We study the nature of the phase transition of lattice gauge theories at high temperature and high density by focusing on the probability distribution function, which represents the probability that a certain density will be realized in a heat bath. The probability distribution function is obtained by creating a canonical partition function fixing the number of particles from the grand partition function. However, if the Z_3 center symmetry, which is important for understanding the finite temperature phase transition of SU(3) lattice gauge theory, is maintained on a finite lattice, the probability distribution function is always zero, except when the number of particles is a multiple of 3. For U(1) lattice gauge theory, this problem is more serious. The probability distribution becomes zero when the particle number is nonzero. This problem is essentially the same as the problem that the expectation value of the Polyakov loop is always zero when calculating with finite volume. In this study, we propose a solution to this problem. We also propose a method to avoid the sign problem, which is an important problem at finite density, using the center symmetry. In the case of U(1) lattice gauge theory with heavy fermions, numerical simulations are actually performed, and we demonstrate that the probability distribution function at a finite density can be calculated by the method proposed in this study. Furthermore, the application of this method to QCD is discussed.
