QCD in one dimension at nonzero chemical potential
QCD in one dimension at nonzero chemical potential
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非零化学势下的一维 QCD
DOI：
10.1103/physrevd.76.054506
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发表时间：
2007
影响因子：
5
通讯作者：
J. Verbaarschot
中科院分区：
文献类型：
--
作者：
L. Ravagli;J. Verbaarschot
利用Conrey， Farmer和Zirnbauer最近导出的积分公式，我们计算了一维交错晶格QCD作用的费米子行列式的相位因子的期望值。我们证明了化学势可以被吸收到夸克质量中；在零化学势的三维空间中，该理论与QCD属于相同的手性对称类。在色数较多和格点数目固定的极限下，手性对称性被自发打破，所得结果与基于手性拉格朗日量的表达式一致。在此极限下，根据QCD的随机矩阵理论，在三维空间中将Dirac算子的特征值关联起来。手性凝聚体的不连续是由于最近发现的四维非零化学势下QCD的Banks-Casher公式的另一种选择。在一个原理图随机矩阵模型中讨论了温度对平均相位因子的影响。
Using an integration formula recently derived by Conrey, Farmer, and Zirnbauer, we calculate the expectation value of the phase factor of the fermion determinant for the staggered lattice QCD action in one dimension. We show that the chemical potential can be absorbed into the quark masses; the theory is in the same chiral symmetry class as QCD in three dimensions at zero chemical potential. In the limit of a large number of colors and fixed number of lattice points, chiral symmetry is broken spontaneously, and our results are in agreement with expressions based on a chiral Lagrangian. In this limit, the eigenvalues of the Dirac operator are correlated according to random matrix theory for QCD in three dimensions. The discontinuity of the chiral condensate is due to an alternative to the Banks-Casher formula recently discovered for QCD in four dimensions at nonzero chemical potential. The effect of temperature on the average phase factor is discussed in a schematic random matrix model.