Bloch Jacques, Wettig Tilo
Institute for Theoretical Physics, University of Regensburg, 93040 Regensburg, Germany.
Phys Rev Lett. 2006 Jul 7;97(1):012003. doi: 10.1103/PhysRevLett.97.012003.
We show how to introduce a quark chemical potential in the overlap Dirac operator. The resulting operator satisfies a Ginsparg-Wilson relation and has exact zero modes. It is no longer gamma5 Hermitian, but its nonreal eigenvalues still occur in pairs. We compute the spectral density of the operator on the lattice and show that, for small eigenvalues, the data agree with analytical predictions of non-Hermitian chiral random matrix theory for both trivial and nontrivial topology. We also explain an observed change in the number of zero modes as a function of chemical potential.
我们展示了如何在重叠狄拉克算子中引入夸克化学势。所得算子满足金斯帕格 - 威尔逊关系且具有精确的零模。它不再是γ5厄米的，但其非实本征值仍成对出现。我们计算了该算子在格点上的谱密度，并表明，对于小本征值，数据与非厄米手征随机矩阵理论对于平凡和非平凡拓扑的解析预测相符。我们还解释了观察到的零模数量作为化学势函数的变化。
