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arXiv 0909.2241hep-lathep-th
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一个不含手征凝聚的手征极限的谱研究

Spectral study of a chiral limit without chiral condensate

Wolfgang Bietenholz, Ivan Hip

备注：
8 pages, 6 figures, contribution to the XXVII International Symposium on Lattice Field Theory (LAT2009) in Beijing
发表信息：
PoS LAT2009:086,2009
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摘要：

随机矩阵理论（RMT）在场论模型中成功地预言了狄拉克谱。然而，RMT的一般假设是手性极限中的非零手性缩合物$Σ$。在这里，我们考虑2味Schwinger模型，这个假设不成立。我们用动力学重叠超立方体费米子模拟了这个模型，并通过分析狄拉克谱进入了未知领域。通常的RMT预测的展开的能级间距分布在一个酉系综被精确地证实。显微光谱不表现出Banks-Casher平台。相反，明显的期望是增加$\propto λ_{1}^{1/3}$的最低本征值$λ_{1}$的密度。这将对应于尺度不变参数$\propto λV^{3/4}$，然而，这与我们的数据不兼容。相反，我们观察到高精度的尺度不变参数$z \propto λV^{5/8}$。这个令人惊讶的结果意味着微观光谱密度$\propto λ_1^{3/5}$，这仍然有待于根据RMT来理解。

英文摘要：

Random Matrix Theory (RMT) has elaborated successful predictions for Dirac spectra in field theoretical models. However, a generic assumption by RMT has been a non-vanishing chiral condensate $Σ$ in the chiral limit. Here we consider the 2-flavour Schwinger model, where this assumption does not hold. We simulated this model with dynamical overlap hypercube fermions, and entered terra incognita by analysing this Dirac spectrum. The usual RMT prediction for the unfolded level spacing distribution in a unitary ensemble is precisely confirmed. The microscopic spectrum does not perform a Banks-Casher plateau. Instead the obvious expectation is a density of the lowest eigenvalue $λ_{1}$ which increases $\propto λ_{1}^{1/3}$. That would correspond to a scale-invariant parameter $\propto λV^{3/4}$, which is, however, incompatible with our data. Instead we observe to high precision a scale-invariant parameter $z \propto λV^{5/8}$. This surprising result implies a microscopic spectral density $\propto λ_1^{3/5}$, which still remains to be understood in the light of RMT.

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