Physics – High Energy Physics – High Energy Physics - Lattice
Scientific paper
2009-09-11
PoS LAT2009:086,2009
Physics
High Energy Physics
High Energy Physics - Lattice
8 pages, 6 figures, contribution to the XXVII International Symposium on Lattice Field Theory (LAT2009) in Beijing
Scientific paper
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 $\Sigma$ 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 $\lambda_{1}$ which increases $\propto \lambda_{1}^{1/3}$. That would correspond to a scale-invariant parameter $\propto \lambda V^{3/4}$, which is, however, incompatible with our data. Instead we observe to high precision a scale-invariant parameter $z \propto \lambda V^{5/8}$. This surprising result implies a microscopic spectral density $\propto \lambda_1^{3/5}$, which still remains to be understood in the light of RMT.
Bietenholz Wolfgang
Hip Ivan
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