Spectral study of a chiral limit without chiral condensate

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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