Spectral study of a chiral limit without chiral condensate

TL;DR

This study investigates the Dirac spectrum of the 2-flavour Schwinger model without a chiral condensate, revealing unexpected scale-invariant spectral properties that challenge traditional Random Matrix Theory predictions.

Contribution

It provides the first detailed analysis of the Dirac spectrum in a model lacking a chiral condensate, showing deviations from standard RMT expectations.

Findings

Confirmed the RMT prediction for level spacing distribution

Observed a scale-invariant parameter proportional to λV^{5/8}

Identified a microscopic spectral density proportional to λ_1^{3/5}

Abstract

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.