Divergent chiral condensate in the quenched Schwinger model

TL;DR

This paper numerically investigates the eigenvalue distribution of the overlap Dirac operator in the quenched Schwinger model, revealing a divergent chiral condensate and contrasting behavior when reweighting for N_f=1, highlighting issues with quenched approximation.

Contribution

It provides the first detailed numerical analysis of the eigenvalue distribution in the quenched Schwinger model, demonstrating the divergence of the chiral condensate and the impact of reweighting for N_f=1.

Findings

Eigenvalue distribution does not match universality classes of spontaneous chiral symmetry breaking.

Chiral condensate in quenched theory is ill-defined and divergent.

Reweighting with the Dirac determinant yields a well-behaved eigenvalue distribution consistent with explicit symmetry breaking.

Abstract

We calculate numerically the eigenvalue distribution of the overlap Dirac operator in the quenched Schwinger model on a lattice. The distribution does not fit any of the three universality classes of spontaneous chiral symmetry breaking, and its strong volume dependence indicates that the chiral condensate in the quenched theory is an ill-defined and divergent quantity. When we reweight configurations with the Dirac determinant to study the theory with N_f=1, we obtain a distribution of eigenvalues that is well-behaved and consistent with the theory of explicit symmetry breaking due to the anomaly.