Universal Distribution of Would-be Topological Zero Modes in Coupled Chiral Systems

TL;DR

This paper studies the universal distribution of near-zero modes in coupled chiral systems, revealing that their distribution follows a finite size chiral Gaussian ensemble with a width scaling as the inverse square root of volume.

Contribution

It introduces a universal distribution for would-be zero modes in coupled chiral systems, linking topology and coupling effects through effective field theory analysis.

Findings

Distribution of near-zero modes is universal.

Width of the distribution scales as inverse square root of volume.

Coupling links topological zero modes across systems.

Abstract

We consider two quenched, chiral ensembles which are coupled in such a way that a combined chiral symmetry is preserved. The coupling also links the topology of the two systems such that the number of exact zero modes in the coupled system equals the sum of the number of zero modes in the two uncoupled systems counted with sign. The canceled modes that turn non-topological due to the coupling become near-zero modes at small coupling. We analyze the distribution of these would-be zero modes using effective field theory. The distribution is universal and, in the limit of small coupling, the would-be zero modes are distributed according to a finite size chiral Gaussian ensemble, where the width of the distribution scales as the inverse square root of the volume.