Effect of boundaries on the spectrum of a one-dimensional random mass Dirac Hamiltonian

TL;DR

This paper derives the average density of states for a one-dimensional Dirac Hamiltonian with random mass on a finite interval, revealing how boundaries influence spectral properties and uncovering a crossover in behavior.

Contribution

It provides an explicit eigenvalue distribution approach to analyze boundary effects on the spectrum of the random mass Dirac Hamiltonian.

Findings

Recovery of Dyson singularity above epsilon_c

Log-normal suppression of DoS below epsilon_c

Explicit eigenvalue distribution method

Abstract

The average density of states (DoS) of the one-dimensional Dirac Hamiltonian with a random mass on a finite interval [0,L] is derived. Our method relies on the eigenvalues distributions (extreme value statistics problem) which are explicitly obtained. The well-known Dyson singularity <rho(epsilon;L)>\sim-L/|epsilon|ln^3|\epsilon| is recovered above the crossover energy epsilon_c\sim exp-sqrt{L}. Below epsilon_c we find a log-normal suppression of the average DoS <rho(epsilon;L)> \sim 1/(|epsilon|sqrt(L))exp(-(ln^2|epsilon|)/L).