Density of states in coupled chains with off-diagonal disorder

TL;DR

This paper analyzes the density of states in coupled chains with off-diagonal disorder, revealing parity-dependent singularities at zero energy and how symmetry affects these features.

Contribution

It provides a detailed calculation of the zero-energy density of states in coupled disordered chains, highlighting the impact of chain number parity and symmetry on spectral singularities.

Findings

Odd N chains have a density of states proportional to 1/(E (ln|E|)^3).

Even N chains exhibit a logarithmic divergence or pseudogap depending on symmetry.

Zero-energy spectral singularities depend critically on the parity of the number of chains.

Abstract

We compute the density of states (d.o.s.) in N coupled chains with random hopping. At zero energy, the d.o.s. shows a singularity that strongly depends on the parity of N. For odd N, the d.o.s. is proportional to 1/(E (\ln |E|)^3), with and without time-reversal symmetry. For even N, the d.o.s. is proportional to \ln |E| in the presence of time-reversal symmetry, while there is a pseudogap, d.o.s. proportional to E \ln |E|, in the absence of time-reversal symmetry.