Spectral Statistics in Chiral-Orthogonal Disordered Systems

TL;DR

This paper investigates the spectral properties and localization phenomena in 2D and 3D chiral symmetric disordered systems with off-diagonal disorder, revealing unique density of states singularities and critical behaviors.

Contribution

It provides a detailed analysis of spectral singularities and level statistics in chiral disordered systems, highlighting differences from non-chiral models and effects of disorder strength.

Findings

Singular density of states in 2D, less pronounced in 3D

Level statistics follow semi-Poisson in 2D and Wigner surmise in 3D

Strong localization with logarithmic disorder and Dyson-like singularities

Abstract

We describe the singularities in the averaged density of states and the corresponding statistics of the energy levels in two- (2D) and three-dimensional (3D) chiral symmetric and time-reversal invariant disordered systems, realized in bipartite lattices with real off-diagonal disorder. For off-diagonal disorder of zero mean we obtain a singular density of states in 2D which becomes much less pronounced in 3D, while the level-statistics can be described by semi-Poisson distribution with mostly critical fractal states in 2D and Wigner surmise with mostly delocalized states in 3D. For logarithmic off-diagonal disorder of large strength we find indistinguishable behavior from ordinary disorder with strong localization in any dimension but in addition one-dimensional $1/|E|$ Dyson-like asymptotic spectral singularities. The off-diagonal disorder is also shown to enhance the propagation of two interacting particles similarly to systems with diagonal disorder. Although disordered models with chiral symmetry differ from non-chiral ones due to the presence of spectral singularities, both share the same qualitative localization properties except at the chiral symmetry point E=0 which is critical.