Scaling and the center of band anomaly in a one-dimensional Anderson model with diagonal disorder

TL;DR

This paper investigates the violation of single parameter scaling at zero energy in a 1D Anderson model with diagonal disorder, revealing it as a boundary between bands due to symmetry properties.

Contribution

It clarifies the nature of the zero-energy anomaly by linking it to band boundary effects caused by Hamiltonian symmetry, resolving a longstanding scaling violation issue.

Findings

Zero energy acts as a band boundary in the model.

States near zero energy behave like band boundary states.

The violation of single parameter scaling is explained by symmetry properties.

Abstract

We resolve the problem of the violation of single parameter scaling at the zero energy of the Anderson tight-binding model with diagonal disorder. It follows from the symmetry properties of the tight-binding Hamiltonian that this spectral point is in fact a boundary between two adjacent bands. The states in the vicinity of this energy behave similarly to states at other band boundaries, which are known to violate single parameter scaling.