"Rare" Fluctuation Effects in the Anderson Model of Localization

TL;DR

This paper investigates how rare fluctuation effects, particularly resonant states, influence eigenstate behavior in the Anderson model of localization, revealing anomalous properties across different disorder regimes and dimensions.

Contribution

It presents numerical evidence of resonant state effects causing anomalous eigenstate behavior in the Anderson model, emphasizing the significance beyond Lifshitz tails and across dimensions.

Findings

Resonant states lead to non-analytic eigenstate properties.

Anomalous behavior occurs for a substantial fraction of eigenstates.

Dimensionality influences the nature of singularities.

Abstract

We discuss the role of rare fluctuation effects in quantum condensed matter systems. In particular, we present recent numerical results of the effect of resonant states in Anderson's original model of electron localization. We find that such resonances give rise to anomalous behavior of eigenstates not just far in the Lifshitz tail, but rather for a substantial fraction of eigenstates, especially for intermediate disorder. The anomalous behavior includes non-analyticity in various properties as a characteristic. The effect of dimensionality on the singularity, which is present in all dimensions, is described, and the behavior for bounded and unbounded disorder is contrasted.