Quasi-localized states in disordered metals and non-analyticity of the level curvature distribution function

TL;DR

This paper investigates how quasi-localized states in disordered metals cause non-analytic behavior in the distribution of level curvatures, revealing a connection to wave function multifractality across different dimensions.

Contribution

It demonstrates the link between non-analytic level curvature distributions and wave function multifractality in disordered systems of various dimensions.

Findings

In 2D systems, P(K) has a branching point at K=0.

In quasi-1D systems, non-analyticity at K=0 is very weak.

In 3D metals, non-analyticity at K=0 is absent.

Abstract

It is shown that the quasi-localized states in weakly disordered systems can lead to the non-analytical distribution of level curvatures. In 2D systems the distribution function P(K) has a branching point at K=0. In quasi-1D systems the non-analyticity at K=0 is very weak, and in 3D metals it is absent at all. Such a behavior confirms the conjecture that the branching at K=0 is due to the multi-fractality of wave functions and thus is a generic feature of all critical eigenstates. The relationsip between the branching power and the multi-fractality exponent $\eta(2)$ is derived.