Strong eigenfunction correlations near the Anderson localization transition

TL;DR

This paper investigates the correlations between different eigenfunctions near the Anderson localization transition, revealing that their mutual overlaps remain significant, which explains the robustness of level statistics in extended states.

Contribution

It provides new insights into eigenfunction overlaps near the Anderson transition using an infinite-dimensional disordered model, highlighting their implications for level statistics.

Findings

Eigenfunction overlaps are comparable to self-overlap near the transition.

Mutual overlaps remain significant for energy separations below a critical value.

Results support the robustness of Wigner-Dyson level statistics in extended states.

Abstract

We study overlap of two different eigenfunctions as compared with self-overlap in the framework of an infinite-dimensional version of the disordered tight-binding model. Despite a very sparse structure of the eigenstates in the vicinity of Anderson transition their mutual overlap is still found to be of the same order as self-overlap as long as energy separation is smaller than a critical value. The latter fact explains robustness of the Wigner-Dyson level statistics everywhere in the phase of extended states. The same picture is expected to hold for usual d-dimensional conductors, ensuring the $s^{\beta}$ form of the level repulsion at critical point.