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Strong eigenfunction correlations near the Anderson localization transition

Yan V. Fyodorov·Alexander D. Mirlin
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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 $s^β$ form of the level repulsion at critical point.

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Yan V. Fyodorov, Alexander D. Mirlin. 1996-12-24. Strong eigenfunction correlations near the Anderson localization transition. https://doi.org/10.1103/physrevb.55.r16001

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