Abstract
Exponential decay of eigenfunctions and of their correlators is shown to occur in two Anderson models on the lattice of arbitrary dimension, with summable decay of infinite-range correlations of the random potential. For the proof, we check the applicability of the Fractional Moment Method.
Highlights
This paper focuses on the localization phenomena in correlated disordered quantum systems on a lattice Zd, d ≥ 1
Aiming to prove Anderson localization in a lattice model via the Fractional Moment Method (FMM; cf. [3, 4]) they examined the regularity of the single-point probability distribution of the potential at an arbitrary point x ∈ Zd conditional on all remaining values {V (y; ω), y ∈ Zd \ {y}}
We show that a solution of the technical problems arising in an attempt to prove Anderson localization for nonlocal alloys, when a fast decay of the eigenfunction correlators (EFCs) is sought, is frustratingly simple for at least
Summary
This paper focuses on the localization phenomena in correlated disordered quantum systems on a lattice Zd, d ≥ 1. Aiming to prove Anderson localization in a lattice model via the Fractional Moment Method (FMM; cf [3, 4]) they examined the regularity of the single-point probability distribution of the potential at an arbitrary point x ∈ Zd conditional on all remaining values {V (y; ω), y ∈ Zd \ {y}}.
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