Multi-Scale Jacobi Method for Anderson Localization
John Z. Imbrie
TL;DR
This paper introduces a novel multi-scale Jacobi method that provides a rigorous proof of Anderson localization by demonstrating exponential decay of eigenfunction correlators, with implications for many-body localization.
Contribution
It presents the first multi-scale analysis proof of Anderson localization using a sequence of local rotations to suppress off-diagonal Hamiltonian elements.
Findings
Proves exponential decay of eigenfunction correlators
Establishes strong dynamical localization
Applicable to many-body localization studies
Abstract
A new KAM-style proof of Anderson localization is obtained. A sequence of local rotations is defined, such that off-diagonal matrix elements of the Hamiltonian are driven rapidly to zero. This leads to the first proof via multi-scale analysis of exponential decay of the eigenfunction correlator (this implies strong dynamical localization). The method has been used in recent work on many-body localization [arXiv:1403.7837].
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