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Multi-Scale Jacobi Method for Anderson Localization

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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 (Imbrie in On many-body localization for quantum spin chains, arXiv:1403.7837, 2014).

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Authors and Affiliations

  1. Department of Mathematics, University of Virginia, Charlottesville, VA, 22904-4137, USA

    John Z. Imbrie

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  1. John Z. Imbrie
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Correspondence to John Z. Imbrie.

Additional information

Communicated by M. Salmhofer

This research was conducted in part while the author was visiting the Institute for Advanced Study in Princeton, supported by The Fund for Math and The Ellentuck Fund.

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Imbrie, J.Z. Multi-Scale Jacobi Method for Anderson Localization. Commun. Math. Phys. 341, 491–521 (2016). https://doi.org/10.1007/s00220-015-2522-6

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  • DOI: https://doi.org/10.1007/s00220-015-2522-6

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