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  • Open Access

Transfer tensor analysis of localization in the Anderson and Aubry-André-Harper models

Michelle C. Anderson* and Chern Chuang†

  • *These authors contributed equally to this work.
  • †Contact author: chern.chuang@unlv.edu
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Phys. Rev. Research 8, 013248 – Published 6 March, 2026

DOI: https://doi.org/10.1103/y49y-7vhp

Abstract

We use the transfer tensor method to analyze localization and transport in simple disordered systems, specifically the Anderson and Aubry-André-Harper models. Emphasis is placed on the memory effects that emerge when ensemble-averaging over disorder, even when individual trajectories are strictly Markovian. We find that transfer tensor memory effects arise to remove fictitious terms that would correspond to redrawing static disorder at each time step, which would create a temporally uncorrelated dynamic disorder. Our results show that while eternal memory is a necessary condition for localization, it is not sufficient. We determine that signatures of localization and transport can be found within the transfer tensors themselves by defining a metric called “outgoing pseudoflux.” This work establishes connections between theoretical research on dynamical maps and Markovianity and localization phenomena in physically realizable model systems.

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Phys. Rev. Research 8, 013248– Published 6 March, 2026
  • Received 13 October 2025
  • Accepted 27 January 2026
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Published by the American Physical Society under the terms of the Creative Commons Attribution 4.0 International license. Further distribution of this work must maintain attribution to the author(s) and the published article's title, journal citation, and DOI.

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