Topologically-protected delocalization in 1d quantum walks

ORAL

Abstract

Disordered systems in low dimension, which are generically Anderson-localized, can be protected from complete localization by being topologically nontrivial. This occurs, for instance, in the integer quantum Hall effect. Moving beyond static systems, we show that delocalization of eigenstates is a topologically-protected feature of single-particle, discrete-time evolutions (e.g., in quantum walks and Floquet systems) in one spatial dimension. Using spectral flow and flux insertion — appropriately modified for unitary operators instead of Hamiltonians — we argue that any topologically nontrivial time evolution operator must have an extensive number of delocalized states with non-vanishing density throughout the quasienergy spectrum.

*This work used computational and storage services associated with the Hoffman2 Shared Cluster provided by UCLA Institute for Digital Research and Education's Research Technology Group. A.B.C acknowledges financial support from the Joseph P. Rudnick Prize Postdoctoral Fellowship (UCLA). P.S. acknowledges the support of NNSA for the U.S. DoE at LANL under Contract No. DE-AC52-06NA25396, and Laboratory Directed Research and Development (LDRD) for support through 20240032DR. LANL is managed by Triad National Security, LLC, for the National Nuclear Security Administration of the U.S. DOE under contract 89233218CNA000001.

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Publication: Manuscript in preparation

Presenters

  • Adrian B Culver

    • University of California, Los Angeles

Authors

  • Adrian B Culver

    • University of California, Los Angeles

  • Pratik Sathe

    • Los Alamos National Laboratory (LANL)

  • Rithwik Pandey

    • University of California, Los Angeles

  • Rahul Roy

    • University of California, Los Angeles