Anderson localization on the Bethe lattice using cages and the Wegner flow

Samuel Savitz, Changnan Peng, and Gil Refael
Phys. Rev. B 100, 094201 – Published 16 September 2019

Abstract

Anderson localization on treelike graphs such as the Bethe lattice, Cayley tree, or random regular graphs has attracted attention due to its apparent mathematical tractability, hypothesized connections to many-body localization, and the possibility of nonergodic extended regimes. This behavior has been conjectured to also appear in many-body localization as a “bad metal” phase, and constitutes an intermediate possibility between the extremes of ergodic quantum chaos and integrable localization. Despite decades of research, a complete consensus understanding of this model remains elusive. Here we use cages, maximally treelike structures from extremal graph theory; and numerical continuous unitary Wegner flows of the Anderson Hamiltonian to develop an intuitive picture which, after extrapolating to the infinite Bethe lattice, appears to capture ergodic, nonergodic extended, and fully localized behavior.

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  • Received 17 June 2019
  • Revised 28 August 2019

DOI:https://doi.org/10.1103/PhysRevB.100.094201

©2019 American Physical Society

Physics Subject Headings (PhySH)

Condensed Matter, Materials & Applied Physics

Authors & Affiliations

Samuel Savitz1,*, Changnan Peng1,2,†, and Gil Refael1,‡

  • 1Institute for Quantum Information and Matter, Department of Physics, California Institute of Technology, Pasadena, California 91125, USA
  • 2Department of Physics, Massachusetts Institute of Technology, Cambridge, Massachusetts 02139, USA

  • *Sam@Savitz.org
  • CnPeng@MIT.edu
  • Refael@Caltech.edu

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Issue

Vol. 100, Iss. 9 — 1 September 2019

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