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arXiv · 1904.07252

Anderson Localization on the Bethe Lattice using Cages and the Wegner Flow

Samuel Savitz·Changnan Peng·Gil Refael
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Abstract

Anderson localization on tree-like 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 non-ergodic 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 tree-like 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, non-ergodic extended, and fully localized behavior.

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BibTeXRIS

Samuel Savitz, Changnan Peng, Gil Refael. 2019-04-15. Anderson Localization on the Bethe Lattice using Cages and the Wegner Flow. https://doi.org/10.1103/physrevb.100.094201

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