Anderson Localization on the Bethe Lattice using Cages and the Wegner Flow
- Creators
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Savitz, Samuel
- Peng, Changnan
- Refael, Gil
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.
Additional Information
© 2019 American Physical Society. Received 17 June 2019; revised manuscript received 28 August 2019; published 16 September 2019. Thanks to Evert van Nieuwenburg, Yuval Baum, Stefan Kehrein, and Matthew Heydeman for fruitful discussions, and to Konstantin Tikhonov, Gabriel Lemarié, Steven Thompson, and our two anonymous referees for their feedback and suggestions regarding our preprint. This work was supported by the Institute for Quantum Information and Matter (IQIM), a National Science Foundation (NSF) frontier center partially funded by the Gordon and Betty Moore Foundation. S.S. was funded by Grant No. DGE-1745301 from the NSF Graduate Research Fellowship. C.P. thanks the Caltech Student–Faculty Programs office and the Blinkenberg family for their support. G.R. acknowledges the generous support of the Packard Foundation and the IQIM. The numerical Wegner flows were implemented using floating-point matrices calculated by the open-source linear algebra library ARMADILLO [114].Attached Files
Published - PhysRevB.100.094201.pdf
Submitted - 1904.07252.pdf
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Additional details
- Eprint ID
- 94979
- Resolver ID
- CaltechAUTHORS:20190425-135640601
- Institute for Quantum Information and Matter (IQIM)
- Gordon and Betty Moore Foundation
- NSF Graduate Research Fellowship
- DGE-1745301
- David and Lucile Packard Foundation
- Created
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2019-04-25Created from EPrint's datestamp field
- Updated
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2021-11-16Created from EPrint's last_modified field
- Caltech groups
- Institute for Quantum Information and Matter