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

Savitz, Samuel and Peng, Changnan and Refael, Gil (2019) Anderson Localization on the Bethe Lattice using Cages and the Wegner Flow. . (Unpublished)

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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.

Item Type:Report or Paper (Discussion Paper)
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URLURL TypeDescription Paper
Savitz, Samuel0000-0003-2112-3758
Additional Information:Thanks to Evert van Nieuwenburg, Yuval Baum, Stefan Kehrein, and Matthew Heydeman for fruitful discussions. 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 double-precision floating-point matrices calculated by the open-source linear algebra library Armadillo. [106]
Group:IQIM, Institute for Quantum Information and Matter
Funding AgencyGrant Number
Institute for Quantum Information and Matter (IQIM)UNSPECIFIED
Gordon and Betty Moore FoundationUNSPECIFIED
NSF Graduate Research FellowshipDGE-1745301
David and Lucile Packard FoundationUNSPECIFIED
Record Number:CaltechAUTHORS:20190425-135640601
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Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:94979
Deposited By: Tony Diaz
Deposited On:25 Apr 2019 21:00
Last Modified:25 Apr 2019 21:00

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