Anderson Localization on the Bethe Lattice using Cages and the Wegner Flow
| Autor: | Savitz, Samuel, Peng, Changnan, Refael, Gil |
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| Rok vydání: | 2019 |
| Předmět: | |
| Zdroj: | Phys. Rev. B 100, 094201 (2019) |
| Druh dokumentu: | Working Paper |
| DOI: | 10.1103/PhysRevB.100.094201 |
| Popis: | 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. Comment: 12 pages, 5 figures, Comments welcome |
| Databáze: | arXiv |
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