Perturbative criteria for Anderson localization in long-ranged 1D tight-binding models
| dc.creator | Akhanjee, Shimul | |
| dc.date | 2008-10-24 | |
| dc.date.accessioned | 2026-07-07T10:13:06Z | |
| dc.date.available | 2026-07-07T10:13:06Z | |
| dc.description | We develop an alternative scaling approach to determine the criteria for Anderson localization in one-dimensional tight-binding models with random site energies having a bandwidth that decays as a power law in space, $H_{ij} \propto |i - j|^{-α}$. At the first order in perturbation theory the scale dependence of the exchange-narrowed energy of the disorder is compared to the energy level spacing of the ideal system to establish whether or not the disorder has a perturbative effect on the Bloch states. We find that at $α=1$, the perturbative condition is satisfied and for sufficiently weak disorder strength all states are extended. For $α> 1$, all states are localized for arbitrary disorder strength, in agreement with the earlier renormalization group treatment by Levitov. | |
| dc.description | 4 Pages, 1 eps figure | |
| dc.identifier | https://arxiv.org/abs/0810.4532 | |
| dc.identifier | http://arxiv.org/abs/0810.4532 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/172413 | |
| dc.subject | Disordered Systems and Neural Networks | |
| dc.title | Perturbative criteria for Anderson localization in long-ranged 1D tight-binding models | |
| dc.type | text |