Study of the Localization Transition on a Cayley-tree via Spectral Statistics
arXiv:cond-mat/0303526 · doi:10.1103/PhysRevB.68.193102
Abstract
The spectral statistics of a Cayley-tree is numerically studied. The statistics are non-universal due to the high ratio of boundary sites. Once the boundary sites are connected to each other in a way that preserves the local structure of the tree the universal statistics of the spectra is recovered. A clear localization transition is observed as function of on-site disorder strength, with a critical disorder and critical index . The value of fits nicely to its mean field value, while the value of is puzzling.
arXiv comment3 pages, 5 figures
References in corpus (4)
- Boundary conditions at the mobility edge
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- Topology dependent quantities at the Anderson transition
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- Quantum Walks on Trees with Disorder: Decay, Diffusion, and Localization
- Spectral analysis of deformed random networks
- The Large Connectivity Limit of the Anderson Model on Tree Graphs
- Two-dimensional quantum breakdown model with Krylov subspace many-body localization
- Entanglement Entropy on the Cayley Tree