Localization transition on a Cayley tree via spectral statistics

[摘要] The spectral statistics of a Cayley tree are numerically studied. The statistics are nonuniversal 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 W-c = 11.44+/-0.08 and critical index nu = 0.51+/-0.05. The value of nu fits nicely to its mean-field value, while the value of W-c is puzzling.

[发布日期] 2003-11-01

[关键词] METAL-INSULATOR-TRANSITION;ANDERSON TRANSITION;DISORDERED-SYSTEMS;CRITICAL-BEHAVIOR;BETHE LATTICE;MODEL;SYMMETRY;POINT