Orateur
Vladimir Kratsov
(ICTP Trieste)
Description
We show that the Anderson model on the random regular graph (RRG) possesses two transitions. One of them is the usual localization transition that happens at the disorder
strength W=W_{c} \approx 18.2 and the other one is the first order transition between the extended ergodic and non-ergodic (multifractal) states. It happens at W=W_{E}\approx 10.0 and manifests itself in the sharp jump in the fractal dimensions D_{1} and D_{2} which is seen at a finite number of sites N>100 000 in the RRG. The results are compared with the calculations of the "Lyapunov exponent" for growing imaginary part of the particle self-energy by the generalized population dynamics method. The results are published as a preprint in arXiv:1605.02295.
