Manuel Pino (Nanotechnology Group, Universidad de Salamanca)

Correlated volumes for metallic wavefunctions on a random-regular graph

We study the metallic phase of the Anderson model in a random-regular graph, specifically the
degree of ergodicity of the high-energy wavefunctions. We use the multifractal formalism to analyze numerical data for unprecedented large system sizes, obtaining a set of correlated volumes which control finite-size effects. Those volumes grow very fast with disorder strength but show no tendency to diverge, at least in an intermediate metallic regime. Close to the Anderson transitions, we characterize the crossover to system sizes much smaller than the first correlated volume. Once this crossover has taken place, we obtain evidence of a scaling in which the derivative of the first fractal dimension behaves critically with an exponent ν = 1.

The talk is based on the following works:

-  Correlated volumes for extended wavefunctions on a random-regular graph.

M Pino, JE Roman arXiv preprint. ArXiv:2311.07690 (2023)

-  Scaling up the Anderson transition in random-regular graphs.

M Pino. Physical Review Research 2 (4), 042031 (2020)

- From ergodic to non-ergodic chaos in Rosenzweig–Porter model.

M Pino, J Tabanera, P Serna Journal of Physics A: Mathematical and Theoretical 52 (47), 475101 (2019)