Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: A random matrix model with localization and ergodic transitions   Motivated by the problem of Many-Body Localization and the recent numerical
results for the level and eigenfunction statistics on the random regular
graphs, a generalization of the Rosenzweig-Porter random matrix model is
suggested that possesses two localization transitions as the parameter $\gamma$
of the model varies from 0 to $\infty$. One of them is the Anderson transition
from the localized to the extended states that happens at $\gamma=2$. The other
one at $\gamma=1$ is the transition from the extended non-ergodic
(multifractal) states to the extended ergodic states similar to the eigenstates
of the Gaussian Orthogonal Ensemble. We computed the two-level spectral
correlation function, the spectrum of multifractality $f(\alpha)$ and the wave
function overlap which all show the transitions at $\gamma=1$ and $\gamma=2$.

5
The categories of this paper are: gr-qc
28
The categories of this paper are: alg-geom
34
The categories of this paper are: chem-ph
13
The categories of this paper are: quant-ph
21
The categories of this paper are: adap-org
20
The categories of this paper are: acc-phys
17
The categories of this paper are: q-fin
26
The categories of this paper are: bayes-an
31
The categories of this paper are: ao-sci
35
The categories of this paper are: mtrl-th
12
The categories of this paper are: nucl-th
11
The categories of this paper are: hep-lat
14
The categories of this paper are: math-ph
19
The categories of this paper are: eess
37
The categories of this paper are: supr-con
6
The categories of this paper are: astro-ph