Dynamical phases in a ``multifractal'' Rosenzweig-Porter model
Abstract
We consider the static and dynamic phases in a Rosenzweig-Porter (RP) random matrix ensemble with the tailed distribution of off-diagonal matrix elements of the form of the large-deviation ansatz. We present a general theory of survival probability in such a random-matrix model and show that the averaged survival probability may decay with time as the simple exponent, as the stretch-exponent and as a power-law or slower. Correspondingly, we identify the exponential, the stretch-exponential and the frozen-dynamics phases. As an example, we consider the mapping of the Anderson model on Random Regular Graph (RRG) onto the "multifractal" RP model and find exact values of the stretch-exponent κ depending on box-distributed disorder in the thermodynamic limit. As another example we consider the logarithmically-normal RP (LN-RP) random matrix ensemble and find analytically its phase diagram and the exponent κ. In addition, our theory allows to compute the shift of apparent phase transition lines at a finite system size and show that in the case of RP associated with RRG and LN-RP with the same symmetry of distribution function of hopping, a finite-size multifractal "phase" emerges near the tricritical point which is also the point of localization transition.
- Publication:
-
SciPost Physics
- Pub Date:
- August 2021
- DOI:
- 10.21468/SciPostPhys.11.2.045
- arXiv:
- arXiv:2106.01965
- Bibcode:
- 2021ScPP...11...45K
- Keywords:
-
- Condensed Matter - Disordered Systems and Neural Networks;
- Mathematical Physics;
- Quantum Physics
- E-Print:
- 31 pages, 8 figures, 73 references + 10 pages, 5 figures in Appendices and references