## Dynamical phases in a ``multifractal'' Rosenzweig-Porter model

Ivan M. Khaymovich, Vladimir E. Kravtsov

SciPost Phys. 11, 045 (2021) · published 31 August 2021

- doi: 10.21468/SciPostPhys.11.2.045
- Submissions/Reports

### Abstract

We consider the static and the dynamic phases in a Rosenzweig-Porter (RP) random matrix ensemble with a 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 {\it averaged} survival probability may decay with time as a simple exponent, as a 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 localization model on Random Regular Graph onto the RP model and find exact values of the stretch-exponent $\kappa$ in the thermodynamic limit. As another example we consider the logarithmically-normal RP random matrix ensemble and find analytically its phase diagram and the exponent $\kappa$. Our theory allows to describe analytically the finite-size multifractality and to compute the critical length with the exponent $\nu_{MF}=1$ associated with it.

### Cited by 7

### Authors / Affiliations: mappings to Contributors and Organizations

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^{1}^{2}Ivan Khaymovich, -
^{3}^{4}Vladimir Kravtsov

^{1}Max-Planck-Institut für Physik komplexer Systeme / Max Planck Institute for the Physics of Complex Systems^{2}Российская академия наук / Russian Academy of Science [RAS]^{3}Centro Internazionale di Fisica Teorica Abdus Salam / Abdus Salam International Centre for Theoretical Physics [ICTP]^{4}Институт теоретической физики им. Л. Д. Ландау / Landau Institute for Theoretical Physics