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

### Submission summary

 As Contributors: Ivan Khaymovich Preprint link: scipost_202106_00010v1 Date submitted: 2021-06-07 16:15 Submitted by: Khaymovich, Ivan Submitted to: SciPost Physics Academic field: Physics Specialties: Condensed Matter Physics - Theory Quantum Physics Approaches: Theoretical, Computational

### 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.

###### Current status:
Editor-in-charge assigned

### Submission & Refereeing History

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Submission scipost_202106_00010v1 on 7 June 2021