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• W3171163182 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 {it 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 $kappa$ 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 $kappa$. 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." @default.
• W3171163182 created "2021-06-22" @default.
• W3171163182 creator A5032462289 @default.
• W3171163182 creator A5043826016 @default.
• W3171163182 date "2021-08-31" @default.
• W3171163182 modified "2023-09-30" @default.
• W3171163182 title "Dynamical phases in a ``multifractal'' Rosenzweig-Porter model" @default.
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• W3171163182 doi "https://doi.org/10.21468/scipostphys.11.2.045" @default.
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