Dynamical phases in a ``multifractal'' RosenzweigPorter model
Abstract
We consider the static and dynamic phases in a RosenzweigPorter (RP) random matrix ensemble with the tailed distribution of offdiagonal matrix elements of the form of the largedeviation ansatz. We present a general theory of survival probability in such a randommatrix model and show that the averaged survival probability may decay with time as the simple exponent, as the stretchexponent and as a powerlaw or slower. Correspondingly, we identify the exponential, the stretchexponential and the frozendynamics 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 stretchexponent κ depending on boxdistributed disorder in the thermodynamic limit. As another example we consider the logarithmicallynormal RP (LNRP) 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 LNRP with the same symmetry of distribution function of hopping, a finitesize 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
 EPrint:
 31 pages, 8 figures, 73 references + 10 pages, 5 figures in Appendices and references