• DOI:10.21468/SciPostPhys.11.2.045
• Corpus ID: 235313320

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

@article{Khaymovich2021DynamicalPI,
  title={Dynamical phases in a ``multifractal'' Rosenzweig-Porter model},
  author={Ivan M Khaymovich and Vladimir E. Kravtsov},
  journal={SciPost Physics},
  year={2021}
}

• Ivan M Khaymovich, V. Kravtsov
• Published 3 June 2021
• Mathematics
• SciPost Physics

We consider the static and the dynamical 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 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 \kappaκ
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 \kappaκ.
Our theory allows to describe analytically the finite-size
multifractality and to compute the critical length with the exponent
\nu_{MF}=1νMF=1
associated with it.