Институт теоретической физики им. Л.Д. Ландау РАН

L.D. Landau Institute for Theoretical Physics RAS

L.D. Landau Institute for Theoretical Physics RAS

"Quantum Fluids, Quantum Field Theory, and Gravity"

Anderson localization and ergodic transitions in the log-normal Rosenzweig-Porter random matrix ensemble

Date/Time: 12:10 18-Oct-2019

Abstract:

It has been recently shown [1] that the $N*N$ generalized Rosenzweig-Porter random matrix model [2] can be in three distinctly different phases: ergodic, fractal and localized, depending on the scaling parameter \gamma in the variance $N^{-\gamma}$ of the i.i.d. Gaussian off-diagonal matrix elements. Several models of disordered systems can be reduced to the logarithmically-normal Rosenzweig-Porter ensemble in which i.i.d. off-diagonal matrix elements have a log-normal distribution with the variance proportional to $\ln N$, while the diagonal matrix elements remain Gaussian distributed with the variance 1. In this case the typical and the averaged values of off-diagonal matrix elements have different scaling with $N$. In the present work we address the question how the tailed distributions of this type alter the phases and phase transitions in the eigenvector statistics.

[1] V. E. Kravtsov, I. M. Khaymovich, E. Cuevas and M. Amini, A random matrix model with localization and ergodic transitions, New J. Phys. 17, 122002 (2015)

[2] N. Rosenzweig and C. E. Porter, "Repulsion of energy levels" in complex atomic spectra, Phys. Rev. 120, 1698 (1960)

[1] V. E. Kravtsov, I. M. Khaymovich, E. Cuevas and M. Amini, A random matrix model with localization and ergodic transitions, New J. Phys. 17, 122002 (2015)

[2] N. Rosenzweig and C. E. Porter, "Repulsion of energy levels" in complex atomic spectra, Phys. Rev. 120, 1698 (1960)

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