Long-range spectral statistics of the Rosenzweig-Porter model

Abstract

The Rosenzweig-Porter model is a single-parameter random matrix ensemble that supports an ergodic, fractal, and localized phase. The names of these phases refer to the properties of the (midspectrum) eigenstates. This work focuses on the long-range spectral statistics of the recently introduced unitary equivalent of this model. By numerically studying the Thouless time obtained from the spectral form factor, it is argued that long-range spectral statistics can be used to probe the transition between the ergodic and the fractal phases. The scaling of the Thouless time as a function of the model parameters is found to be similar to the scaling of the spreading width of the eigenstates. Provided that the transition between the fractal and the localized phases can be probed through short-range level statistics, such as the average ratio of consecutive level spacings, this work establishes that spectral statistics are sufficient to probe both transitions present in the phase diagram.

8 pages, 3 figures

References in corpus (19)

• Anderson Transitions
• Localization of interacting fermions at high temperature
• The distribution of the ratio of consecutive level spacings in random matrix ensembles
• Many-body localization in periodically driven systems
• A Floquet Model for the Many-Body Localization Transition
• From non-ergodic eigenvectors to local resolvent statistics and back: a random matrix perspective
• Dynamical phases in a "multifractal" Rosenzweig-Porter model
• The Lévy-Rosenzweig-Porter random matrix ensemble
• Eigenvectors under a generic perturbation: non-perturbative results from the random matrix approach
• Non-Hermitian Rosenzweig-Porter random-matrix ensemble: Obstruction to the fractal phase
• Scale-Invariant Survival Probability at Eigenstate Transitions
• Absence of Mobility Edge in Short-range Uncorrelated Disordered Model: Coexistence of Localized and Extended States
• Scale-invariant critical dynamics at eigenstate transitions
• Localization challenges quantum chaos in the finite two-dimensional Anderson model
• Tuning the phase diagram of a Rosenzweig-Porter model with fractal disorder
• On the Spectral Form Factor for Random Matrices
• Spectral statistics of a minimal quantum glass model
• Experimental test of the Rosenzweig-Porter model for the transition from Poisson to Gaussian unitary ensemble statistics
• Anatomy of the eigenstates distribution: a quest for a genuine multifractality

Cited by in corpus (8)

• The Rosenzweig Porter model revisited for the three Wigner Dyson symmetry classes
• Free Probability approach to spectral and operator statistics in Rosenzweig-Porter random matrix ensembles
• Power-law banded random matrix ensemble as a model for quantum many-body Hamiltonians
• Efficient circular Dyson Brownian motion algorithm
• The Wishart--Rosenzweig--Porter random matrix ensemble
• Relaxation Fluctuations of Correlation Functions: Spin and Random Matrix Models
• Higher-Order Krylov State Complexity in Random Matrix Quenches
• Many-body spectral transitions through the lens of the variable-range SYK2 model