Spread of wave packets in disordered hierarchical lattices

Abstract

We consider the spreading of the wave packet in the generalized Rosenzweig-Porter random matrix ensemble in the region of non-ergodic extended states $1<\gamma <2$. We show that despite non-trivial fractal dimensions $0<D_q=2-\gamma <1$ characterize wave function statistics in this region, the wave packet spreading $⟨r^2⟩\propto t^{\beta }$ is governed by the "diffusion" exponent $\beta =1$ outside the ballistic regime $t>\tau \sim 1$ and $⟨r^2⟩\propto t^2$ in the ballistic regime for $t<\tau \sim 1$. This demonstrates that the multifractality exhibits itself only in {\it local} quantities like the wave packet survival probability but not in the large-distance spreading of the wave packet.

Accepted in EPL

References in corpus (3)

• Anderson Transitions
• From non-ergodic eigenvectors to local resolvent statistics and back: a random matrix perspective
• Levy flights and multifractality in quantum critical diffusion and in classical random walks on fractals

Cited by in corpus (23)

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• The Lévy-Rosenzweig-Porter random matrix ensemble
• Non-Ergodic Delocalization in the Rosenzweig-Porter Model
• Multifractality without fine-tuning in a Floquet quasiperiodic chain
• Robustness of delocalization to the inclusion of soft constraints in long-range random models
• From ergodic to non-ergodic chaos in Rosenzweig-Porter model
• Level compressibility for the Anderson model on regular random graphs and the eigenvalue statistics in the extended phase
• Critical-to-Insulator Transitions and Fractality Edges in Perturbed Flatbands
• Flat-band-based multifractality in the all-band-flat diamond chain
• Scaling up the Anderson transition in random-regular graphs
• Fully localized and partially delocalized states in the tails of Erdös-Rényi graphs in the critical regime
• Multifractal phase in the weighted adjacency matrices of random Erdös-Rényi graphs
• Spectral statistics of a minimal quantum glass model
• Dynamical Signatures of Chaos to Integrability Crossover in $2\times 2$ Generalized Random Matrix Ensembles
• Critical dynamics of long-range quantum disordered systems
• Power-law banded random matrix ensemble as a model for quantum many-body Hamiltonians
• Anomalous energy correlations and spectral form factor in the nonergodic phase of the $\beta$-ensemble
• Circular Rosenzweig-Porter random matrix ensemble
• The Wishart--Rosenzweig--Porter random matrix ensemble
• Replica approach to the generalized Rosenzweig-Porter model