Power-law random banded matrices and ultrametric matrices: eigenvector distribution in the intermediate regime

Abstract

The power-law random banded matrices and the ultrametric random matrices are investigated numerically in the regime where eigenstates are extended but all integer matrix moments remain finite in the limit of large matrix dimensions. Though in this case standard analytical tools are inapplicable, we found that in all considered cases eigenvector distributions are extremely well described by the generalised hyperbolic distribution which differs considerably from the usual Porter-Thomas distribution but shares with it certain universal properties.

arXiv comment20 pages, 12 figures

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• The Lévy-Rosenzweig-Porter random matrix ensemble
• Multifractality meets entanglement: relation for non-ergodic extended states
• Multifractality and its role in anomalous transport in the disordered XXZ spin-chain
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• Localization transition on the Random Regular Graph as an unstable tricritical point in a log-normal Rosenzweig-Porter random matrix ensemble
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• Entanglement of midspectrum eigenstates of chaotic many-body systems: Reasons for deviation from random ensembles
• Scale-invariant critical dynamics at eigenstate transitions
• Out of equilibrium Phase Diagram of the Quantum Random Energy Model
• Anisotropy-mediated reentrant localization
• Fully localized and partially delocalized states in the tails of Erdös-Rényi graphs in the critical regime
• Spectral statistics of a minimal quantum glass model
• The Rosenzweig Porter model revisited for the three Wigner Dyson symmetry classes
• Approaching Thouless Energy and Griffiths Regime in Random Spin Systems By Singular Value Decomposition
• Power-Law Random Banded Matrix Ensemble as the Effective Model for Many-Body Localization Transition
• Emergent multifractality in power-law decaying eigenstates
• Delocalization and continuous spectrum for ultrametric random operators
• Characterizing quantum chaoticity of kicked spin chains
• Quantum logarithmic multifractality
• Power-law banded random matrix ensemble as a model for quantum many-body Hamiltonians
• Many-body spectral transitions through the lens of the variable-range SYK2 model