Eigenfunction distribution for the Rosenzweig-Porter model

Abstract

The statistical distribution of eigenfunctions for the Rosenzweig-Porter model is derived for the region where eigenfunctions have fractal behaviour. The result is based on simple physical ideas and leads to transparent explicit formulas which agree very well with numerical calculations. It constitutes a rare case where a non-trivial eigenfunction distribution is obtained in a closed form.

arXiv comment5 pages, 4 figures

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Cited by in corpus (44)

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• Robustness of delocalization to the inclusion of soft constraints in long-range random models
• Critical properties of the Anderson transition in random graphs: two-parameter scaling theory, Kosterlitz-Thouless type flow and many-body localization
• From ergodic to non-ergodic chaos in Rosenzweig-Porter model
• Emergent fractal phase in energy stratified random models
• Power-law random banded matrices and ultrametric matrices: eigenvector distribution in the intermediate regime
• On super-Poissonian behavior of the Rosenzweig-Porter model in the non-ergodic extended regime
• Non-Hermitian Rosenzweig-Porter random-matrix ensemble: Obstruction to the fractal phase
• Flat-band-based multifractality in the all-band-flat diamond chain
• Tuning the phase diagram of a Rosenzweig-Porter model with fractal disorder
• Sensitivity of (multi)fractal eigenstates to a perturbation of the Hamiltonian
• Multifractal phase in the weighted adjacency matrices of random Erdös-Rényi graphs
• Eigenvalue Statistics for Generalized Symmetric and Hermitian Matrices
• Experimental test of the Rosenzweig-Porter model for the transition from Poisson to Gaussian unitary ensemble statistics
• Robust non-ergodicity of ground state in the $\beta$ ensemble
• Anatomy of the eigenstates distribution: a quest for a genuine multifractality
• Dynamical Signatures of Chaos to Integrability Crossover in $2\times 2$ Generalized Random Matrix Ensembles
• Reducing dynamical fluctuations and enforcing self-averaging by opening many-body quantum systems
• Large scale behavior of the energy spectra of the quantum random antiferromagnetic Ising chain with mixed transverse and longitudinal fields
• The Rosenzweig Porter model revisited for the three Wigner Dyson symmetry classes
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• Multifractality in the interacting disordered Tavis-Cummings model
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• Investigating finite-size effects in random matrices by counting resonances
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• Quantum logarithmic multifractality
• Free Probability approach to spectral and operator statistics in Rosenzweig-Porter random matrix ensembles
• Refined cyclic renormalization group in Russian Doll model
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• Localization and fractality in disordered Russian Doll model