Eigenvectors under a generic perturbation: non-perturbative results from the random matrix approach

Abstract

We consider eigenvectors of the Hamiltonian $H_0$ perturbed by a generic perturbation $V$ modelled by a random matrix from the Gaussian Unitary Ensemble (GUE). Using the supersymmetry approach we derive analytical results for the statistics of the eigenvectors, which are non-perturbative in $V$ and valid for an arbitrary deterministic $H_0$. Further we generalise them to the case of a random $H_0$, focusing, in particular, on the Rosenzweig-Porter model. Our analytical predictions are confirmed by numerical simulations.

6 pages, 4 figures

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• Multifractality without fine-tuning in a Floquet quasiperiodic chain
• Robustness of delocalization to the inclusion of soft constraints in long-range random models
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• Flat-band-based multifractality in the all-band-flat diamond chain
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