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

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\...

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Bibliographic Details
Published inarXiv.org
Main Authors Truong, Kevin, Ossipov, Alexander
Format Paper Journal Article
LanguageEnglish
Published Ithaca Cornell University Library, arXiv.org 12.12.2016
Subjects
Computer simulation
Eigenvectors
Mathematical models
Mathematics - Mathematical Physics
Perturbation methods
Physics - Disordered Systems and Neural Networks
Physics - Mathematical Physics
Physics - Quantum Physics
Physics - Statistical Mechanics
Supersymmetry
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Summary: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.
ISSN:2331-8422
DOI:10.48550/arxiv.1609.03467