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arXiv · 1609.03467

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

Kevin Truong·Alexander Ossipov
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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.

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Kevin Truong, Alexander Ossipov. 2016-09-12. Eigenvectors under a generic perturbation: non-perturbative results from the random matrix approach. https://doi.org/10.1209/0295-5075/116/37002

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