| Issue |
EPL
Volume 116, Number 3, November 2016
|
|
|---|---|---|
| Article Number | 37002 | |
| Number of page(s) | 6 | |
| Section | Condensed Matter: Electronic Structure, Electrical, Magnetic and Optical Properties | |
| DOI | https://doi.org/10.1209/0295-5075/116/37002 | |
| Published online | 09 December 2016 | |
Eigenvectors under a generic perturbation: Non-perturbative results from the random matrix approach
School of Mathematical Sciences, University of Nottingham - Nottingham NG7 2RD, UK
Received: 12 September 2016
Accepted: 21 November 2016
We consider eigenvectors of the Hamiltonian H0 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 H0. Further we generalise them to the case of a random H0, focusing, in particular, on the Rosenzweig-Porter model. Our analytical predictions are confirmed by numerical simulations.
PACS: 72.15.Rn – Localization effects (Anderson or weak localization) / 05.45.Mt – Quantum chaos; semiclassical methods / 71.30.+h – Metal-insulator transitions and other electronic transitions
© EPLA, 2016
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