Volume 116, Number 3, November 2016
|Number of page(s)||6|
|Section||Condensed Matter: Electronic Structure, Electrical, Magnetic and Optical Properties|
|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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