Volume 115, Number 4, August 2016
|Number of page(s)||7|
|Section||Condensed Matter: Electronic Structure, Electrical, Magnetic and Optical Properties|
|Published online||27 September 2016|
From non-ergodic eigenvectors to local resolvent statistics and back: A random matrix perspective
1 Department of Mathematics, King's College London - Strand, London WC2R 2LS, UK
2 IPhT, CEA/DSM-CNRS/URA 2306, CEA Saclay - F-91191 Gif-sur-Yvette Cedex, France
3 Laboratoire de Physique Statistique, Ecole Normale Supérieure, PSL Research University, Université Paris Diderot Sorbonne Paris-Cité, Sorbonne Universités UPMC Université Paris 06, CNRS 24 rue Lhomond, F-75005 Paris, France
Received: 27 July 2016
Accepted: 7 September 2016
We study the statistics of the local resolvent and non-ergodic properties of eigenvectors for a generalised Rosenzweig-Porter random matrix model, undergoing two transitions separated by a delocalised non-ergodic phase. Interpreting the model as the combination of on-site random energies and a structurally disordered hopping, we found that each eigenstate is delocalised over sites close in energy in agreement with Kravtsov et al. (New J. Phys., 17 (2015) 122002). Our other main result, obtained combining a recurrence relation for the resolvent matrix with insights from Dyson's Brownian motion, is to show that the properties of the non-ergodic delocalised phase can be probed studying the statistics of the local resolvent in a non-standard scaling limit.
PACS: 72.15.Rn – Localization effects (Anderson or weak localization) / 71.30.+h – Metal-insulator transitions and other electronic transitions / 05.30.-d – Quantum statistical mechanics
© EPLA, 2016
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