From non-ergodic eigenvectors to local resolvent statistics and back: A random matrix perspective

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Abstract

We study the statistics of the local resolvent and non-ergodic properties of eigenvectors for a generalised Rosenzweig-Porter N × N random matrix model, undergoing two transitions separated by a delocalised non-ergodic phase. Interpreting the model as the combination of onsite random energies {ai} and a structurally disordered hopping, we found that each eigenstate is delocalised over N2-γ sites close in energy |aj - ai| ≤ N1-γ 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.

Original languageEnglish
Article number47003
Number of pages8
JournalEUROPHYSICS LETTERS
Volume115
Issue number4
Early online date27 Sept 2016
DOIs
Publication statusE-pub ahead of print - 27 Sept 2016

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