Multifractal dimensions for critical random matrix ensembles

• Published in: Europhysics letters Vol. 98; no. 3; p. 37006
• Main Authors: Méndez-Bermúdez, J. A., Alcázar-López, A., Varga, Imre
• Format: Journal Article
• Language: English
• Published: EPS, SIF, EDP Sciences and IOP Publishing 01.05.2012
• Subjects: 05.45.Df; 71.30.+h
• ISSN: 0295-5075; 1286-4854
• DOI: 10.1209/0295-5075/98/37006

Based on heuristic arguments we conjecture that an intimate relation exists between the eigenfunction multifractal dimensions Dq of the eigenstates of critical random matrix ensembles Dq′≈qDq[q′ +(q− q′ )Dq]−1, 1⩽q⩽2. We verify this relation by extensive numerical calculations. We also demonstrate that the level compressibility χ describing level correlations can be related to Dq in a unified way as Dq=(1− χ)[1+(q−1)χ]−1, thus generalizing existing relations with relevance to the disorder-driven Anderson transition.