Correlation of eigenstates in the critical regime of quantum Hall systems

• Published in: Journal of physics. Condensed matter Vol. 8; no. 38; pp. 7147 - 7159
• Main Authors: Pracz, Krystian, Janssen, Martin, Freche, Peter
• Format: Journal Article
• Language: English
• Published: Bristol IOP Publishing 16.09.1996; Institute of Physics
• Subjects: Condensed matter: electronic structure, electrical, magnetic, and optical properties; Electron states; Electronic structure and electrical properties of surfaces, interfaces, thin films and low-dimensional structures; Electronic transport in interface structures; Exact sciences and technology; Physics; Quantum hall effect (including fractional); Theories and models of many electron systems; Eigenstates; Scaling laws; Theoretical study; Quantum Hall effect; Wave functions; Multifractal system; Critical exponents
• ISSN: 0953-8984; 1361-648X
• DOI: 10.1088/0953-8984/8/38/017

We extend the multifractal analysis of the statistics of critical wave functions in quantum Hall systems by calculating numerically the correlations of local amplitudes corresponding to eigenstates at two different energies. Our results confirm multifractal scaling relations which are different from those occurring in conventional critical phenomena. The critical exponent corresponding to the typical amplitude, [Formula: see text], gives an almost complete characterization of the critical behaviour of eigenstates, including correlations. Our results support the interpretation of the local density of states being an order parameter of the Anderson transition.