Universal and non-universal features of the multifractality exponents of critical wave-functions

Abstract

We calculate perturbatively the multifractality spectrum of wave-functions in critical random matrix ensembles in the regime of weak multifractality. We show that in the leading order the spectrum is universal, while the higher order corrections are model-specific. Explicit results for the anomalous dimensions are derived in the power-law and ultrametric random matrix ensembles.

9 pages

References in corpus (2)

• Exact relations between multifractal exponents at the Anderson transition
• The supersymmetry method of random matrix theory

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