Multifractal dimensions for critical random matrix ensembles

Abstract

Based on heuristic arguments we conjecture that an intimate relation exists between the eigenfunction multifractal dimensions $D_q$ of the eigenstates of critical random matrix ensembles $D_{q^{\prime }}\approx q{D}_q[q^{\prime }+(q-q^{\prime })D_q{]}^{-1}$, $1\le q\le 2$. We verify this relation by extensive numerical calculations. We also demonstrate that the level compressibility $\chi$ describing level correlations can be related to $D_q$ in a unified way as $D_q=(1-\chi )[1+(q-1)\chi {]}^{-1}$, thus generalizing existing relations with relevance to the disorder driven Anderson--transition.

6 pages, 9 figures

References in corpus (10)

• Anderson Transitions
• Exact relations between multifractal exponents at the Anderson transition
• The Quantum Hall Transition in Real Space: From Localized to Extended States
• Eigenfunction entropy and spectral compressibility for critical random matrix ensembles
• Dynamical scaling for critical states: is Chalker's ansatz valid for strong fractality?
• Perturbation approach to multifractal dimensions for certain critical random matrix ensembles
• Multifractal dimensions for all moments for certain critical random matrix ensembles in the strong multifractality regime
• Multifractality and intermediate statistics in quantum maps
• Scattering at the Anderson transition: Power--law banded random matrix model
• Universal and non-universal features of the multifractality exponents of critical wave-functions

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