Extreme value statistics of Schmidt eigenvalues reveal deviations from Wishart behavior in ergodic eigenstates of ultrametric random matrices and the Quantum Sun model.
Universal and non-universal features of the multifractality exponents of critical wave-functions
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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.
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How Random Are Ergodic Eigenstates of the Ultrametric Random Matrices and the Quantum Sun Model?
Extreme value statistics of Schmidt eigenvalues reveal deviations from Wishart behavior in ergodic eigenstates of ultrametric random matrices and the Quantum Sun model.