Extreme value statistics of Schmidt eigenvalues reveal deviations from Wishart behavior in ergodic eigenstates of ultrametric random matrices and the Quantum Sun model.
Anderson localization transition and eigenfunction multifractality in ensemble of ultrametric random matrices
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abstract
We demonstrate that by considering disordered single-particle Hamiltonians (or their random matrix versions) on ultrametric spaces one can generate an interesting class of models exhibiting Anderson metal-insulator transition. We use the weak disorder virial expansion to determine the critical value of the parameters and to calculate the values of the multifractal exponents for inverse participation ratios. Direct numerical simulations agree favourably with the analytical predictions.
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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.