Level spacings at the metal-insulator transition in the Anderson Hamiltonians and multifractal random matrix ensembles

Shinsuke M. Nishigaki

doi:10.1103/physreve.59.2853

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Level spacings at the metal-insulator transition in the Anderson Hamiltonians and multifractal random matrix ensembles

Shinsuke M. Nishigaki

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Abstract

We consider orthogonal, unitary, and symplectic ensembles of random matrices with (1/a)(ln x)^2 potentials, which obey spectral statistics different from the Wigner-Dyson and are argued to have multifractal eigenstates. If the coefficient $a$ is small, spectral correlations in the bulk are universally governed by a translationally invariant, one-parameter generalization of the sine kernel. We provide analytic expressions for the level spacing distribution functions of this kernel, which are hybrids of the Wigner-Dyson and Poisson distributions. By tuning the single parameter, our results can be excellently fitted to the numerical data for three symmetry classes of the three-dimensional Anderson Hamiltonians at the metal-insulator transition, previously measured by several groups using exact diagonalization.

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Shinsuke M. Nishigaki. 1999-01-14. Level spacings at the metal-insulator transition in the Anderson Hamiltonians and multifractal random matrix ensembles. https://doi.org/10.1103/physreve.59.2853

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