Level spacings at the metal-insulator transition in the Anderson Hamiltonians and multifractal random matrix ensembles
Level spacings at the metal-insulator transition in the Anderson Hamiltonians and multifractal random matrix ensembles
We consider orthogonal, unitary, and symplectic ensembles of random matrices with $(1/a)(\mathrm{ln}{x)}^{2}$ 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 …