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We show that non-interacting disordered electrons on a Bethe lattice display a new intermediate phase which is delocalized but non-ergodic, i.e.
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Localization was studied on both Cayley trees and Bethe lattices. The formers might display some spurious behavior due to the peculiarity of having a finite fraction of sites on the boundary, as shown in [ 17 ] for the level statistics. Whether the delocalized non-ergodic phase found in this work for Bethe lattices also shows up for Cayley trees is a question worth addressing
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For W = W T W=W_{T} we expect P ( r ) P(r) to converge to a universal distribution different from GOE and Poisson
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M. Aizenman, S. Warzel, arXiv:1104.0969
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