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We review the state of the art on the delocalized non-ergodic regime of the Anderson model on Bethe lattices.
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A. De Luca and A. Scardicchio, Europhysics Letters 101
2013
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A. De Luca, B. L. Altshuler, V. E. Kravtsov, and A. Scardicchio, Phys. Rev. Lett. 113
2014
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V. Bapst, G. Semerjian, J. Stat. Phys. 145
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2014
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2004
Cited alongside, same era.
D. M. Basko, I. L. Aleiner, and B. L. Altshuler, Annals of Physics 321
2006
Cited alongside, same era.
Interestingly, it is rigorously known that that random Schrödinger operator on the so-called canopy graph (i.e., an infinite tree that represents a n g → ∞ n_{g}\rightarrow\infty limit of a sequence of Cayley trees of radius n g n_{g} from the perspective of a boundary site) have pure-point spectrum for any strength of disorder [see M. Aizenman and S. Warzel, Mathematical Physics, Analysis and Geometry 9
2006
Cited alongside, same era.
E. Cuevas and V. E. Kravtsov, Phys. Rev. B 76
2007
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V. Oganesyan, D. Huse, Phys. Rev. B 75
2007
Cited alongside, same era.
H. Hu, A. Strybulevych, J. H. Page, S. E. Skipetrov, B. A. van Tiggelen, Nat. Phys. 4
2008
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V. E. Kravtsov, I.M . Khaymovich, E. Cuevas, M. Amini, New Journal of Physics 17
2015
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B. L. Altshuler, E. Cuevas, L. B. Ioffe, V. E. Kravtsov, Phys. Rev. Lett. 117
2016
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D. Facoetti, P. Vivo, G. Biroli, EPL (Europhysics Letters), 115
2016
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K. S. Tikhonov, A. D. Mirlin, M. A. Skvortsov, Phys. Rev. B 94
2016
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E. Tarquini, G. Biroli, and M. Tarzia, Phys. Rev. Lett. 116
2016
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E Tarquini, G Biroli, M Tarzia, Phys. Rev. B 95
2017
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K. S. Tikhonov and A. D. Mirlin, Phys. Rev. B 94
2017
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I. Garcia-Mata, O. Giraud, B. Georgeot, J. Martin, R. Dubertrand, G. Lemarié, Phys. Rev. Lett. 118
2017
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F. L. Metz and I. Pérez Castillo, Phys. Rev. B 96
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G. Biroli and M. Tarzia, Phys. Rev. B 96
2017
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R. Bauerschmidt, J. Huang, A. Knowles, and H.-T. Yau, Ann. Probab. 45
2017
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V. E. Kravtsov, B. L. Altshuler, L. B. Ioffe, Annals of Physics 389
2018
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