2014
DOI: 10.1103/physrevlett.113.046806
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Anderson Localization on the Bethe Lattice: Nonergodicity of Extended States

Abstract: Statistical analysis of the eigenfunctions of the Anderson tight-binding model with on-site disorder on regular random graphs strongly suggests that the extended states are multifractal at any finite disorder. The spectrum of fractal dimensions f (α) defined in Eq.(3), remains positive for α noticeably far from 1 even when the disorder is several times weaker than the one which leads to the Anderson localization, i.e. the ergodicity can be reached only in the absence of disorder. The oneparticle multifractalit… Show more

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Cited by 274 publications
(383 citation statements)
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“…It is not presently clear whether or not the stretched-exponential effective interactions that occur at putative critical points within the MBL phase [9,14,21,22] substantially modify the above story. Also, our analysis of near-transition behavior assumes that the delocalized phase is thermal, and thus may not apply to hypothesized transitions between an MBL phase and a nonthermal delocalized phase [47][48][49].…”
Section: Discussionmentioning
confidence: 99%
“…It is not presently clear whether or not the stretched-exponential effective interactions that occur at putative critical points within the MBL phase [9,14,21,22] substantially modify the above story. Also, our analysis of near-transition behavior assumes that the delocalized phase is thermal, and thus may not apply to hypothesized transitions between an MBL phase and a nonthermal delocalized phase [47][48][49].…”
Section: Discussionmentioning
confidence: 99%
“…[45,46]. This delocalized non-ergodic scenario is usually explained within the point of view that the MBL transition is somewhat similar to an Anderson Localization transition in the Hilbert space of 'infinite dimensionality' as a consequence of the exponential growth of the size of the Hilbert space with the volume [47][48][49][50][51][52][53]. Note however that the existence of a non-ergodic delocalized phase remains very controversial even for Random-Regular-Graphs that are locally tree-like without boundaries, as shown by the two very recent studies with opposite conclusions [54,55].…”
Section: Introductionmentioning
confidence: 99%
“…These effects cause an overestimate of the stability of the MBL phase, which actually becomes unstable to thermalization earlier only at much longer length scales. Note that an interesting alternate possibility is the existence of an intermediate phase between the ETH and MBL phase, with neither thermal nor area-law entanglement [64][65][66], which we do not pursue further. This onset of thermalization at high order is what one would expect from a long lengthscale delocalization mechanism.…”
mentioning
confidence: 99%