Fractality of wave functions on a Cayley tree: Difference between tree and locally treelike graph without boundary

K. S. Tikhonov, A. D. Mirlin

Research output: Contribution to journalArticlepeer-review

59 Citations (Scopus)

Abstract

We investigate analytically and numerically eigenfunction statistics in a disordered system on a finite Bethe lattice (Cayley tree). We show that the wave-function amplitude at the root of a tree is distributed fractally in a large part of the delocalized phase. The fractal exponents are expressed in terms of the decay rate and the velocity in a problem of propagation of a front between unstable and stable phases. We demonstrate a crucial difference between a loopless Cayley tree and a locally treelike structure without a boundary (random regular graph) where extended wave functions are ergodic.

Original languageEnglish
Article number184203
JournalPhysical Review B
Volume94
Issue number18
DOIs
Publication statusPublished - 2016
Externally publishedYes

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