CMSP Seminar @ICTP Wednesday 28 Sept. at 11:00 a.m. - L.Stasi Seminar Room - V.E. Kravtsov

[Condensed Matter Section]

Condensed Matter & Statistical Physics Seminar
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Wednesday 28 September at 11.00 a.m.
Luigi Stasi Seminar Room, first floor, ICTP Leonardo Building

Vladimir E. KRAVTSOV
ICTP, Trieste

'Multifractal States in a Self-Consistent Theory of Localization:
Analytical Solution'

Abstract:

We consider disordered tight-binding models which Green's functions obey 
the self-consistent  cavity equations. Based on these equations and the 
replica trick with the one-step replica symmetry breaking, we derive an 
analytical expression for the  fractal dimension D_{1} that 
distinguishes between the extended ergodic (D_{1}=1), and extended 
non-ergodic (multifractal) (0<D_{1}<1) states and prove the existence of 
the latter in a broad range of parameters as well as existence of 
transitions between the extended ergodic and extended non-ergodic 
states. The results are applied to the systems with local tree structure 
(random regular graphs) and to the systems with infinite connectivity 
(Rosenzweig-Poter random matrix theory). They are potentially important 
for the problem of many-body localization, as the Fock space of 
interacting systems has a local tree structure. The non-ergodic extended 
phase in the many-body systems would imply a new state of matter in 
which usual Boltzmann statistics does not apply as in MBL phases and 
which in many respects is similar to the glass.