[Landau ITP Seminars] Friday 05.04.2019

[Serge Krashakov]

Уважаемые сотрудники ИТФ,

В пятницу 5 апреля состоится коллоквиум, на котором будет заслушан доклад:

Владимир Кравцов
*Correlation-induced localization*

Conventional Anderson localization is due to destructive interference of 
matter waves described by local random Hamiltonians. Correlations in 
random diagonal elements of such a Hamiltonian are known to favor 
delocalization. Recently systems with non-local Hamiltonians become 
experimentally accessible. We consider two families of such random 
matrix Hamiltonians with correlations in the long-range hopping terms 
and demonstrate that localization is enhanced and the wave function 
ergodicity is progressively degrading as the correlations become 
stronger. We review the localization/delocalization criteria of Mott and 
Anderson and show that the former is the sufficient criterion of weak 
ergodicity and the latter is the sufficient criterion of localization. 
The fact that these two criteria are not complimentary is the reason why 
the non-ergodic extended (multifractal) states may exist when neither 
the Mott, nor the Anderson criterion is fulfilled.
We suggest a new class of random matrix models (Toeplitz RMT) with 
translation-invariant hopping integrals and identify the character of 
eigenfunction and eigenvalue statistics in them. We formulate the 
principles of level statistics if the type of eigenfunction statistics 
is known both in the coordinate and in the momentum basis and 
demonstrate that for the Toeplitz RMT the ergodic delocalization in the 
coordinate space may coexist with the Poisson level statistics.
Finally, we suggest a matrix-inversion trick that allows to identify 
uniquely the type of eigenfunction statistics and prove the absence of 
delocalized states in the bulk of spectrum of long-range Hamiltonians 
with deterministic (fully correlated) hopping.

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