Anderson Localization for a Class of Models with a Sign-Indefinite Single-Site Potential via Fractional Moment Method

Alexander Elgart, Martin Tautenhahn, Ivan Veselić

Research output: Contribution to journalArticlepeer-review

21 Scopus citations

Abstract

A technically convenient signature of Anderson localization is exponential decay of the fractional moments of the Green function within appropriate energy ranges. We consider a random Hamiltonian on a lattice whose randomness is generated by the sign-indefinite single-site potential, which is however sign-definite at the boundary of its support. For this class of Anderson operators, we establish a finite-volume criterion which implies that the fractional moment decay property holds. This constructive criterion is satisfied at typical perturbative regimes, e. g. at spectral boundaries which satisfy "Lifshitz tail estimates" on the density of states and for sufficiently strong disorder. We also show how the fractional moment method facilitates the proof of exponential (spectral) localization for such random potentials.

Original languageEnglish
Pages (from-to)1571-1599
Number of pages29
JournalAnnales Henri Poincare
Volume12
Issue number8
DOIs
StatePublished - 1 Dec 2011
Externally publishedYes

ASJC Scopus subject areas

  • Statistical and Nonlinear Physics
  • Nuclear and High Energy Physics
  • Mathematical Physics

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