Non-ergodic delocalization in the Rosenzweig–Porter model

Per von Soosten, Simone Warzel

Research output: Contribution to journalArticlepeer-review

36 Scopus citations

Abstract

We consider the Rosenzweig–Porter model H=V+TΦ, where V is a N× N diagonal matrix, Φ is drawn from the N× N Gaussian Orthogonal Ensemble, and N - 1 ≪ T≪ 1. We prove that the eigenfunctions of H are typically supported in a set of approximately NT sites, thereby confirming the existence of a previously conjectured non-ergodic delocalized phase. Our proof is based on martingale estimates along the characteristic curves of the stochastic advection equation satisfied by the local resolvent of the Brownian motion representation of H.

Original languageEnglish
Pages (from-to)905-922
Number of pages18
JournalLetters in Mathematical Physics
Volume109
Issue number4
DOIs
StatePublished - 3 Apr 2019

Keywords

  • Characteristics
  • Non-ergodicity
  • Resolvent flow
  • Rosenzweig–Porter model

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