Incompressibility Estimates for the Laughlin Phase

Nicolas Rougerie (Korresp. Autor*in), Jakob Yngvason

Veröffentlichungen: Beitrag in FachzeitschriftArtikelPeer Reviewed

Abstract

This paper has its motivation in the study of the Fractional Quantum Hall Effect. We consider 2D quantum particles submitted to a strong perpendicular magnetic field, reducing admissible wave functions to those of the Lowest Landau Level. When repulsive interactions are strong enough in this model, highly correlated states emerge, built on Laughlin’s famous wave function. We investigate a model for the response of such strongly correlated ground states to variations of an external potential. This leads to a family of variational problems of a new type. Our main results are rigorous energy estimates demonstrating a strong rigidity of the response of strongly correlated states to the external potential. In particular, we obtain estimates indicating that there is a universal bound on the maximum local density of these states in the limit of large particle number. We refer to these as incompressibility estimates.
OriginalspracheEnglisch
Seiten (von - bis)1109-1140
Seitenumfang32
FachzeitschriftCommunications in Mathematical Physics
Jahrgang336
Ausgabenummer3
Frühes Online-Datum4 Dez. 2014
DOIs
PublikationsstatusVeröffentlicht - Juni 2015

ÖFOS 2012

  • 103019 Mathematische Physik

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