Incompressibility Estimates for the Laughlin Phase

Autor(en)

Nicolas Rougerie, Jakob Yngvason

Abstrakt

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.

Organisation(en)

Mathematische Physik, Forschungsplattform Internationales Erwin Schrödinger Institut für Mathematik und Physik

Externe Organisation(en)

Université Joseph-Fourier (Grenoble-I)

Journal

Communications in Mathematical Physics

Band

336

Seiten

1109-1140

Anzahl der Seiten

32

ISSN

0010-3616

DOI

https://doi.org/10.1007/s00220-014-2232-5

Publikationsdatum

12-2014

Peer-reviewed

Ja

ÖFOS 2012

103019 Mathematische Physik

ASJC Scopus Sachgebiete

Statistical and Nonlinear Physics, Mathematical Physics

Link zum Portal

https://ucrisportal.univie.ac.at/de/publications/15cc1f75-d5a3-4751-9739-2948994f9a0a