Incompressibility Estimates for the Laughlin Phase, Part II

Autor(en)

Nicolas Rougerie, Jakob Yngvason

Abstrakt

We consider fractional quantum Hall states built on Laughlin's original N-body wave-functions, i.e., they are of the form holomorphic * gaussian and vanish when two particles come close, with a given polynomial rate. Such states appear naturally when looking for the ground state of 2D particles in strong magnetic fields, interacting via repulsive forces and subject to an external potential due to trapping and/or disorder. We prove that all functions in this class satisfy a universal local density upper bound, in a suitable weak sense. Such bounds are useful to investigate the response of fractional quantum Hall phases to variations of the external potential. Contrary to our previous results for a restricted class of wave-functions, the bound we obtain here is not optimal, but it does not require any additional assumptions on the wave-function, besides analyticity and symmetry of the pre-factor modifying the Laughlin function.

Organisation(en)

Mathematische Physik

Externe Organisation(en)

Université Joseph-Fourier (Grenoble-I)

Journal

Communications in Mathematical Physics

Band

339

Seiten

263-277

Anzahl der Seiten

15

ISSN

0010-3616

DOI

https://doi.org/10.1007/s00220-015-2400-2

Publikationsdatum

10-2015

Peer-reviewed

Ja

ÖFOS 2012

103019 Mathematische Physik

Schlagwörter

ASJC Scopus Sachgebiete

Statistical and Nonlinear Physics, Mathematical Physics

Link zum Portal

https://ucrisportal.univie.ac.at/de/publications/f917d15e-774d-4cd7-b7bd-3ce51c47ba76