Matrix oscillator and Laughlin Hall states

Details Matrix oscillator and Laughlin Hall states Matrix oscillator and Laughlin Hall states

2004-12-07

arxiv.org/abs/hep-th/0412068v2

Phys.Lett. A351 (2006) 246-250

Physics

High Energy Physics

High Energy Physics - Theory

18 pages, no figures, LaTex; revised version, to appear in Phys.Lett.A

Scientific paper

10.1016/j.physleta.2005.11.008

We propose a quantum matrix oscillator as a model that provides the construction of the quantum Hall states in a direct way. A connection of this model to the regularized matrix model introduced by Polychronakos is established . By transferring the consideration to the Bargmann representation with the help of a particular similarity transformation, we show that the quantum matrix oscillator describes the quantum mechanics of electrons in the lowest Landau level with the ground state described by the Laughlin-type wave function. The equivalence with the Calogero model in one dimension is emphasized. It is shown that the quantum matrix oscillator and the finite matrix Chern-Simons model have the same spectrum on the singlet state sector.

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