Quantum Hall Droplets on Disc and Effective Wess-Zumino-Witten Action for Edge States

Abstract

We algebraically analysis the quantum Hall effect of a system of particles living on the disc ${\mathbf{B}}^1$ in the presence of an uniform magnetic field $B$. For this, we identify the non-compact disc with the coset space $SU(1,1)/U(1)$. This allows us to use the geometric quantization in order to get the wavefunctions as the Wigner $\mathcal{D}$-functions satisfying a suitable constraint. We show that the corresponding Hamiltonian coincides with the Maass Laplacian. Restricting to the lowest Landau level, we introduce the noncommutative geometry through the star product. Also we discuss the state density behavior as well as the excitation potential of the quantum Hall droplet. We show that the edge excitations are described by an effective Wess-Zumino-Witten action for a strong magnetic field and discuss their nature. We finally show that LLL wavefunctions are intelligent states.

arXiv comment18 pages, clarifications and misprints corrected, version published in IJGMMP

References in corpus (5)

• Conformal Symmetry and Universal Properties of Quantum Hall States
• Quantum Hall Effect on Higher Dimensional Spaces
• W_{\infty} Gauge Transformations and the Electromagnetic Interactions of Electrons in the Lowest Landau Level
• Field theory of anyons in the lowest Landau level
• Effective Wess-Zumino-Witten Action for Edge States of Quantum Hall Systems on Bergman Ball

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• Symplectic Fluctuations for Electromagnetic Excitations of Hall Droplets
• Electromagnetic Excitations of A_n Quantum Hall Droplets
• Noncommutative scalar fields from symplectic deformation
• Electromagnetic Excitations of Hall Systems on Four Dimensional Space