CP_N Solitons in Quantum Hall Systems

Abstract

We will present here an elementary pedagogical introduction to $C{P}_N$ solitons in quantum Hall systems. We begin with a brief introduction to both $C{P}_N$ models and to quantum Hall (QH) physics. Then we focus on spin and layer-spin degrees of freedom in QH systems and point out that these are in fact $C{P}_N$ fields for N=1 and N=3. Excitations in these degrees of freedom will be shown to be topologically non-trivial soliton solutions of the corresponding $C{P}_N$ field equations. This is followed by a brief summary of our own recent work in this area, done with Sankalpa Ghosh. [ Invited Plenary Lecture at the International Conference on Geometry, Integrability and Nonlinearity in Condensed Matter & Soft Condensed Matter Physics held at Bansko, Bulgaria, July 15-20, 2001. ]

Standard revtex format, 18 pages, no figures

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• Soliton surfaces associated with CP^{N-1} sigma models
• The Painlevé property of $\mathbb{C}{P}^{N-1}$ sigma models
• Structural equations of supermanifolds immersed in the superspace ${\mathcal{M}}^{(3|2)}(c)$ with a prescribed curvature
• Analysis of $C{P}^{N-1}$ sigma models via projective structure
• The $\mathfrak{su}(2)$ spin $s$ representations via $\mathbb{C}{P}^{2s}$ sigma models