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arXiv · hep-th/0203264

Quantum Hall Effect in Higher Dimensions

Dimitra Karabali·V. P. Nair
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Abstract

Following recent work on the quantum Hall effect on $S^4$, we solve the Landau problem on the complex projective spaces ${\bf C}P^k$ and discuss quantum Hall states for such spaces. Unlike the case of $S^4$, a finite spatial density can be obtained with a finite number of internal states for each particle. We treat the case of ${\bf C}P^2$ in some detail considering both Abelian and nonabelian background fields. The wavefunctions are obtained and incompressibility of the Hall states is shown. The case of ${\bf C}P^3$ is related to the case of $S^4$.

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Dimitra Karabali, V. P. Nair. 2002-03-28. Quantum Hall Effect in Higher Dimensions. https://doi.org/10.1016/s0550-3213(02)00634-x

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