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Theory of Four-dimensional Fractional Quantum Hall States

Chyh-Hong Chern
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Abstract

We propose a pseudo-potential Hamiltonian for the Zhang-Hu's generalized fractional quantum Hall states to be the exact and unique ground states. Analogously to Laughlin's quasi-hole (quasi-particle), the excitations in the generalized fractional quantum Hall states are extended objects. They are vortex-like excitations with fractional charges $+(-)1/m^3$ in the total configuration space CP$^3$. The density correlation function of the Zhang-Hu states indicates that they are incompressible liquid.

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Chyh-Hong Chern. 2006-08-28. Theory of Four-dimensional Fractional Quantum Hall States. https://doi.org/10.1016/j.aop.2006.11.011

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