Theory of Four-dimensional Fractional Quantum Hall States

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.

arXiv comment4 pages

References in corpus (7)

• Dissipationless Quantum Spin Current at Room Temperature
• A Four Dimensional Generalization of the Quantum Hall Effect
• The Eight Dimensional Quantum Hall Effect and the Octonions
• Noncommutative Gauge Theory on Fuzzy Four-Sphere and Matrix Model
• Effective field theory description of the higher dimensional quantum Hall liquid
• Higher-Dimensional Quantum Hall Effect in String Theory
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Cited by in corpus (3)

• Fractionalized Metals and Superconductors in Three Dimensions
• Fractional Quantum Hall States on CP2 Space
• Deconfined Fractionally Charged Excitation in Any Dimensions