Theory of Four-dimensional Fractional Quantum Hall States

TL;DR

This paper introduces a Hamiltonian for generalized four-dimensional fractional quantum Hall states, revealing their incompressible liquid nature and vortex-like excitations with fractional charges in a higher-dimensional space.

Contribution

It formulates an exact Hamiltonian for Zhang-Hu's four-dimensional fractional quantum Hall states, characterizing their excitations and incompressibility.

Findings

Exact pseudo-potential Hamiltonian derived for 4D FQH states

Excitations are vortex-like objects with fractional charges

States exhibit properties of an incompressible liquid

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.