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Topological Entanglement and Clustering of Jain Hierarchy States
We obtain the clustering properties and part of the structure of zeroes of the Jain states at filling $\frac{k}{2k+1}$: they are a direct product of a Vandermonde determinant (which has to exist for any fermionic state) and a bosonic polynomial at filling $\frac{k}{k+1}$ which vanishes when $k+1$ particles cluster together. …