Generalized Quantum Hall Projection Hamiltonians

Certain well known quantum Hall states including the Laughlin states, the Moore-Read Pfaf- fian, and the Read-Rezayi Parafermion states can be defined as the unique lowest degree symmet- ric analytic function that vanishes as at least p powers as some number (g+1) of particles approach the same point. 

Analogously, these same quantum Hall states can be generated as the exact highest density zero energy state of simple angular momentum projection operators. Following this theme we determine the highest density zero energy state for many other values of p and g.