Local two-body parent Hamiltonians for the entire Jain sequence

Using an algebra of second quantized operators, we develop local two-body parent Hamiltonians for all unprojected Jain states at filling factor $n\mathrm{/}(2n\mathsf{p}+1)$, with integer $n$, and (half-)integer $\mathsf{p}$. We rigorously establish that these states are uniquely stabilized and that zero mode counting reproduces mode counting in the associated edge conformal field theory. We further establish an associated “entangled Pauli principle” describing these states and associated zero mode spaces, as well as an emergent SU($n$) symmetry.