Parent-Hamiltonians for any Jain composite fermion state

Jain's composite fermion (CF) picture is a remarkable generalization of Laughlin's wavefunction, explaining a great many observed quantum Hall plateaux and associated low energy spectra in a unified approach. A solvable local Hamiltonian that stabilizes these states, however, is lacking in almost all cases, unlike for Laughlin states and many other seemingly more complicated (non-Abelian) fractional quantum Hall states. Here we resolve this issue by departing from the usual construction scheme of quantum Hall parent Hamiltonians, which emphasizes analytic clustering properties. Based on a recent recursion relation for unprojected CF states, and an associated operator algebra of ``zero mode generators'', we construct a class of universal two-body pseudo-potentials in the presence of Landau level mixing that can be used to construct local parent Hamiltonians uniquely stabilizing Jain states for any filling fraction of the form n/(2 p n+1). The structure of the resulting zero mode spaces is governed by an ``entangled Pauli principle'', and zero mode counting agrees with the expected (multiple branch) free chiral boson edge conformal field theory.