Entangled Pauli Principles: the DNA of Quantum Hall Fluids

A formalism is developed for the rigorous study of solvable fractional quantum Hall parent Hamiltonians with Landau level mixing. The idea of organization through ``generalized Pauli principles''
is expanded to allow for root level entanglement, giving rise to ``entangled Pauli principles''. Through the latter, aspects of the effective field theory description become ingrained in exact microscopic solutions for a great wealth of phases for which no similar single Landau level description is known.
We discuss in detail rigorous zero mode counting, edge theory, and braiding statistics for the Jain-221 state as derived from a microscopic Hamiltonian. The relevant root-level entanglement is found to feature an AKLT-type MPS structure related to an emergent SU(2) symmetry.