Non-abelian parton states from two body interactions on a lattice

Much attention has been given recently to a special class of multi-component fractional quantum Hall states that can be stabilized by solvable two-body interactions and feature excitations with non-abelian statistics. Owing to the simplicity of their parent hamiltonians, these parton states can be rigorously analyzed in terms of clustering conditions and zero-mode counting, even though the presence of higher Landau levels prompts one to resort to a second-quantized treatment, at least in part. The same simplicity might render these states attractive candidates to be realized in quantum simulators, provided that we connect them to appropriate lattice Hamiltonians; this talk will introduce a scheme for developing discrete Hamiltonians that faithfully represent the physics of continuum mixed Landau level fractional quantum Hall states on a lattice.