Flat bands supporting non-Abelian phases via local 2-body interaction

Since Laughlin's ansatz for the state at 1/3 filling, it has been known that much of the essential character of fractional quantum Hall physics is captured by the order of the zeros in the ground-state wavefunction which occur when two particles meet. While in first quantization these so-called analytic clustering conditions form an infinite set of constraints on the space of holomorphic sections, recent work on generalized and entangled Pauli-principles demonstrate an equivalence to finitely many relations on the second quantized operator algebra for certain classes of fractional quantum hall states. As I will discuss, this simplification holds for several parton states with known, two-body-interacting parent Hamiltonians, opening the door to non-Abelian anyons in models with few degrees of freedom.