Minimal order in a variety of fractional quantum Hall settings

In this talk I will demonstrate how to prove a lower bound on the number of anyons that a gapped fractional quantum Hall (FQH) state must possess. This provides a lower bound on the ground state degeneracy on a torus of such a state, creating a useful tool for exact diagonalization studies. I will discuss how this tool has already been used to constrain the possible topological orders found in the three-quarter filled fermionic FQH state. I will close with a discussion of possible extensions of this proof to the exciting setting of fractional Chern insulators/fractional quantum anlomalous Hall states, recently observed in a number of two-dimensional Van der Waals materials.