Chiral gapped states are universally non-topological

We propose an operator generalization of the Li-Haldane conjecture regarding the entanglement Hamiltonian of a disk in a 2+1D chiral gapped groundstate. The logic applies to regions with sharp corners, from which we derive several universal properties regarding corner entanglement. These universal properties follow from a set of locally-checkable conditions on the wavefunction. We also define a quantity \(mathfrak{c}_tot\)_min that reflects the robustness of corner entanglement contributions, and show that it provides an obstruction to a gapped boundary. One reward from our analysis is that we can construct a local gapped Hamiltonian within the same chiral gapped phase from a given wavefunction; we conjecture that it is closer to the low-energy renormalization group fixed point than the original parent Hamiltonian. Our analysis of corner entanglement reveals the emergence of a universal conformal geometry encoded in the entanglement structure of bulk regions of chiral gapped states that is not visible in topological field theory. Our formalism also gives an explanation of the modular commutator formula for the chiral central charge.