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 $(\mathfrak{c}{\text{tot}}){\text{min}}$ 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.

💡 Research Summary

The paper develops a comprehensive framework for understanding entanglement structures in 2+1‑dimensional chiral gapped phases, extending the Li‑Haldane conjecture from a spectral statement to an operator‑level bulk/edge correspondence. The authors first show that the entanglement Hamiltonian K_A of any disk region A can be written as a sum of local operators h_rec(v) supported on lattice sites v∈A. These operators reproduce the low‑energy Virasoro modes of the chiral edge conformal field theory (CFT), so that K_A and the physical Hamiltonian H share the same low‑lying spectrum (up to overall rescaling and shift). By extending the sum over the whole system they define a reconstructed Hamiltonian H_rec = Σ_{v∈D} h_rec(v) which lives in the same phase as the original H. Numerical tests demonstrate that the ground state of H_rec is closer to the zero‑correlation‑length RG fixed point, suggesting an iterative “reconstruct‑and‑relax” procedure that drives a generic wavefunction toward the fixed point without increasing system size.

The second major contribution concerns regions with sharp corners. The authors regularize a corner by carving out a small hole; the edge CFT lives on the hole’s boundary. This construction leads to a universal corner contribution to the entanglement entropy, \