Many-body systems with spurious modular commutators

Gapped (2+1)D quantum many body systems can exhibit low-energy, chiral edge modes that are characterized by a topological invariant known as the chiral central charge (CCC). Though the name alludes to an effective boundary CFT, the CCC is independent of the conditions on the edge and is instead a property of the bulk ground state wave function. Recently, it has been conjectured that the CCC is proportional to a ground state entanglement measure known as the modular commutator. While there is significant evidence to support this relation, I will show in this talk that it is not universal—that there exist systems with vanishing CCC which nevertheless give nonzero ``spurious" values for the modular commutator.