Modular commutator in gapped quantum many-body systems

Understand

In arXiv:2110.06932, we argued that the chiral central charge -- a topologically protected quantity characterizing the edge theory of a gapped (2+1)-dimensional system -- can be extracted from the bulk by using an order parameter called the modular commutator.

• In this paper, we reveal general properties of the modular commutator and strengthen its relationship with the chiral central charge.
• First, we identify connections between the modular commutator and conditional mutual information, time reversal, and modular flow.
• Second, we prove, within the framework of the entanglement bootstrap program, that two topologically ordered media connected by a gapped domain wall must have the same modular commutator in their respective bulk.