



01471nas a2200157   4500008004100000245005900041210005800100260001400158490000800172520102100180100001901201700001501220700001801235700002301253856003701276       2022                        eng d00aModular commutator in gapped quantum many-body systems0 aModular commutator in gapped quantum manybody systems  c8/26/20220 v1063 a<p>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. Third, we numerically calculate the value of the modular commutator for a bosonic lattice Laughlin state for finite sizes and extrapolate to the infinite-volume limit. The result of this extrapolation is consistent with the proposed formula up to an error of about 0.7%.</p>1 aKim, Isaac, H.1 aShi, Bowen1 aKato, Kohtaro1 aAlbert, Victor, V.  uhttps://arxiv.org/abs/2110.10400