Interplay between short and long-range entanglement in symmetry protected phases

摘要

We study a variety of questions related to entanglement in symmetry protectedphases, especially those introduced in arXiv:1106.4772 (Chen et al., 2011).These phases are analogous to topological insulators in that they are shortrange entangled states with symmetry protected edge or surface states. We showthat the now standard bulk-edge correspondence relating the entanglementspectrum to the gapless edge spectrum holds for these phases as well. We alsoconsider the question of coupling these models to gauge fields or equivalentlyof introducing long range entanglement. We argue that this procedure yieldsmodels with perturbatively stable edge or surface states at a variety ofinterface types. The non-onsite nature of the edge symmetry plays an importantrole in our considerations.