Entanglement properties of one-dimensional topological insulators

There is still much to learn about the entanglement properties of symmetry protected topological insulators. Symmetries can be of the spatial form (Inversion, Cn rotation) or of the non-spatial form (chiral, time-reversal, particle-hole). For the non-spatial chiral symmetry, we establish here, for the first time, a rigorous relation between a Z-invariant (winding number) and protected eigenvalues in the entanglement spectrum. For the spatial C2 symmetry, we prove minimum entanglement bounds on two symmetry resolved components: the configurational and number entropy.