We consider entanglement properties of symmetry-protected topological insulators. We do this through both numerical studies and analytic proofs. We consider both spatial and non-spatial symmetries. We show how topological invariants determine the entanglement spectrum and the symmetry-resolved entanglement components. The configurational entanglement entropy component indicates the operational usefulness of entanglement. On the other hand, the number entropy is more easily measurable.

One of the contributions of this thesis is showing that topological edge states can be used for entanglement experiments. We consider two subsystems on opposite ends of the system and determine the requirements necessary for long-range operational entanglement.

The second contribution was done by considering a general one-dimensional insulator with chiral symmetry, an example of a non-spatial symmetry. For a topological invariant I, we show that a periodic chain has at least 2|I| protected eigenvalues at 1/2 in the single-particle entanglement spectrum.

For our third contribution, we present the first proof of topologically protected symmetry-resolved entanglement components in a lattice model. In particular, we consider a C₂ spatial symmetry where the invariant Δ is the absolute value of the difference between the filled symmetric and anti-symmetric states.

Our final contribution is a set of general bounds for symmetry-resolved entanglement in density matrices. We apply these general bounds to systems with chiral symmetry and Cₙ rotational symmetries. We also find improvements on previously known bounds for the von-Neumann entanglement entropy in Cₙ-symmetric systems.

We now have a fairly thorough set of results on the topological protection of symmetry-resolved entanglement in lattice models. The operational and configurational entanglement results are useful for foundational entanglement experiments. On the other hand, the number entropy is useful for identifying topological phases as it is a readily measurable quantity.