Topological entanglement entropy is a useful measure to detect topologically ordered states. Recent progress has shown that there are different kinds of topological states called symmetry protected topological (SPT) phases. Despite that they show some topological properties such as gapless edge modes, they have no topological order and the topological entanglement entropy simply vanishes as in the case of trivial phases.
Therefore, the topological entanglement entropy cannot distinguish SPT phases from trivial phases. In this talk, I will introduce a new quantum measure, a grand canonical entanglement entropy, and show that it gives a topological invariant which distinguishes SPT phases from trivial phases. If time permits, I will also explain an edge theory approach to compute mutual information and entanglement negativity in Chern-Simons theories.
