Entanglement spectroscopy of anomalous surface states

We study entanglement spectra of gapped states on the surfaces of symmetry-protected topological phases. These surface states carry anomalies that do not allow them to be terminated by a trivial state. Their entanglement spectra are dominated by non-universal features, which reflect the underlying bulk. We introduce a modified type of entanglement spectra that incorporate the anomaly and argue that they correspond to physical edge states between different surface states. We support these arguments by explicit analytical and numerical calculations for free and interacting surfaces of three-dimensional topological insulators of electrons.