Entanglement spectroscopy of anomalous surface states*

I will show the 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. I will introduce a modified type of entanglement spectra that incorporate the anomaly and argue that they correspond to physical edge states between different surface states. Then, I will present explicit analytical and numerical calculations for free and interacting surfaces of three-dimensional topological insulators of electrons in support of these arguments.