Speaker: Arjun Dey (Weizmann Institute of Science)

Title: Entanglement spectroscopy of anomalous surface states

Abstract: Entanglement spectroscopy has recently become the gold standard for identifying topological phases.

For a wide range of phases, the entanglement spectrum (ES) computed from a ground state wave function qualitatively matches the energy spectrum the same phase would exhibit at a physical edge with vacuum. Consequently, ES can identify short-range entangled topological phases and long-range topological order. The correspondence between ES and physical edge spectrum fails for states that reside on the surface of a topologically non-trivial bulk. A topologically non-trivial vacuum state is disallowed by the anomaly that characterizes such surfaces. 

In this work, we demonstrate how the topological nature of anomalous surface states can still be extracted from the entanglement properties of a single wave function. To this end, 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.