Entanglement spectroscopy of anomalous surface states

by Arjun Dey (Weizmann Institute)

Friday 6 Jan 2023, 11:00 → 12:00 Europe/Zurich

WHGA/121

Entanglement spectroscopy has recently become the gold standard for identifying topologicalphases. For a wide range of phases, the entanglement spectrum (ES) computed from a groundstate wave function qualitatively matches the energy spectrum the same phase would exhibit ata physical edge with vacuum. Consequently, ES can identify short-range entangled topologicalphases and long-range topological order. The correspondence between ES and physical edgespectrum fails for states that reside on the surface of a topologically non-trivial bulk. Atopologically non-trivial vacuum state is disallowed by the anomaly that characterizes suchsurfaces.In this work, we demonstrate how the topological nature of anomalous surface states can stillbe extracted from the entanglement properties of a single wave function. To this end, weintroduce a modified type of entanglement spectra that incorporate the anomaly and arguethat they correspond to physical edge states between different surface states. We support thesearguments by explicit analytical and numerical calculations for free and interacting surfaces ofthree-dimensional topological insulators of electrons.