Holographic entanglement renormalization of topological insulators

In this work we study the real-space entanglement renormalization group (RG) flows and associated emergent holographic geometry of topological band insulators in (2+1) dimensions with continuum multi-scale entanglement renormalization ansatz (cMERA). Given a ground state of a topological insulator at the UV layer, we study how the Berry curvature as well as the quantum metric evolve in the bulk of cMERA. Besides the nontrivial topological properties in the bulk of cMERA, it is found that the UV state flows to a nontrivial IR state which carries a nonzero Berry flux. Our result is in parallel with the picture in lattice MERA that a nontrivial UV state corresponds to a nontrivial IR state. On the other hand, if we try to construct the UV state with a trivial IR state, we find there is a ``phase transition'' feature in the bulk of cMERA.