Holographic Entanglement Renormalization of Topological Insulators

TL;DR

This paper explores how the entanglement renormalization group flow of topological insulators can be understood through a holographic perspective using cMERA, revealing topological properties are preserved across energy scales.

Contribution

It demonstrates that topological features, like Berry flux, are maintained in the cMERA flow and highlights the difficulty of constructing a topologically trivial IR state for topological insulators.

Findings

Berry flux flows from UV to IR in cMERA

Topological properties are preserved across scales

Obstruction exists for trivial IR state in topological insulators

Abstract

We study the real-space entanglement renormalization group flows of topological band insulators in (2+1) dimensions by using the continuum multi-scale entanglement renormalization ansatz (cMERA). Given the ground state of a Chern insulator, we construct and study its cMERA by paying attention, in particular, to how the bulk holographic geometry and the Berry curvature depend on the topological properties of the ground state. It is found that each state defined at different energy scale of cMERA carries a nonzero Berry flux, which is emanated from the UV layer of cMERA, and flows towards the IR. Hence, a topologically nontrivial UV state flows under the RG to an IR state, which is also topologically nontrivial. On the other hand, we found that there is an obstruction to construct the exact ground state of a topological insulator with a topologically trivial IR state. I.e., if we try to construct a cMERA for the ground state of a Chern insulator by taking a topologically trivial IR state, the resulting cMERA does not faithfully reproduce the exact ground state at all length scales.