Entanglement renormalization and topological order

TL;DR

This paper demonstrates that MERA provides a natural and efficient framework for describing topological states of matter, exemplified by Kitaev's toric code, and extends to quantum double models.

Contribution

It shows that MERA can effectively represent topological states, revealing their fixed point nature under entanglement renormalization and simplifying their topological degrees of freedom.

Findings

MERA offers a simple description of the toric code.

Kitaev states are fixed points of the RG flow in MERA.

Results generalize to quantum double models.

Abstract

The multi-scale entanglement renormalisation ansatz (MERA) is argued to provide a natural description for topological states of matter. The case of Kitaev's toric code is analyzed in detail and shown to possess a remarkably simple MERA description leading to distillation of the topological degrees of freedom at the top of the tensor network. Kitaev states on an infinite lattice are also shown to be a fixed point of the RG flow associated with entanglement renormalization. All these results generalize to arbitrary quantum double models.