From entanglement renormalisation to the disentanglement of quantum double models

TL;DR

This paper develops a universal entanglement renormalisation method for topological lattice models, including Abelian and non-Abelian quantum doubles, simplifying their Hamiltonians and lattice connectivity, with implications for continuum theories.

Contribution

It introduces a general entanglement renormalisation procedure for quantum double models, extending known mappings and analyzing non-Abelian cases.

Findings

Re-derivation of the toric code to Ising chains mapping.

Extension of the method to non-Abelian models.

Discussion of the space of states on the torus.

Abstract

We describe how the entanglement renormalisation approach to topological lattice systems leads to a general procedure for treating the whole spectrum of these models, in which the Hamiltonian is gradually simplified along a parallel simplification of the connectivity of the lattice. We consider the case of Kitaev's quantum double models, both Abelian and non-Abelian, and we obtain a rederivation of the known map of the toric code to two Ising chains; we pay particular attention to the non-Abelian models and discuss their space of states on the torus. Ultimately, the construction is universal for such models and its essential feature, the lattice simplification, may point towards a renormalisation of the metric in continuum theories.