From entanglement renormalisation to the disentanglement of quantum double models

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.

46 pages, 25 eps figures

References in corpus (17)

• A class of quantum many-body states that can be efficiently simulated
• Criticality, the area law, and the computational power of PEPS
• PEPS as ground states: degeneracy and topology
• The Quantum Double Model with Boundary: Condensations and Symmetries
• A Family of Non-Abelian Kitaev Models on a Lattice: Topological Confinement and Condensation
• Entanglement renormalization and topological order
• Quantum circuits for strongly correlated quantum systems
• Explicit tensor network representation for the ground states of string-net models
• Mapping Kitaev's quantum double lattice models to Levin and Wen's string-net models
• Entanglement renormalization and gauge symmetry
• Exact entanglement renormalization for string-net models
• A hierarchy of topological tensor network states
• Simulation of anyons with tensor network algorithms
• Electric-magnetic duality of lattice systems with topological order
• Anyonic entanglement renormalization
• Toric codes and quantum doubles from two-body Hamiltonians
• Tensor-product representations for string-net condensed states

Cited by in corpus (6)

• Tensor Networks for Lattice Gauge Theories with continuous groups
• A hierarchy of topological tensor network states
• Bifurcation in entanglement renormalization group flow of a gapped spin model
• Algorithms for entanglement renormalization: boundaries, impurities and interfaces
• Spin chains, defects, and quantum wires for the quantum-double edge
• Finite-group gauge theories on lattices as Hamiltonian systems with constraints