An algebraic quantum field theoretic approach to toric code with gapped boundary
arXiv:2212.01952 · doi:10.1063/5.0149891
Abstract
Topologically ordered quantum spin systems have become an area of great interest, as they may provide a fault-tolerant means of quantum computation. One of the simplest examples of such a spin system is Kitaev's toric code. Naaijkens made mathematically rigorous the treatment of toric code on an infinite planar lattice (the thermodynamic limit), using an operator algebraic approach via algebraic quantum field theory. We adapt his methods to study the case of toric code with gapped boundary. In particular, we recover the condensation results described in Kitaev and Kong and show that the boundary theory is a module tensor category over the bulk, as expected.
arXiv comment38 pages, 12 figures. An error pointed out by Yoshiko Ogata in what is now section 6 has been corrected. In addition, this paper includes revisions in response to the referee's comments. These revisions include a new section 2 and an additional reference, as well as modifications to most of the sections in the original paper to make it more accessible to a wider audience
References in corpus (13)
- Fault-tolerant quantum computation by anyons
- Non-Abelian Anyons and Topological Quantum Computation
- Anyons in an exactly solved model and beyond
- Models for gapped boundaries and domain walls
- Multi-interval Subfactors and Modularity of Representations in Conformal Field Theory
- A statistical mechanics view on Kitaev's proposal for quantum memories
- Localized endomorphisms in Kitaev's toric code on the plane
- Entanglement, Haag-duality and type properties of infinite quantum spin chains
- Haag duality for Kitaev's quantum double model for abelian groups
- Haag duality and the distal split property for cones in the toric code
- A derivation of braided -tensor categories from gapped ground states satisfying the approximate Haag duality
- Kosaki-Longo index and classification of charges in 2D quantum spin models
- Type of local von Neumann algebras in abelian quantum double model