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.
38 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 (5)
- Non-Abelian Anyons and Topological Quantum Computation
- 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
- Type of local von Neumann algebras in abelian quantum double model