Anyonic Chains – $$\alpha $$-Induction – CFT – Defects – Subfactors

Given a unitary fusion category, one can define the Hilbert space of so-called ``anyonic spin-chain'' and nearest neighbor Hamiltonians providing real-time evolution. There is considerable evidence that suitable scaling limits such systems lead to $1+1$-dimensional conformal field theories (CFTs), in fact, be used potentially construct novel classes CFTs. Besides their densities, spin chain known carry an algebra symmetry operators commuting with Hamiltonian, these have interesting representation as matrix-product-operators (MPOs). On other hand, categories are well-known arise from von Neumann algebra-subfactor pair. In this work, we investigate some consequences structures for corresponding anyonic spin-chain model. One our main results construction MPOs acting on bi-partite chain. We show precisely isomorphic defect $1+1$ CFTs constructed by Fr\" ohlich et al. Bischoff al., even though model defined finite lattice. thus conjecture its central projections associated irreducible vertical (transparent) defects limit Our partly rely observation closely related ``double triangle algebra'' arising subfactor theory. subsequent constructions, use insights into structure double B\" ockenhauer based braided $\alpha$-induction. The introductory section paper subfactors has character review.