Citation: Feiguin, Adrian, et al. "Interacting anyons in topological quantum liquids: The golden chain." Physical review letters 98.16 (2007): 160409.
Web: https://arxiv.org/abs/cond-mat/0612341
Tags: Conformal-field-theory, TQFT
This paper introduced the golden chain - a spin chain based on Fibonacci anyons. The idea is that there is a chain with outward facing nodes, and those nodes are supposed to behave like Fibonacci anyons. In particular, when other Fibonacci anyons are fused into the chain they should behave as one would expect from the F-symbols. This gives an explicit Hamiltonian for the Fibonacci spin chain. Since the dimension of this spin chain grows like the golden ratio to the power of its length, this is called the golden chain. There is no natural tensor product decomposition on the Hilbert space of this spin chain.
The main result of this paper is the study of the chain as it gets longer and longer, towards its thermodynamic limit. The amazing result is that it is gapless, and behaves like a (1+1)D conformal field theory with chiral central charge c=7/10.
This model and its relation to conformal field theory led to a lot of interest and follow-up work. In particular, given any fusion category one can define an anyonic spin chain. This only limits to a CFT when the fusion category is a modular category. For the special case of the anyonic chain based on Ising anyons and its relationship to the Ising model, the best reference is
> Aasen, David, Roger SK Mong, and Paul Fendley. "Topological defects on the lattice: I. The Ising model." Journal of Physics A: Mathematical and Theoretical 49.35 (2016): 354001.
The references in
> Hollands, Stefan. "Anyonic chains-alpha-induction-CFT-defects-subfactors." Communications in Mathematical Physics 399.3 (2023): 1549-1621.
are a good place to get acquainted with the modern approaches to anyonic chains.