Anyonic quantum chains - a twist on strongly correlated systems
Holger Frahm (Hannover)
Thursday 26th November, 2015 16:00-17:00 Maths 522
Starting from a given set of fusion rules one-dimensional lattice models of interacting anyons can be constructed. For a system of particles satisfying the fusion rules of $SO(5)_2$ fine-tuning of the coupling constants leads to integrable anyon chains with commuting transfer matrices of 'interactions round the face' (IRF) type. The conserved topological charges of the anyon chain are recovered from the transfer matrices in the limit of large spectral parameter. The properties of the models in the thermodynamic limit and the low energy excitations are studied using Bethe ansatz methods. We find two critical points which are effectively described by rational conformal field theories invariant under extensions of the Virasoro algebra related to the underlying $SO(5)$ symmetry of the anyon chain. The modular partition function and fusion rules of these RCFTs are derived.