Abstract
Starting from the fusion rules for the algebra SO(5)2 we construct one-dimensional lattice models of interacting anyons 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. Two of the anyon models are critical at zero temperature. From the analysis of the finite size spectrum we find that they are effectively described by rational conformal field theories invariant under extensions of the Virasoro algebra, namely WB2 and WD5, respectively. The latter contains primaries with half and quarter spin. The modular partition function and fusion rules are derived and found to be consistent with the results for the lattice model.
Highlights
Starting withBethe’s study of the spin-Heisenberg chain integrable models in low dimensions have provided important insights into the peculiarities of correlated many-body systems subject to strong quantum fluctuations [1,2,3,4], e.g. the appearance of quasi-particles with exotic properties such as fractional quantum numbers and with unusual braiding statistics
Non-Abelian anyons can be realized as local modes with zero energy at junctions of spin-orbit coupled quantum wires through the ’topological’ Kondo effect [9,10,11]. Additional interest in these objects arises from the fact that non-Abelian anyons are protected by their topological charge which makes them potentially interesting as resources for quantum computation [12, 13]
A class of integrable models describing interacting non-Abelian anyons in one dimension can be obtained from two dimensional classical lattice systems with interactions round the face (IRF) such as the restricted solid on solid (RSOS) models [14] in their Hamiltonian limit
Summary
Heisenberg chain integrable models in low dimensions have provided important insights into the peculiarities of correlated many-body systems subject to strong quantum fluctuations [1,2,3,4], e.g. the appearance of quasi-particles with exotic properties such as fractional quantum numbers and with unusual braiding statistics. New models can be defined by labeling the local height variables on neighboring sites of the lattice by adjacent roots in the A-D-E Dynkin diagrams or, more generally by primary fields of a general rational conformal field theory related through the corresponding fusion algebra [28, 29] For these models to be integrable one has to find a parameterization of the Boltzmann weights for the configuration allowed around a face of the lattice which satisfies the Yang-Baxter equation. For a consistent anyon theory braids have to commute with fusion and satisfy the Yang-Baxter relation Both properties follow from the Hexagon equation for F - and R-moves. Note that the matrix elements of these operators depend on triples of neighboring labels ai−1aiai+1 in the fusion path but only the middle one may change under the action of the p(ib)
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