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The exact solution for the energy spectrum of a one-dimensional Hamiltonianwith local two-site interactions and periodic boundary conditions isdetermined. The two-site Hamiltonians commute with the symmetry algebra givenby the Drinfeld double D(D_3) of the dihedral group D_3. As such the modeldescribes local interactions between non-Abelian anyons, with fusion rulesgiven by the tensor product decompositions of the irreducible representationsof D(D_3). The Bethe ansatz equations which characterise the exact solution arefound through the use of functional relations satisfied by a set of mutuallycommuting transfer matrices.

Bethe ansatz solution of an integrable, non-Abelian anyon chain with D(D_3) symmetry