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

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

2010-03-18

arxiv.org/abs/1003.3514v1

Nucl.Phys.B836:171-185,2010

Physics

Condensed Matter

Statistical Mechanics

19 pages

Scientific paper

10.1016/j.nuclphysb.2010.04.014

The exact solution for the energy spectrum of a one-dimensional Hamiltonian with local two-site interactions and periodic boundary conditions is determined. The two-site Hamiltonians commute with the symmetry algebra given by the Drinfeld double D(D_3) of the dihedral group D_3. As such the model describes local interactions between non-Abelian anyons, with fusion rules given by the tensor product decompositions of the irreducible representations of D(D_3). The Bethe ansatz equations which characterise the exact solution are found through the use of functional relations satisfied by a set of mutually commuting transfer matrices.

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