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

TL;DR

This paper provides an exact Bethe ansatz solution for a one-dimensional non-Abelian anyon chain with D(D_3) symmetry, revealing detailed spectral properties of a model with complex fusion rules.

Contribution

It introduces the first exact Bethe ansatz solution for an integrable non-Abelian anyon chain with D(D_3) symmetry, connecting algebraic structures to physical models.

Findings

Exact energy spectrum derived

Bethe ansatz equations established

Model describes non-Abelian anyons with D(D_3) symmetry

Abstract

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.