Ground-state phase diagram for a system of interacting, $D(D_3)$ non-Abelian anyons

We study an exactly solvable model of $D(D_3)$ non-Abelian anyons on a one-dimensional lattice with a free coupling parameter in the Hamiltonian. For certain values of the coupling parameter level crossings occur, which divide the ground-state phase diagram into four regions. We obtain explicit expressions for the ground-state energy in each phase, for both closed and open chain boundary conditions. For the closed chain case we show that chiral phases occur which are characterised by non-zero ground-state momentum.