Low-energy behavior of the generalized Golden chain at an integrable point

Recently, properties of collective states of interacting non-Abelian anyons have attracted a considerable attention. In particular, it has been shown to that the generalization of the Golden chain, a chain of interacting Fibonacci anyons, has a rich phase diagram with various critical and gapped phases. In additions, several integrable points have also been studied. We identify a new integrable point in the parameter space of the model and diagonalize the Hamiltonian exactly using the Bethe Ansatz method. To describe the corresponding low-energy conformal field theory, we perform the finite-size analysis to calculate the central charge and critical exponents.