We study a string-net ladder in the presence of a string tension. Focusing on the simplest non-Abelian anyon theory with a quantum dimension larger than two, we determine the phase diagram and find a Russian doll spectrum featuring size-independent energy levels as well as highly degenerate zero-energy eigenstates. At the self-dual points, we compute the gap exactly by using a mapping onto the Temperley-Lieb chain. These results are in stark constrast with the ones obtained for Fibonacci or Ising theories.
We consider the string-net model on the honeycomb lattice for Ising anyons in the presence of a string tension. This competing term induces a nontrivial dynamics of the non-Abelian anyonic quasiparticles and may lead to a breakdown of the topological phase. Using high-order series expansions and exact diagonalizations, we determine the robustness of this doubled Ising phase which is found to be separated from two gapped phases. An effective quantum dimer model emerges in the large tension limit giving rise to two different translation symmetry-broken phases. Consequently, we obtain four transition points, two of which are associated with first-order transitions whereas the two others are found to be continuous and provide examples of recently proposed Bose condensation for anyons.
We examine the zero-temperature phase diagram of the two-dimensional Levin-Wen string-net model with Fibonacci anyons in the presence of competing interactions. Combining high-order series expansions around three exactly solvable points and exact diagonalizations, we find that the non-Abelian doubled Fibonacci topological phase is separated from two nontopological phases by different second-order quantum critical points, the positions of which are computed accurately. These trivial phases are separated by a first-order transition occurring at a fourth exactly solvable point where the ground-state manifold is infinitely many degenerate. The evaluation of critical exponents suggests unusual universality classes.
We study the robustness of a generalized Kitaevs toric code with Z_N degrees of freedom in the presence of local perturbations. For N=2, this model reduces to the conventional toric code in a uniform magnetic field. A quantitative analysis is performed for the perturbed Z_3 toric code by applying a combination of high-order series expansions and variational techniques. We provide strong evidences for first- and second-order phase transitions between topologically-ordered and polarized phases. Most interestingly, our results also indicate the existence of topological multi-critical points in the phase diagram.
