M. D. Schulz, S. Dusuel, K. P. Schmidt, J. Vidal
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 trivial phases by different second-order quantum critical points, the positions of which are computed accurately. The 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.
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http://arxiv.org/abs/1212.4109
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