Abstract

Phase transitions in topologically ordered systems remain a widely unexplored domain mainly due to the lack of theoretical tools to analyze them. In the absence of effective field theory, microscopic models are important to investigate the possible condensation mechanisms driving transitions. In this context, the string-net model introduced ten years ago by M. Levin and X.-G. Wen is especially attractive since it allows to study any (doubled achiral) topological phase. In the absence of perturbation, string-net condensates can be seen as deconfined phases in which excitations are anyons. In this talk, I will discuss the influence of a string tension in non-Abelian string-net models and I will show that it leads to phase transitions which depend on the anyon theory considered. I will also address the issue of anyonic bound states that may be generated by this string tension and their possible relevance to understand the nature of the phase transitions.