Title: Anyon condensation and its applications,
Abstract: Bose condensation is central to our understanding of quantum phases of
matter. Here we review Bose condensation in topologically ordered phases (also
called topological symmetry breaking), where the condensing bosons have
non-trivial mutual statistics with other quasiparticles in the system. We give
a non-technical overview of the relationship between the phases before and
after condensation, drawing parallels with more familiar symmetry-breaking
transitions. We then review two important applications of this phenomenon.
First, we describe the equivalence between such condensation transitions and
pairs of phases with gappable boundaries, as well as examples where multiple
types of gapped boundary between the same two phases exist. Second, we discuss
how such transitions can lead to global symmetries which exchange or permute
anyon types. Finally we discuss the nature of the critical point, which can be
mapped to a conventional phase transition in some -- but not all -- cases.