Anyon condensation and its applications

By F. Burnell. 2017

142 citations recorded by the source corpus.

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 nontrivial mutual statistics with other quasiparticles in the system. We give a nontechnical 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 that 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.

Subfields: Atomic and Molecular Physics, and Optics

View Paper: https://www.semanticscholar.org/paper/a87d164e53dbc46fc6db3b144a20da5101da9ea7

Citations in the corpus

• Generalized Symmetries in Condensed Matter (2022, unknown): “Thus, gauging a 1-form symmetry in 2+1 dimensions means proliferating the worldlines of the associated anyons (16, 62); this is ‘anyon condensation’ (63).”