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The algebraic tools used to study topological phases of matter are notclearly suited to studying processes in which the bulk energy gap closes, suchas phase transitions. We describe an elementary two edge thought experimentwhich reveals the effect of an anyon condensation phase transition on therobust edge properties of a sample, bypassing a limitation of the algebraicdescription. In particular, the two edge construction allows some edge degreesof freedom to be tracked through the transition, despite the bulk gap closing.The two edge model demonstrates that bulk anyon condensation induces symmetrybreaking in the edge model. Further, the construction recovers the expectedresult that the number of chiral current carrying modes at the edge cannotchange through anyon condensation. We illustrate the construction throughdetailed analysis of anyon condensation transitions in an achiral phase, thetoric code, and in chiral phases, the Kitaev spin liquids.

Edge Theories for Anyon Condensation Phase Transitions