Condensation transitions in critical spin chains

We show that two well known one-dimensional spin chains, namely the XY spin chain and the transverse field Ising model with only next-nearest neighbor interactions, can be related at their critical points via an exact mapping. For periodic boundary conditions, the two chains only differ by a boundary term, which accounts for the differences in the critical behavior. We argue that the boundary term induces a ``condensation transition,'' which is closely related to condensation transitions between gapped two-dimensional topological phases.