Fri, Mar 15, 2013, 1:15 pm to 2:30 pm
We show that the framework of condensate-induced transitions between two-dimensional topological phases can be used to relate one-dimensional spin models at their critical points. To illustrate this, we show that two well-known spin chains, namely the XY chain and the transverse field Ising chain with only next-nearest-neighbor interactions, differ at their critical points only by a non-local boundary term and can be related via an exact mapping. The boundary term constrains the set of possible boundary conditions of the transverse field Ising chain, reducing the number of primary fields in the conformal field theory that describes its critical behavior. We argue that the reduction of the field content is equivalent to the confinement of a set of primary fields, in precise analogy to the confinement of quasiparticles resulting from a condensation of a boson in a topological phase. To provide evidence for the generality of the framework we apply it to the XY chain with only next-nearest-neighbor interactions. In the presence of a confining boundary term, this XY chain can be mapped to a spin chain with the u(1)_2 ×u(1)_2 critical behavior predicted by the condensation framework.