Abstract

Ville Lahtinen, University of Amsterdam

Condensate-induced transitions and critical spin chains

We show that condensate-induced transitions between two-dimensional topological phases provide a general framework to relate one-dimensional spin models at their critical points. We demonstrate this using two examples. First, we show that two well-known spin chains, namely the XY chain and the transverse fi.eld Ising chain with only next-nearest-neighbor interactions, diff er 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 fi.eld 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 con.finement of a set of primary fi.elds, in precise analogy to the con.finement of quasiparticles resulting from a condensation of a boson in a topological phase. As the second example we show that when a similar con.ning boundary term is applied to the XY chain with only next-nearest-neighbor interactions, the resulting system can be mapped to a local spin chain with the u(1)_2 x u(1)_2 critical behavior predicted by the condensation.