Condensate-induced transitions and critical spin chains

TL;DR

This paper explores how condensate-induced transitions in topological phases can relate different one-dimensional spin models at their critical points, revealing new mappings and boundary effects that influence their conformal field theories.

Contribution

It introduces a framework connecting topological phase transitions to critical spin chains, demonstrating exact mappings and boundary effects that alter their critical behavior.

Findings

XY and transverse field Ising chains differ only by a boundary term

Boundary term constrains boundary conditions and reduces primary fields

Confinement of quasiparticles relates to boundary-induced critical behavior

Abstract

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 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. As the second example we show that when a similar confining 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 framework.