We construct a two-dimensional (2D) quantum spin model that realizes an Ising paramagnet with gapless edge modes protected by Ising symmetry. This model provides an example of a "symmetry-protected topological phase." We describe a simple physical construction that distinguishes this system from a conventional paramagnet: We couple the system to a Z 2 gauge field and then show that the π-flux excitations have different braiding statistics from that of a usual paramagnet. In addition, we show that these braiding statistics directly imply the existence of protected edge modes. Finally, we analyze a particular microscopic model for the edge and derive a field theoretic description of the low energy excitations. We believe that the braiding statistics approach outlined in this paper can be generalized to a large class of symmetry-protected topological phases.
|Journal||Physical Review B - Condensed Matter and Materials Physics|
|State||Published - 10 Sep 2012|
ASJC Scopus subject areas
- Electronic, Optical and Magnetic Materials
- Condensed Matter Physics