Year: 2012
Type: article
Abstract: 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 ${\mathbb{Z}}_{2}$ gauge field and then show that the $\ensuremath{\pi}$-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.
Source: Physical Review B
Authors: Michael Levin, Zheng-Cheng Gu
Language: English
Subfield: Condensed Matter Physics
Field: Physics and Astronomy
Domain: Physical Sciences
Open Access status: green
Funder: National Science Foundation
OpenAlex ID: W2104740527