We demonstrate that the anyon statistics and three-loop statistics of various 2d and 3d topological phases can be derived using semiclassical nonlinear sigma model field theories with a topological Θ term. In our formalism, the braiding statistics has a natural geometric meaning: The braiding process of anyons or loops leads to a nontrivial field configuration in the space-time, which will contribute a braiding phase factor due to the Θ term.
|Original language||English (US)|
|Journal||Physical Review B - Condensed Matter and Materials Physics|
|State||Published - Aug 18 2014|
All Science Journal Classification (ASJC) codes
- Electronic, Optical and Magnetic Materials
- Condensed Matter Physics