Classification and Description of Bosonic Symmetry Protected Topological Phases with semiclassical Nonlinear Sigma models

@article{Bi2014ClassificationAD,
  title={Classification and Description of Bosonic Symmetry Protected Topological Phases with semiclassical Nonlinear Sigma models},
  author={Zhen Bi and Alex Rasmussen and Kevin Slagle and Cenke Xu},
  journal={Physical Review B},
  year={2014},
  volume={91},
  pages={134404}
}
In this paper we systematically classify and describe bosonic symmetry protected topological (SPT) phases in all physical spatial dimensions using semiclassical nonlinear Sigma model (NLSM) field theories. All the SPT phases on a $d-$dimensional lattice discussed in this paper can be described by the same NLSM, which is an O(d+2) NLSM in $(d+1)-$dimensional space-time, with a topological $\Theta-$term. The field in the NLSM is a semiclassical Landau order parameter with a unit length constraint… 
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