Geometry defects in bosonic symmetry-protected topological phases

Yizhi You, Yi-Zhuang You
2016 Physical review B  
In this paper we focus on the interplay between geometry defects and topological properties in bosonic symmetry protected topological(SPT) phases. We start from eight copies of 3D time-reversal(T) invariant topological superconductors(TSC) on a crystal lattice. We melt the lattice by condensation of disclinations and therefore restore the rotation symmetry. Such disclination condensation procedure confines the fermion and afterwards turns the system into a 3D boson topological liquid
more » ... ). The low energy effective theory of this crystalline-liquid transition contains a topological term inherited from the geometry axion response in TSC. In addition, we investigate the interplay between dislocation and superfluid vortex on the surface of TCL. We demonstrate that the T and translation invariant surface state is a double [eTmT] state with intrinsic surface topological order. We also look into the exotic behavior of dislocation in 2D boson SPT state described by an O(4) non-linear σ-model(NLσ M) with topological Θ-term. By dressing the O(4) vector with spiral order and gauge the symmetry, the dislocation has mutual semion statistics with the gauge flux. Further reduce the O(4) NLσ M to the Ising limit, we arrive at the Levin-Gu model with stripy modulation whose dislocation has nontrivial braiding statistics.
doi:10.1103/physrevb.93.245135 fatcat:xig77wohhzcaff5kjsond7jcae