Line defects in three-dimensional symmetry-protected topological phases

Abstract

A 3d symmetry protected topological phase, by definition must have symmetry\nprotected nontrivial boundary states, namely its 2d boundary must be either\ngapless or degenerate. In this work we demonstrate that once we couple a 3d SPT\nphase to a lattice dynamical Z2 gauge field, in many cases the Z2 vison loop\nexcitation (line defect) can be viewed as a "1d boundary" of the 3d SPT phase,\nand this line defect is guaranteed to have gapless or degenerate spectrum,\nwhich is also protected by the symmetry of the SPT phase.\n