Line defects in Three dimensional Symmetry Protected Topological Phases

TL;DR

This paper shows that line defects in 3D symmetry protected topological phases, when coupled to a Z2 gauge field, exhibit protected gapless or degenerate spectra, revealing new boundary-like properties of these defects.

Contribution

It introduces the concept that Z2 vison loop excitations act as 1D boundaries with protected spectra in 3D SPT phases coupled to gauge fields.

Findings

Z2 vison loops serve as 1D boundaries of 3D SPT phases.

Line defects exhibit symmetry-protected gapless or degenerate spectra.

Coupling to gauge fields reveals new boundary phenomena in SPT phases.

Abstract

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