Wave Functions of Bosonic Symmetry Protected Topological Phases

Understand

We study the structure of the ground state wave functions of bosonic Symmetry Protected Topological (SPT) insulators in 3 space dimensions.

• We demonstrate that the differences with conventional insulators are captured simply in a dual vortex description.
• As an example we show that a previously studied bosonic topological insulator with both global U(1) and time-reversal symmetry can be described by a rather simple wave function written in terms of dual "vortex ribbons".
• The wave function is a superposition of all the vortex ribbon configurations of the boson, and a factor (-1) is associated with each self-linking of the vortex ribbons.