Microscopic Realization of 2-Dimensional Bosonic Topological Insulators

It is well known that a Bosonic Mott insulator can be realized by condensing vortices of a boson condensate. Usually, a vortex becomes an anti-vortex (and vice-versa) under time reversal symmetry, and the condensation of vortices results in a trivial Mott insulator. However, if each vortex/anti-vortex interacts with a spin trapped at its core, the time reversal transformation of the composite vortex operator will contain an extra minus sign. It turns out that such a composite vortex condensed state is a bosonic topological insulator (BTI) with gapless boundary excitations protected by $U(1) Z_2^T$ symmetry. We point out that in BTI, an external $\pi$ flux monodromy defect carries a Kramers doublet. We propose lattice model Hamiltonians to realize the BTI phase, which might be implemented in cold atom systems or spin-$1$ solid state systems.