Microscopic Realization of Two-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 antivortex (and vice versa) under time reversal symmetry, and the condensation of vortices results in a trivial Mott insulator. However, if each vortex or antivortex 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)⋊Z2(T) symmetry. We point out that in BTI, an external π-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.