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We study a topological phase of interacting bosons in (3+1) dimensions whichis protected by charge conservation and time-reversal symmetry. We present anexplicit lattice model which realizes this phase and which can be studied insign-free Monte Carlo simulations. The idea behind our model is to bind bosonsto topological defects called hedgehogs. We determine the phase diagram of themodel and identify a phase where such bound states are proliferated. In thisphase we observe a Witten effect in the bulk whereby an external monopole bindshalf of the elementary boson charge, which confirms that it is a bosonictopological insulator. We also study the boundary between the topologicalinsulator and a trivial insulator. We find a surface phase diagram whichincludes exotic superfluids, a topologically ordered phase, and a phase with aHall effect quantized to one-half of the value possible in a purelytwo-dimensional system. We also present models that realize symmetry-enrichedtopologically-ordered phases by binding multiple hedgehogs to each boson; thesephases show charge fractionalization and intrinsic topological order as well asa fractional Witten effect.

Model Realization and Numerical Studies of a Three-Dimensional Bosonic Topological Insulator and Symmetry-Enriched Topological Phases