Abstract
We study a topological phase of interacting bosons in (3+1) dimensions which is protected by charge conservation and time-reversal symmetry. We present an explicit lattice model which realizes this phase and which can be studied in sign-free Monte Carlo simulations. The idea behind our model is to bind bosons to topological defects called hedgehogs. We determine the phase diagram of the model and identify a phase where such bound states are proliferated. In this phase we observe a Witten effect in the bulk whereby an external monopole binds half of the elementary boson charge, which confirms that it is a bosonic topological insulator. We also study the boundary between the topological insulator and a trivial insulator. We find a surface phase diagram which includes exotic superfluids, a topologically ordered phase, and a phase with a Hall effect quantized to one-half of the value possible in a purely two-dimensional system. We also present models that realize symmetry-enriched topologically-ordered phases by binding multiple hedgehogs to each boson; these phases show charge fractionalization and intrinsic topological order as well as a fractional Witten effect.
Highlights
The study of topological phases of matter has been a major component of condensed matter research in recent decades
If we imagine introducing a tunneling between the two Uð1Þ symmetries, which would reduce the total symmetry to Uð1Þ × ZT2 [or Uð1Þ ⋊ ZT2 ], the discrete symmetry should treat both spin and boson variables in the same way. We find that this condition is satisfied as long as the above symmetries are understood as antiunitary; we refer to these symmetries as ZT2
Vishwanath and Senthil [6] predicted another exotic phase on the surface of the bosonic topological insulator— a phase that breaks the ZT2 symmetry and has a Hall conductivity quantized to an odd integer
Summary
The study of topological phases of matter has been a major component of condensed matter research in recent decades. It is possible to have a surface phase that breaks no symmetries but has a symmetry-enriched intrinsic topological order of a kind impossible in a purely twodimensional system with these symmetries In both the two- and three-dimensional cases, the topological behavior can be thought of as coming from the binding of bosons to point topological defects, and the condensation of such objects. We find a surface phase that breaks none of the symmetries of the model We suspect that this phase has symmetry-enriched intrinsic topological order of the kind predicted by Vishwanath and Senthil [6], but we do not know how to test this using Monte Carlo techniques.
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