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

TL;DR

This paper introduces a lattice model for a three-dimensional bosonic topological insulator protected by charge and time-reversal symmetries, demonstrating novel bulk and surface phenomena including the Witten effect and exotic surface phases.

Contribution

The authors present an explicit sign-free lattice model for a 3D bosonic topological insulator, including detailed phase diagrams and boundary states, advancing understanding of symmetry-protected topological phases.

Findings

Observation of the Witten effect in the bulk

Identification of exotic surface phases including superfluids and topologically ordered states

Realization of symmetry-enriched topologically-ordered phases with charge fractionalization

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.