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

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.

arXiv comment26 pages, 16 figures

References in corpus (29)

• Topological Insulators
• Topological insulators and superconductors
• Symmetry protected topological orders and the group cohomology of their symmetry group
• Pyrochlore Photons: The U(1) Spin Liquid in a S=1/2 Three-Dimensional Frustrated Magnet
• Symmetry Protected Topological phases of Quantum Matter
• Physics of three dimensional bosonic topological insulators: Surface Deconfined Criticality and Quantized Magnetoelectric Effect
• Theory and classification of interacting 'integer' topological phases in two dimensions: A Chern-Simons approach
• A classification of symmetry enriched topological phases with exactly solvable models
• Emergent Photons and New Transitions in the O(3) Sigma Model with Hedgehog Suppression
• Boson topological insulators: A window into highly entangled quantum phases
• Classifying fractionalization: symmetry classification of gapped Z2 spin liquids in two dimensions
• Integer quantum Hall effect for bosons: A physical realization
• Bosonic topological insulator in three dimensions and the statistical Witten effect
• Exotic order in simple models of bosonic systems
• Anomalous Symmetry Fractionalization and Surface Topological Order
• Witten effect in a crystalline topological insulator
• Classification and Description of Bosonic Symmetry Protected Topological Phases with semiclassical Nonlinear Sigma models
• Ground states of quantum antiferromagnets in two dimensions
• On the origin of artificial electrodynamics and other stories in three-dimensional bosonic models
• Conflicting Symmetries in Topologically Ordered Surface States of Three-dimensional Bosonic Symmetry Protected Topological Phases
• Constructing symmetric topological phases of bosons in three dimensions via fermionic projective construction and dyon condensation
• Symmetry-protected topological phases with charge and spin symmetries: response theory and dynamical gauge theory in 2D, 3D and the surface of 3D
• Topological Quantum Field Theory, Nonlocal Operators, and Gapped Phases of Gauge Theories
• Exact realization of Integer and Fractional Quantum Hall Phases in U(1)xU(1) models in (2+1)d
• A gauge theory generalization of the fermion-doubling theorem
• Monte Carlo Study of a U(1)xU(1) system with π-statistical Interaction
• Comparative study of Higgs transition in one-component and two-component lattice superconductor models
• Monte Carlo Study of a $U(1)\times U(1)$ Loop Model with Modular Invariance
• Model of Fractionalization of Faraday Lines in Compact Electrodynamics

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• Half-filled Landau level, topological insulator surfaces, and three dimensional quantum spin liquids
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• Vortex-line condensation in three dimensions: A physical mechanism for bosonic topological insulators
• Topological quantum field theory of three-dimensional bosonic Abelian-symmetry-protected topological phases
• Multi-kink topological terms and charge-binding domain-wall condensation induced symmetry-protected topological states: Beyond Chern-Simons/BF theory
• Topological Phases Protected By Reflection Symmetry and Cross-cap States
• Composite Particle Theory of Three-dimensional Gapped Fermionic Phases: Fractional Topological Insulators and Charge-Loop Excitation Symmetry
• Quantum Paramagnet and Frustrated Quantum Criticality in a Spin-One Diamond Lattice Antiferromagnet
• Interacting surface states of three-dimensional topological insulators
• Walker-Wang models and axion electrodynamics
• Generalized Lieb-Schultz-Mattis theorem on bosonic symmetry protected topological phases
• Fractionalizing Global Symmetry on Looplike Topological Excitations
• Finite temperature bosonic charge and current densities in compactified cosmic string spacetime
• Fermionic Symmetry-Protected Topological Phase in a Two-Dimensional Hubbard Model