Vortex-line condensation in three dimensions: A physical mechanism for bosonic topological insulators

Abstract

Bosonic topological insulators (BTI) in three dimensions are symmetry-protected topological phases (SPT) protected by time-reversal and boson number conservation {symmetries}. BTI in three dimensions were first proposed and classified by the group cohomology theory which suggests two distinct root states, each carrying a ${\mathbb{Z}}_2$ index. Soon after, surface anomalous topological orders were proposed to identify different root states of BTI, which even leads to a new BTI root state beyond the group cohomology classification. In this paper, we propose a universal physical mechanism via \textit{vortex-line condensation} {from} a 3d superfluid to achieve all {three} root states. It naturally produces bulk topological quantum field theory (TQFT) description for each root state. Topologically ordered states on the surface are \textit{rigorously} derived by placing TQFT on an open manifold, which allows us to explicitly demonstrate the bulk-boundary correspondence. Finally, we generalize the mechanism to $Z_N$ symmetries and discuss potential SPT phases beyond the group cohomology classification.

arXiv commentReVTeX 4.1 (published version)

References in corpus (59)

• Topological Insulators
• Topological insulators and superconductors
• Fault-tolerant quantum computation by anyons
• Anyons in an exactly solved model and beyond
• Topological Insulators in Three Dimensions
• Discovery (theoretical prediction and experimental observation) of a large-gap topological-insulator class with spin-polarized single-Dirac-cone on the surface
• Topological Field Theory of Time-Reversal Invariant Insulators
• Topological invariants of time-reversal-invariant band structures
• Entanglement spectrum of a topological phase in one dimension
• Symmetry protected topological orders and the group cohomology of their symmetry group
• Topological orders and Edge excitations in FQH states
• Tensor-Entanglement-Filtering Renormalization Approach and Symmetry Protected Topological Order
• Three dimensional topological invariants for time reversal invariant Hamiltonians and the three dimensional quantum spin Hall effect
• Local unitary transformation, long-range quantum entanglement, wave function renormalization, and topological order
• Braiding statistics approach to symmetry-protected topological phases
• 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
• Boson topological insulators: A window into highly entangled quantum phases
• Symmetry protected topological phases from decorated domain walls
• Integer quantum Hall effect for bosons: A physical realization
• Classifying gauge anomalies through SPT orders and classifying gravitational anomalies through topological orders
• Classification and analysis of two dimensional abelian fractional topological insulators
• Exactly Soluble Model of a 3D Symmetry Protected Topological Phase of Bosons with Surface Topological Order
• Field theory representation of gauge-gravity symmetry-protected topological invariants, group cohomology and beyond
• Symmetry Enforced Non-Abelian Topological Order at the Surface of a Topological Insulator
• A Time-Reversal Invariant Topological Phase at the Surface of a 3D Topological Insulator
• Gapped Symmetry Preserving Surface-State for the Electron Topological Insulator
• Bosonic topological insulator in three dimensions and the statistical Witten effect
• Topological BF field theory description of topological insulators
• Bulk-Edge Correspondence in 2+1-Dimensional Abelian Topological Phases
• Classification and Description of Bosonic Symmetry Protected Topological Phases with semiclassical Nonlinear Sigma models
• Wave Functions of Bosonic Symmetry Protected Topological Phases
• On the origin of artificial electrodynamics and other stories in three-dimensional bosonic models
• Symmetry-protected topological invariants of symmetry-protected topological phases of interacting bosons and fermions
• Symmetry protected Spin Quantum Hall phases in 2-Dimensions
• Quantum Hall Effect of Two-Component Bosons at Fractional and Integral Fillings
• Construction of bosonic symmetry-protected-trivial states and their topological invariants via $G\times SO(\infty )$ non-linear $\sigma$-models
• Integer Quantum Hall State in Two-Component Bose Gases in a Synthetic Magnetic Field
• Symmetry-protected topological phases and orbifolds: Generalized Laughlin's argument
• Composite Dirac liquids: parent states for symmetric surface topological order
• Topological Response Theory of Abelian Symmetry-Protected Topological Phases in Two Dimensions
• Microscopic model for the boson integer quantum Hall effect
• Effective field theories for topological insulators by functional bosonization
• A K matrix Construction of Symmetry Enriched Phases of Matter
• Canonical BF-type Topological Field Theory and Fractional Statistics of Strings
• Constructing symmetric topological phases of bosons in three dimensions via fermionic projective construction and dyon condensation
• Projective construction of two-dimensional symmetry-protected topological phases with U(1), SO(3), or SU(2) symmetries
• Symmetry-protected topological phases with charge and spin symmetries: response theory and dynamical gauge theory in 2D, 3D and the surface of 3D
• Microscopic Realization of 2-Dimensional Bosonic Topological Insulators
• $U(1)\times U(1)$ Symmetry Protected Topological Order in Gutzwiller Wave Functions
• Vortex-boson duality in four space-time dimensions
• Short-Range Entangled Bosonic States with Chiral Edge Modes and $T$-duality of Heterotic Strings
• Two dimensional Symmetry Protected Topological Phases with PSU(N) and time reversal symmetry
• Spin quantum Hall effects in a spin-1 topological paramagnet
• Model Realization and Numerical Studies of a Three-Dimensional Bosonic Topological Insulator and Symmetry-Enriched Topological Phases
• Line defects in Three dimensional Symmetry Protected Topological Phases
• String Holonomy and Extrinsic Geometry in Four-dimensional Topological Gauge Theory
• The Partially-Split Hall Bar: Tunneling in the Bosonic Integer Quantum Hall Effect

Cited by in corpus (47)

• Self-induced topological transitions and edge states supported by nonlinear staggered potentials
• Fractonic Superfluids
• Dual gauge field theory of quantum liquid crystals in three dimensions
• Bulk-boundary correspondence in (3+1)-dimensional topological phases
• Bosonic Integer Quantum Hall effect in an interacting lattice model
• A classification of 3+1D bosonic topological orders (II): the case when some point-like excitations are fermions
• Quantum 4d Yang-Mills Theory and Time-Reversal Symmetric 5d Higher-Gauge Topological Field Theory
• 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
• Braiding with Borromean Rings in (3+1)-Dimensional Spacetime
• Wire constructions of Abelian topological phases in three or more dimensions
• Composite Particle Theory of Three-dimensional Gapped Fermionic Phases: Fractional Topological Insulators and Charge-Loop Excitation Symmetry
• Fractonic superfluids. (II). Condensing subdimensional particles
• Generalized Wen-Zee Terms
• Field Theories for Gauged Symmetry Protected Topological Phases: Abelian Gauge Theories with non-Abelian Quasiparticles
• Exactly soluble local bosonic cocycle models, statistical transmutation, and simplest time-reversal symmetric topological orders in 3+1D
• Topological Quantum Field Theory for Abelian Topological Phases and Loop Braiding Statistics in $(3+1)$-Dimensions
• Symmetry Enrichment in Three-Dimensional Topological Phases
• On the Symmetry TFT of Yang-Mills-Chern-Simons theory
• Fractional $S$-duality, Classification of Fractional Topological Insulators and Surface Topological Order
• Topological Electromagnetic Responses of Bosonic Quantum Hall, Topological Insulator, and Chiral Semi-Metal phases in All Dimensions
• Quantum Paramagnet and Frustrated Quantum Criticality in a Spin-One Diamond Lattice Antiferromagnet
• Effective hydrodynamic field theory and condensation picture of topological insulators
• Theory of the fractional quantum Hall effect in Weyl semimetals
• Physics of Symmetry Protected Topological phases involving Higher Symmetries and their Applications
• Non-Abelian Gauged Fracton Matter Field Theory: New Sigma Models, Superfluids and Vortices
• Theory of oblique topological insulators
• Compatible braidings with Hopf links, multi-loop, and Borromean rings in $(3+1)$-dimensional spacetime
• Evolution of Dynamical Signature in the X-cube Fracton Topological Order
• Geometry defects in Bosonic symmetry protected topological phases
• Topological Orders, Braiding Statistics, and Mixture of Two Types of Twisted $BF$ Theories in Five Dimensions
• Detecting Subsystem Symmetry Protected Topological Order Through Strange Correlators
• Fractionalizing Global Symmetry on Looplike Topological Excitations
• Higher-Order Cellular Automata Generated Symmetry-Protected Topological Phases and Detection Through Multi-Point Strange Correlators
• Hierarchical Proliferation of Higher-Rank Symmetry Defects in Fractonic Superfluids
• Topological order in interacting semimetals
• Continuum field theory of 3D topological orders with emergent fermions and braiding statistics
• Generalized toric codes on twisted tori for quantum error correction
• Anomalies and symmetry fractionalization in reflection-symmetric topological order
• Fusion rules and shrinking rules of topological orders in five dimensions
• A Bosonic Analog of a Topological Dirac Semi-Metal: Effective Theory, Neighboring Phases, and Wire Construction
• Topological Phases for Extended Objects: Semiclassical Phase-Space Approach with Tensorial Coordinates
• Diagrammatics, Pentagon Equations, and Hexagon Equations of Topological Orders with Loop- and Membrane-like Excitations
• Perturbative and global anomalies in bosonic analogues of integer quantum Hall and topological insulator phases
• Infinite-component $BF$ field theory: Connection of fracton order, Toeplitz braiding, and non-Hermitian amplification
• Preparing Code States via Seed-Entangler-Enriched Sequential Quantum Circuits: Application to Tetra-Digit Topological Error-Correcting Codes
• Spurious Strange Correlators in Symmetry-Protected Topological Phases