Geometry defects in Bosonic symmetry protected topological phases

Abstract

In this paper we focus on the interplay between geometry defects and topological properties in bosonic symmetry protected topological(SPT) phases. We start from eight copies of 3D time-reversal($\mathcal{T}$) invariant topological superconductors(TSC) on a crystal lattice. We melt the lattice by condensation of disclinations and therefore restore the rotation symmetry. Such disclination condensation procedure confines the fermion and afterwards turns the system into a 3D boson topological liquid crystal(TCL). The low energy effective theory of this crystalline-liquid transition contains a topological term inherited from the geometry axion response in TSC. In addition, we investigate the interplay between dislocation and superfluid vortex on the surface of TCL. We demonstrate that the $\mathcal{T}$ and translation invariant surface state is a double $[e\mathcal{T}m\mathcal{T}]$ state with intrinsic surface topological order. We also look into the exotic behavior of dislocation in 2D boson SPT state described by an $O(4)$ non-linear $\sigma$-model(NL$\sigma$M) with topological $\Theta$-term. By dressing the $O(4)$ vector with spiral order and gauge the symmetry, the dislocation has mutual semion statistics with the gauge flux. Further reduce the $O(4)$ NL$\sigma M$ to the Ising limit, we arrive at the Levin-Gu model with stripy modulation whose dislocation has nontrivial braiding statistics.

References in corpus (45)

• Anyons in an exactly solved model and beyond
• Local unitary transformation, long-range quantum entanglement, wave function renormalization, and topological order
• Braiding statistics approach to symmetry-protected topological phases
• Coupling a QFT to a TQFT and Duality
• Physics of three dimensional bosonic topological insulators: Surface Deconfined Criticality and Quantized Magnetoelectric Effect
• Helical Metal Inside a Topological Band Insulator
• Topological Order with a Twist: Ising Anyons from an Abelian Model
• Hall Viscosity and Electromagnetic Response
• Electromagnetic and gravitational responses and anomalies in topological insulators and superconductors
• Interacting fermionic topological insulators/superconductors in three dimensions
• Genons, twist defects, and projective non-Abelian braiding statistics
• Classification of interacting electronic topological insulators in three dimensions
• Integer quantum Hall effect for bosons: A physical realization
• Classification of Two Dimensional Topological Crystalline Superconductors and Majorana Bound States at Disclinations
• Braiding statistics of loop excitations in three dimensions
• Exactly Soluble Model of a 3D Symmetry Protected Topological Phase of Bosons with Surface Topological Order
• Theory of defects in Abelian topological states
• Field theory representation of gauge-gravity symmetry-protected topological invariants, group cohomology and beyond
• Majorana Fermions and Disclinations in Topological Crystalline Superconductors
• Symmetry Enforced Non-Abelian Topological Order at the Surface of a Topological Insulator
• Electromagnetic and gravitational responses of two-dimensional non-interacting electrons in background magnetic field
• Bosonic topological insulator in three dimensions and the statistical Witten effect
• Framing Anomaly in the Effective Theory of Fractional Quantum Hall Effect
• Anomalous Symmetry Fractionalization and Surface Topological Order
• Topological field theory and thermal responses of interacting topological superconductors
• Symmetry Protected Topological States of Interacting Fermions and Bosons
• Classification and Description of Bosonic Symmetry Protected Topological Phases with semiclassical Nonlinear Sigma models
• Wave Functions of Bosonic Symmetry Protected Topological Phases
• Generalized modular transformations in 3+1D topologically ordered phases and triple linking invariant of loop braiding
• Geometry of Fractional Quantum Hall Fluids
• Layer construction of 3D topological states and string braiding statistics
• Hall viscosity, topological states and effective theories
• Theory of Nematic Fractional Quantum Hall State
• Synthetic Topological Degeneracy by Anyon Condensation
• Majorana zero modes in dislocations of Sr${}_2$RuO${}_4$
• 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
• World Nematic Crystal Model of Gravity Explaining the Absence of Torsion
• Multi-kink topological terms and charge-binding domain-wall condensation induced symmetry-protected topological states: Beyond Chern-Simons/BF theory
• Vortex-boson duality in four space-time dimensions
• Bridging Fermionic and Bosonic Short Range Entangled States
• Disclination classes, fractional excitations, and the melting of quantum liquid crystals
• Field Theory of Nematicity in the Spontaneous Quantum Anomalous Hall effect
• Anyon and Loop Braiding Statistics in Field Theories with a Topological $\Theta -$term
• Condensation of Lattice Defects and Melting Transitions in Quantum Hall phases

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