Soft symmetries of topological orders

Abstract

(2+1)D topological orders possess emergent symmetries given by a group $\text{Aut}(\mathcal{C})$, which consists of the braided tensor autoequivalences of the modular tensor category $\mathcal{C}$ that describes the anyons. In this paper we discuss cases where $\text{Aut}(\mathcal{C})$ has elements that neither permute anyons nor are associated to any symmetry fractionalization but are still non-trivial, which we refer to as soft symmetries. We point out that one can construct topological defects corresponding to such exotic symmetry actions by decorating with a certain class of gauged SPT states that cannot be distinguished by their torus partition function. This gives a physical interpretation to work by Davydov on soft braided tensor autoequivalences. This has a number of important implications for the classification of gapped boundaries, non-invertible spontaneous symmetry breaking, and the general classification of symmetry-enriched topological phases of matter. We also demonstrate analogous phenomena in higher dimensions, such as (3+1)D gauge theory with gauge group given by the quaternion group $Q_8$.

23 pages, 10 figures. added refs, added comments on open questions regarding H3 obstruction for soft symmetries

References in corpus (51)

• Fault-tolerant quantum computation by anyons
• Anyons in an exactly solved model and beyond
• Quantum Spin Liquids
• Classification of Gapped Symmetric Phases in 1D Spin Systems
• Observation of the e/3 Fractionally Charged Laughlin Quasiparticles
• Symmetry Fractionalization, Defects, and Gauging of Topological Phases
• Models for gapped boundaries and domain walls
• Exotic non-Abelian anyons from conventional fractional quantum Hall states
• Topological Order with a Twist: Ising Anyons from an Abelian Model
• Detection of Symmetry Protected Topological Phases in 1D
• On finite symmetries and their gauging in two dimensions
• Genons, twist defects, and projective non-Abelian braiding statistics
• Topological Nematic States and Non-Abelian Lattice Dislocations
• Fractionalizing Majorana fermions: non-abelian statistics on the edges of abelian quantum Hall states
• Protected edge modes without symmetry
• Topological boundary conditions in abelian Chern-Simons theory
• On 2-Group Global Symmetries and Their Anomalies
• The Quantum Double Model with Boundary: Condensations and Symmetries
• Categorical symmetry and non-invertible anomaly in symmetry-breaking and topological phase transitions
• Superconducting Proximity Effect on the Edge of Fractional Topological Insulators
• Translational symmetry and microscopic constraints on symmetry-enriched topological phases: a view from the surface
• A Family of Non-Abelian Kitaev Models on a Lattice: Topological Confinement and Condensation
• Bicategories for boundary conditions and for surface defects in 3-d TFT
• Gapped Domain Walls, Gapped Boundaries and Topological Degeneracy
• Classification of Topological Defects in Abelian Topological States
• Fractional Quantum Hall Hierarchy and the Second Landau Level
• Poking holes and cutting corners to achieve Clifford gates with the surface code
• Higher central charges and topological boundaries in 2+1-dimensional TQFTs
• On Gauging Symmetry of Modular Categories
• Symmetry-Enriched Quantum Spin Liquids in $(3+1)d$
• Synthetic Topological Qubits in Conventional Bilayer Quantum Hall Systems
• $U(1)\times U(1)⋊Z_2$ Chern-Simons Theory and Z_4 Parafermion Fractional Quantum Hall States
• Hamiltonian and Algebraic Theories of Gapped Boundaries in Topological Phases of Matter
• Codimension-2 defects and higher symmetries in (3+1)D topological phases
• Gapped Phases with Non-Invertible Symmetries: (1+1)d
• Microscopic definitions of anyon data
• Time-reversal and spatial reflection symmetry localization anomalies in (2+1)D topological phases of matter
• Relative Anomalies in (2+1)D Symmetry Enriched Topological States
• Higher-group symmetry in finite gauge theory and stabilizer codes
• Higher cup products on hypercubic lattices: application to lattice models of topological phases
• Absolute anomalies in (2+1)D symmetry-enriched topological states and exact (3+1)D constructions
• Bogomolov multiplier, double class-preserving automorphisms and modular invariants for orbifolds
• Realizing anomalous anyonic symmetries at the surfaces of 3d gauge theories
• Quantum Origami: Transversal Gates for Quantum Computation and Measurement of Topological Order
• Low overhead Clifford gates from joint measurements in surface, color, and hyperbolic codes
• A remark on gapped domain walls between topological phases
• Qutrit Toric Code and Parafermions in Trapped Ions
• A 3-categorical perspective on G-crossed braided categories
• Quantum Hall valley Ferromagnets as a platform for topologically protected quantum memory
• Projective Representations, Bogomolov Multiplier, and Their Applications in Physics
• Genus-One data and Anomaly Detection

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