Non-Abelian fracton order from gauging a mixture of subsystem and global symmetries

Abstract

We demonstrate a general gauging procedure of a pure matter theory on a lattice with a mixture of subsystem and global symmetries. This mixed symmetry can be either a semidirect product of a subsystem symmetry and a global symmetry, or a non-trivial extension of them. We demonstrate this gauging procedure on a cubic lattice in three dimensions with four examples: $G={\mathbb{Z}}_3^{\text{sub}}⋊{\mathbb{Z}}_2^{\text{glo}}$, $G=({\mathbb{Z}}_2^{\text{sub}}\times {\mathbb{Z}}_2^{\text{sub}})⋊{\mathbb{Z}}_2^{\text{glo}}$, $1\to {\mathbb{Z}}_2^{\text{sub}}\to G\to {\mathbb{Z}}_2^{\text{glo}}\to 1$, and $1\to {\mathbb{Z}}_2^{\text{sub}}\to G\to K_4^{\text{glo}}\to 1$. The former two cases and the last one produce the non-Abelian fracton orders. Our construction of the gauging procedure provides an identification of the electric charges of these fracton orders with irreducible representations of the symmetry. Furthermore, by constraining the local Hilbert space, the magnetic fluxes with different geometry (tube-like and plaquette-like) satisfy a subalgebra of the quantum double models (QDMs). This algebraic structure leads to an identification of the magnetic fluxes to the conjugacy classes of the symmetry.

arXiv comment2 columns, 24 pages, 4 tables

References in corpus (49)

• Fault-tolerant quantum computation by anyons
• Anyons in an exactly solved model and beyond
• Local stabilizer codes in three dimensions without string logical operators
• Braiding statistics approach to symmetry-protected topological phases
• Quantum Glassiness
• Fractons
• A New Kind of Topological Quantum Order: A Dimensional Hierarchy of Quasiparticles Built from Stationary Excitations
• Fracton Phases of Matter
• Analytic and numerical demonstration of quantum self-correction in the 3D Cubic Code
• Exotic topological order in fractal spin liquids
• Topological order in an exactly solvable 3D spin model
• Quantum memories at finite temperature
• Topological Entanglement Entropy in Chern-Simons Theories and Quantum Hall Fluids
• Quantum Field Theory of X-Cube Fracton Topological Order and Robust Degeneracy from Geometry
• Glassy quantum dynamics in translation invariant fracton models
• Fracton Models on General Three-Dimensional Manifolds
• Fracton topological order via coupled layers
• Foliated fracton order from gauging subsystem symmetries
• Fracton Topological Order from Nearest-Neighbor Two-Spin Interactions and Dualities
• Fracton topological phases from strongly coupled spin chains
• Topological Entanglement Entropy of Fracton Stabilizer Codes
• Fractional excitations in foliated fracton phases
• X-Cube Fracton Model on Generic Lattices: Phases and Geometric Order
• On the energy landscape of 3D spin Hamiltonians with topological order
• Twisted Fracton Models in Three Dimensions
• Cage-Net Fracton Models
• Fractons from Partons
• Pinch Point Singularities of Tensor Spin Liquids
• Topological Defect Networks for Fractons of all Types
• Entanglement Entropy From Tensor Network States for Stabilizer Codes
• Correlation function diagnostics for type-I fracton phases
• Universal quantum computation using fractal symmetry-protected cluster phases
• Isotropic Layer Construction and Phase Diagram for Fracton Topological Phases
• Recoverable Information and Emergent Conservation Laws in Fracton Stabilizer Codes
• Deciphering the nonlocal entanglement entropy of fracton topological orders
• Topological entanglement negativity in Chern-Simons theories
• Universal entanglement signatures of foliated fracton phases
• Gauging fractons: immobile non-Abelian quasiparticles, fractals, and position-dependent degeneracies
• Ungauging quantum error-correcting codes
• Non-Abelian Hybrid Fracton Orders
• A simple anisotropic three-dimensional quantum spin liquid with fracton topological order
• Gauging permutation symmetries as a route to non-Abelian fractons
• A Generalization of Non-Abelian Anyons in Three Dimensions
• Subsystem symmetry enriched topological order in three dimensions
• Hybrid Fracton Phases: Parent Orders for Liquid and Non-Liquid Quantum Phases
• Higher-Rank Tensor Non-Abelian Field Theory: Higher-Moment or Subdimensional Polynomial Global Symmetry, Algebraic Variety, Noether's Theorem, and Gauging
• Generalized $U(1)$ Gauge Field Theories and Fractal Dynamics
• Non-Abelian Gauged Fracton Matter Field Theory: New Sigma Models, Superfluids and Vortices
• Higher-Rank Tensor Field Theory of Non-Abelian Fracton and Embeddon