Fracton-like phases from subsystem symmetries

Abstract

We study models with fracton-like order based on ${\mathbb{Z}}_2$ lattice gauge theories with subsystem symmetries in $d=2$ and $d=3$ spatial dimensions. The $3d$ model reduces to the $3$-dimensional Toric Code when subsystem symmetry is broken, giving an example of a subsystem symmetry enriched topological phase (SSET). Although not topologically protected, its ground state degeneracy has as leading contribution a term which grows exponentially with the square of the linear size of the system. Also, there are completely mobile gauge charges living along with immobile fractons. Our method shows that fracton-like phases are also present in more usual lattice gauge theories. We calculate the entanglement entropy $S_A$ of these models in a sub-region $A$ of the lattice and show that it is equal to the logarithm of the ground state degeneracy of a particular restriction of the full model to $A$.

16 pages, 10 figures. Version to appear in PRB

References in corpus (10)

• Non-Abelian Anyons and Topological Quantum Computation
• Local stabilizer codes in three dimensions without string logical operators
• A classification of symmetry enriched topological phases with exactly solvable models
• A Family of Non-Abelian Kitaev Models on a Lattice: Topological Confinement and Condensation
• Symmetry Protected Topological Phases, Anomalies, and Cobordisms: Beyond Group Cohomology
• Mapping Kitaev's quantum double lattice models to Levin and Wen's string-net models
• Quantum mechanical and information theoretic view on classical glass transitions
• Isotropic Layer Construction and Phase Diagram for Fracton Topological Phases
• Sorting topological stabilizer models in three dimensions
• A simple anisotropic three-dimensional quantum spin liquid with fracton topological order

Cited by in corpus (7)

• Topological Defect Networks for Fractons of all Types
• Subsystem Non-Invertible Symmetry Operators and Defects
• Generating Lattice Non-invertible Symmetries
• Boson-fermion duality with subsystem symmetry
• Subsystem Symmetry-Protected Topological Phases from Subsystem SymTFT of 2-Foliated Exotic Tensor Gauge Theory
• Hidden subsystem symmetry protected states in competing topological orders
• Finite-group gauge theories on lattices as Hamiltonian systems with constraints