Topological order and Fractons from Gauging Exponential Symmetries

Abstract

We broaden the scope of quantum field theory by introducing a general class of discrete gauge theories that realize either topological order or fracton behavior across dimensions. We start from translation-invariant systems endowed with unconventional charge-conservation laws, which we term \textit{exponential polynomial symmetries}. Gauging these symmetries yields ${\mathbb{Z}}_N$ gauge theories in 2D that exhibit topological order whose quasiparticles have constrained mobility and whose ground-state degeneracy shows ultraviolet (UV) dependence. These features are reminiscent of spatial symmetry-enriched topological order, wherein quasiparticle excitations transform nontrivially under lattice translations. We further propose a Chern-Simons variant that produces non-CSS stabilizer codes and outline a framework for exponentially symmetric subsystem SPT phases. Finally, we extend this gauging procedure to 3D, obtaining new variants of fracton topological order.

arXiv comment24 pages, 18 figures. v5: typos fixed;

References in corpus (47)

• Fault-tolerant quantum computation by anyons
• Topological entanglement entropy
• Detecting topological order in a ground state wave function
• Quantum Spin Liquids
• Topological orders and Edge excitations in FQH states
• Local stabilizer codes in three dimensions without string logical operators
• Fracton Topological Order, Generalized Lattice Gauge Theory and Duality
• Quantum Glassiness
• Quantum orders in an exact soluble model
• Subdimensional Particle Structure of Higher Rank U(1) Spin Liquids
• Fracton Phases of Matter
• Quantum Field Theory of X-Cube Fracton Topological Order and Robust Degeneracy from Geometry
• Exotic Symmetries, Duality, and Fractons in 2+1-Dimensional Quantum Field Theory
• Subsystem symmetry protected topological order
• The Higgs Mechanism in Higher-Rank Symmetric $U(1)$ Gauge Theories
• Fracton topological order from Higgs and partial confinement mechanisms of rank-two gauge theory
• Emergent Phases of Fractonic Matter
• Strong-weak coupling self-duality in the two-dimensional quantum phase transition of $p+ip$ superconducting arrays
• Global Dipole Symmetry, Compact Lifshitz Theory, Tensor Gauge Theory, and Fractons
• Fractional excitations in foliated fracton phases
• Classification of subsystem symmetry-protected topological phases
• Fractonic Matter in Symmetry-Enriched U(1) Gauge Theory
• Cage-Net Fracton Models
• Spurious topological entanglement entropy from subsystem symmetries
• Resonating plaquette phases in large spin cold atom systems
• Symmetric Tensor Gauge Theories on Curved Spaces
• Topological Defect Networks for Fractons of all Types
• Fractons from vector gauge theory
• Bond algebraic liquid phase in strongly correlated multiflavor cold atom systems
• Fractonic Chern-Simons and BF theories
• Twisted foliated fracton phases
• Position-Dependent Excitations and UV/IR Mixing in the ${\mathbb{Z}}_N$ Rank-2 Toric Code and its Low-Energy Effective Field Theory
• Rank-2 Toric Code in Two Dimensions
• Fracton physics of spatially extended excitations
• Ground state degeneracy on torus in a family of ${\mathbb{Z}}_N$ toric code
• Effective Fractonic Behavior in a Two-Dimensional Exactly Solvable Spin Liquid
• Foliated BF theories and Multipole symmetries
• A Chern-Simons theory for dipole symmetry
• Aspects of ${\mathbb{Z}}_N$ rank-2 gauge theory in $(2+1)$ dimensions: construction schemes, holonomies, and sublattice one-form symmetries
• Effective Field Theory of Dipolar Braiding Statistics in Two Dimensions
• Anisotropic higher rank ${\mathbb{Z}}_N$ topological phases on graphs
• Spontaneous symmetry breaking without ground state degeneracy in generalized $N$-state clock model
• A Quantum Breakdown Model: from Many-body Localization to Chaos with Scars
• Anyon condensation web and multipartite entanglement in 2D modulated gauge theories
• Non-invertible duality and symmetry topological order of one-dimensional lattice models with spatially modulated symmetry
• Unveiling UV/IR Mixing via Symmetry Defects: A View from Topological Entanglement Entropy
• Noninvertible symmetry and topological holography for modulated SPT in one dimension

Cited by in corpus (7)

• Gauging modulated symmetries: Kramers-Wannier dualities and non-invertible reflections
• Unveiling UV/IR Mixing via Symmetry Defects: A View from Topological Entanglement Entropy
• Noninvertible symmetry and topological holography for modulated SPT in one dimension
• Gauging Modulated Symmetries via Multiple Gauge Symmetry Operators and Adaptive Quantum Circuits
• Topological Dipole Insulator
• Symmetry-enriched topological order and quasifractonic behavior in ${\mathbb{Z}}_N$ stabilizer codes
• Exponential $U(1)$ Symmetry-Breaking Phase as a Disorder-Free Quantum Glass