Fractons from vector gauge theory

Abstract

Motivated by the prediction of fractonic topological defects in a quantum crystal, we utilize a reformulated elasticity duality to derive a description of a fracton phase in terms of coupled vector U(1) gauge theories. The fracton order and restricted mobility emerge as a result of an unusual Gauss law where electric field lines of one gauge field act as sources of charge for others. At low energies this vector gauge theory reduces to the previously studied fractonic symmetric tensor gauge theory. We construct the corresponding lattice model and a number of generalizations, which realize fracton phases via a condensation of string-like excitations built out of charged particles, analogous to the p-string condensation mechanism of the gapped X-cube fracton phase.

7 pages, 1 figure. v2 (published version) includes generalization to the vector-charge theory, and improved discussion of compactness and associated symmetries in 2D

References in corpus (2)

• Local stabilizer codes in three dimensions without string logical operators
• Isotropic Layer Construction and Phase Diagram for Fracton Topological Phases

Cited by in corpus (49)

• Fracton hydrodynamics
• Foliated Quantum Field Theory of Fracton Order
• The dipolar Bose-Hubbard model
• Breakdown of hydrodynamics below four dimensions in a fracton fluid
• Fractonic Superfluids
• Crystal-to-Fracton Tensor Gauge Theory Dualities
• Topological Defect Networks for Fractons of all Types
• Spontaneous breaking of multipole symmetries
• Fracton phases via exotic higher-form symmetry-breaking
• Strong planar subsystem symmetry-protected topological phases and their dual fracton orders
• Crystalline gauge fields and quantized discrete geometric response for Abelian topological phases with lattice symmetry
• Fracton-elasticity duality of two-dimensional superfluid vortex crystals: defect interactions and quantum melting
• Quantum smectic gauge theory
• On duality between Cosserat elasticity and fractons
• Fractonic superfluids. (II). Condensing subdimensional particles
• Hohenberg-Mermin-Wagner-type theorems and dipole symmetry
• Fracton physics of spatially extended excitations
• Hydrodynamics of dipole-conserving fluids
• Effective field theories for gapless phases with fractons via a coset construction
• Fracton Topological Order at Finite Temperature
• Lifshitz gauge duality
• A Chern-Simons theory for dipole symmetry
• A symmetry principle for gauge theories with fractons
• Aspects of ${\mathbb{Z}}_N$ rank-2 gauge theory in $(2+1)$ dimensions: construction schemes, holonomies, and sublattice one-form symmetries
• Planar p-String Condensation: Chiral Fracton Phases from Fractional Quantum Hall Layers and Beyond
• Emergent Dipole Gauge Fields and Fractons
• Fractonic gauge theory of smectics
• Fracton physics of spatially extended excitations. II. Polynomial ground state degeneracy of exactly solvable models
• Non-Abelian Gauged Fracton Matter Field Theory: New Sigma Models, Superfluids and Vortices
• Fracton-elasticity duality in twisted moiré superlattices
• Fractons, non-Riemannian Geometry, and Double Field Theory
• Realization of fractonic quantum phases in the breathing pyrochlore lattice
• Renormalization group analysis on emergence of higher rank symmetry and higher moment conservation
• Fracton gravity from spacetime dipole symmetry
• Note on Generalized Symmetries, Gapless Excitations, Generalized Symmetry Protected Topological states, and Anomaly
• Anyon condensation web and multipartite entanglement in 2D modulated gauge theories
• Electric Circuit Realizations of Fracton Physics
• Fracton-elasticity duality on curved manifolds
• Quantum vortex lattice: Lifshitz duality, topological defects and multipole symmetries
• Elastic Liénard-Wiechert potentials of dynamical dislocations from tensor gauge theory in 2+1 dimensions
• Dissipative fracton superfluids
• Asymptotic symmetries and soft charges of fractons
• Topological order and Fractons from Gauging Exponential Symmetries
• Electric-Magnetic Duality for Symmetric Tensor Gauge Theories and Immobile $p$-branes
• Vortices in fracton type gauge theories
• Topological stabilizer models on continuous variables
• Non-equilibrium charge-vortex duality
• Emblems of pair density waves: dual identity of topological defects and their transport signatures
• Covariant Fracton Electrodynamics in Six Dimensions