Fractons on the edge
arXiv:2411.19620 · doi:10.1103/ggls-zhl8
Abstract
We develop a theory of edge excitations of fractonic systems in two dimensions, and elucidate their connections to bulk transport properties and quantum statistics of bulk excitations. The system we consider has immobile point charges, dipoles constrained to move only along lines perpendicular to their moment, and freely mobile quadrupoles and higher multipoles, realizing a bulk fractonic analog of fractional quantum Hall phases. We demonstrate that a quantized braiding phase between two bulk excitations is obtained only in two cases: when a point quadrupole braids around an immobile point charge, or when two non-orthogonal point dipoles braid with one another. The presence of a boundary edge in the system entails types of gapless edge excitation modes, one that is fractonic with immobile charges and longitudinal dipoles, and a second non-fractonic mode consisting of transverse dipoles. We derive a novel current algebra of the fractonic edge modes. Further, investigating the effect of local edge-to-edge tunneling on these modes, we find that such a process is a relevant perturbation suggesting the possibility of edge deformation.
6 pages, 4 figures, Supplemental Material (8 pages, 1 figure)
References in corpus (47)
- Topological Insulators
- Topological insulators and superconductors
- Fault-tolerant quantum computation by anyons
- Classification of topological quantum matter with symmetries
- Topological insulators and superconductors: ten-fold way and dimensional hierarchy
- Periodic table for topological insulators and superconductors
- Zoo of quantum-topological phases of matter
- Local stabilizer codes in three dimensions without string logical operators
- Fracton Topological Order, Generalized Lattice Gauge Theory and Duality
- Quantum Glassiness
- Fractons
- A New Kind of Topological Quantum Order: A Dimensional Hierarchy of Quasiparticles Built from Stationary Excitations
- Subdimensional Particle Structure of Higher Rank U(1) Spin Liquids
- Fracton Phases of Matter
- Analytic and numerical demonstration of quantum self-correction in the 3D Cubic Code
- Generalized Electromagnetism of Subdimensional Particles: A Spin Liquid Story
- Fracton-Elasticity Duality
- 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
- Fracton Models on General Three-Dimensional Manifolds
- Towards classification of Fracton phases: the multipole algebra
- Gravitational Anomalies and Thermal Hall effect in Topological Insulators
- Dual gauge field theory of quantum liquid crystals in two dimensions
- Field Theories With a Vector Global Symmetry
- Chiral Topological Elasticity and Fracton Order
- Topological Quantum Glassiness
- Higher-Spin Witten Effect and Two-Dimensional Fracton Phases
- Gapless Bosonic Excitation without symmetry breaking: Novel Algebraic Spin liquid with soft Gravitons
- Emergent Phases of Fractonic Matter
- Foliated Quantum Field Theory of Fracton Order
- Fractional excitations in foliated fracton phases
- X-Cube Fracton Model on Generic Lattices: Phases and Geometric Order
- Symmetry Enriched Fracton Phases from Supersolid Duality
- Duality in 2+1D Quantum Elasticity: superconductivity and Quantum Nematic Order
- Fractonic Chern-Simons and BF theories
- Fracton fusion and statistics
- On duality between Cosserat elasticity and fractons
- -fractonic Maxwell theory
- 2+1d Compact Lifshitz Theory, Tensor Gauge Theory, and Fractons
- Effective Fractonic Behavior in a Two-Dimensional Exactly Solvable Spin Liquid
- Boundary theory of the X-cube model in the continuum
- A degeneracy bound for homogeneous topological order
- Fracton Self-Statistics
- Tearing Fractons
- Boundary Modes in the Chamon Model
- On quantum melting of superfluid vortex crystals: from Lifshitz scalar to dual gravity
- Ungappable edge theories with finite dimensional Hilbert spaces