Fractonic topological phases from coupled wires

Abstract

In three dimensions, gapped phases can support "fractonic" quasiparticle excitations, which are either completely immobile or can only move within a low-dimensional submanifold, a peculiar topological phenomenon going beyond the conventional framework of topological quantum field theory. In this work we explore fractonic topological phases using three-dimensional coupled wire constructions, which have proven to be a successful tool to realize and characterize topological phases in two dimensions. We find that both gapped and gapless phases with fractonic excitations can emerge from the models. In the gapped case, we argue that fractonic excitations are mobile along the wire direction, but their mobility in the transverse plane is generally reduced. We show that the excitations in general have infinite-order fusion structure, distinct from previously known gapped fracton models. Like the 2D coupled wire constructions, many models exhibit gapless (or even chiral) surface states, which can be described by infinite-component Luttinger liquids. However, the universality class of the surface theory strongly depends on the surface orientation, thus revealing a new type of bulk-boundary correspondence unique to fracton phases.

arXiv comment11+12 pages, 7 figures. (v2) Updated with additional references. v(3) Updated with journal format

References in corpus (45)

• Local stabilizer codes in three dimensions without string logical operators
• Fracton Topological Order, Generalized Lattice Gauge Theory and Duality
• Symmetry Fractionalization, Defects, and Gauging of Topological Phases
• 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
• Fractional topological insulators
• Generalized Electromagnetism of Subdimensional Particles: A Spin Liquid Story
• Exotic topological order in fractal spin liquids
• The Fractional Quantum Hall effect in an array of quantum wires
• From Luttinger liquid to non-Abelian quantum Hall states
• Topological order in an exactly solvable 3D spin model
• Exotic $U(1)$ Symmetries, Duality, and Fractons in 3+1-Dimensional Quantum Field Theory
• Fracton Models on General Three-Dimensional Manifolds
• Classification and analysis of two dimensional abelian fractional topological insulators
• Fracton topological order via coupled layers
• Fractional topological liquids with time-reversal symmetry and their lattice realization
• Stability of Chiral Luttinger Liquids and Abelian Quantum Hall States.
• Foliated fracton order from gauging subsystem symmetries
• Towards classification of Fracton phases: the multipole algebra
• Field Theories With a Vector Global Symmetry
• Fracton topological phases from strongly coupled spin chains
• Fractional excitations in foliated fracton phases
• Commuting Pauli Hamiltonians as maps between free modules
• Foliated Field Theory and String-Membrane-Net Condensation Picture of Fracton Order
• Twisted Fracton Models in Three Dimensions
• Fractonic Matter in Symmetry-Enriched U(1) Gauge Theory
• Cage-Net Fracton Models
• Symmetric Fracton Matter: Twisted and Enriched
• Topological Defect Networks for Fractons of all Types
• Twisted foliated fracton phases
• Fracton fusion and statistics
• Sorting topological stabilizer models in three dimensions
• A systematic construction of gapped non-liquid states
• Wire constructions of Abelian topological phases in three or more dimensions
• Compactifying fracton stabilizer models
• Coupled-wire constructions: a Luttinger liquid approach to topology
• Type-II fractons from coupled spin chains and layers
• Non-diagonal anisotropic quantum Hall states
• Planar p-String Condensation: Chiral Fracton Phases from Fractional Quantum Hall Layers and Beyond
• From coupled-wire construction of quantum Hall states to wave functions and hydrodynamics
• Formalism for the solution of quadratic Hamiltonians with large cosine terms
• From coupled wires to coupled layers: Model with three-dimensional fractional excitations

Cited by in corpus (8)

• Subdimensional criticality: condensation of lineons and planons in the X-cube model
• Interaction Enabled Fractonic Higher-Order Topological Phases
• Disentangling (2+1)d Topological States of Matter with the Entanglement Negativity
• Bridging three-dimensional coupled-wire models and cellular topological states: Solvable models for topological and fracton orders
• Fractonic criticality in Rydberg atom arrays
• Dihedral twist liquid models from emergent Majorana fermions
• Topological Dipole Insulator
• Unidirectional subsystem symmetry in a hole-doped honeycomb-lattice Ising magnet