Subdimensional Particle Structure of Higher Rank U(1) Spin Liquids

Abstract

Spin liquids are conventionally described by gauge theories with a vector gauge field. However, there exists a wider class of spin liquids with higher rank tensors as the gauge variable. In this work, we focus on (3+1)-dimensional spin liquids described by U(1) symmetric tensor gauge theories, which have recently been shown to be stable gapless spin liquids. We investigate the particle structure of these tensor gauge theories and find that they have deep connections with the "fracton" models recently discovered by Vijay, Haah, and Fu. Tensor gauge theories have more conservation laws than the simple charge conservation law of rank 1 theories. These conservation laws place severe restrictions on the motion of particles. Particles in some models are fully immobile (fractons), while other models have particles restricted to motion along lower-dimensional subspaces.

11+2 pages

References in corpus (12)

• Zoo of quantum-topological phases of matter
• Local stabilizer codes in three dimensions without string logical operators
• Pyrochlore Photons: The U(1) Spin Liquid in a S=1/2 Three-Dimensional Frustrated Magnet
• Fracton Topological Order, Generalized Lattice Gauge Theory and Duality
• On the stability of U(1) spin liquids in two dimensions
• Glassy quantum dynamics in translation invariant fracton models
• Fracton topological order via coupled layers
• Gapless Bosonic Excitation without symmetry breaking: Novel Algebraic Spin liquid with soft Gravitons
• Isotropic Layer Construction and Phase Diagram for Fracton Topological Phases
• A lattice bosonic model as a quantum theory of gravity
• Novel Algebraic Boson Liquid phase with soft Graviton excitations
• Lattice Gerbe Theory

Cited by in corpus (286)

• Fractons
• Localization from Hilbert space shattering: from theory to physical realizations
• Local constraints can globally shatter Hilbert space: a new route to quantum information protection
• Ergodicity-breaking arising from Hilbert space fragmentation in dipole-conserving Hamiltonians
• Generalized Symmetries in Condensed Matter
• Fracton Phases of Matter
• Generalized Electromagnetism of Subdimensional Particles: A Spin Liquid Story
• Fracton-Elasticity Duality
• Fracton hydrodynamics
• The Fracton Gauge Principle
• Hilbert-Space Fragmentation from Strict Confinement
• 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
• Glassy quantum dynamics in translation invariant fracton models
• Exotic $U(1)$ Symmetries, Duality, and Fractons in 3+1-Dimensional Quantum Field Theory
• Fracton Models on General Three-Dimensional Manifolds
• Anomalous Diffusion in Dipole- and Higher-Moment Conserving Systems
• Fracton topological order via coupled layers
• Statistical localization: from strong fragmentation to strong edge modes
• Foliated fracton order from gauging subsystem symmetries
• Towards classification of Fracton phases: the multipole algebra
• The Higgs Mechanism in Higher-Rank Symmetric $U(1)$ Gauge Theories
• Fractons, dipole symmetries and curved spacetime
• Fracton topological order from Higgs and partial confinement mechanisms of rank-two gauge theory
• Emergent Gravity of Fractons: Mach's Principle Revisited
• Chiral Topological Elasticity and Fracton Order
• Localization in fractonic random circuits
• Higher-Spin Witten Effect and Two-Dimensional Fracton Phases
• Anomalous Subdiffusion from Subsystem Symmetries
• Emergent Phases of Fractonic Matter
• Dynamical scar states in driven fracton systems
• Global Dipole Symmetry, Compact Lifshitz Theory, Tensor Gauge Theory, and Fractons
• Fracton topological phases from strongly coupled spin chains
• Topological Entanglement Entropy of Fracton Stabilizer Codes
• Foliated Quantum Field Theory of Fracton Order
• Fractal Symmetric Phases of Matter
• Thermalization and its absence within Krylov subspaces of a constrained Hamiltonian
• X-Cube Fracton Model on Generic Lattices: Phases and Geometric Order
• Hyperbolic Fracton Model, Subsystem Symmetry, and Holography
• Foliated Field Theory and String-Membrane-Net Condensation Picture of Fracton Order
• Multipole conservation laws and subdiffusion in any dimension
• Twisted Fracton Models in Three Dimensions
• Breakdown of hydrodynamics below four dimensions in a fracton fluid
• Experimental probes of Stark many-body localization
• The dipolar Bose-Hubbard model
• Fractonic Matter in Symmetry-Enriched U(1) Gauge Theory
• Cage-Net Fracton Models
• Exotic ${\mathbb{Z}}_N$ Symmetries, Duality, and Fractons in 3+1-Dimensional Quantum Field Theory
• Fractonic Superfluids
• Symmetric Fracton Matter: Twisted and Enriched
• Fractons from Partons
• Rank-2 $U(1)$ spin liquid on the breathing pyrochlore lattice
• Pinch Point Singularities of Tensor Spin Liquids
• Multipolar Topological Field Theories: Bridging Higher Order Topological Insulators and Fractons
• Hydrodynamics of ideal fracton fluids
• Topological Defect Networks for Fractons of all Types
• Symmetric Tensor Gauge Theories on Curved Spaces
• Crystal-to-Fracton Tensor Gauge Theory Dualities
• Correlation function diagnostics for type-I fracton phases
• Entanglement Entropy From Tensor Network States for Stabilizer Codes
• Symmetry Enriched Fracton Phases from Supersolid Duality
• Minimal model for Hilbert space fragmentation with local constraints
• Fractonic line excitations : an inroad from 3d elasticity theory
• Fractons from vector gauge theory
• Spontaneous breaking of multipole symmetries
• Recoverable Information and Emergent Conservation Laws in Fracton Stabilizer Codes
• Deciphering the nonlocal entanglement entropy of fracton topological orders
• Fractonic Chern-Simons and BF theories
• Universal entanglement signatures of foliated fracton phases
• Twisted foliated fracton phases
• Fracton fusion and statistics
• Foliated fracton order in the checkerboard model
• Volume-preserving diffeomorphism as nonabelian higher-rank gauge symmetry
• Higher order topological superconductors as generators of quantum codes
• Symmetry enforced fractonicity and $2d$ quantum crystal melting
• Higher Rank Deconfined Quantum Criticality at the Lifshitz Transition and the Exciton Bose Condensate
• Gauging fractons: immobile non-Abelian quasiparticles, fractals, and position-dependent degeneracies
• Braiding and Gapped Boundaries in Fracton Topological Phases
• Strong planar subsystem symmetry-protected topological phases and their dual fracton orders
• Fractonic Luttinger Liquids and Supersolids in a Constrained Bose-Hubbard Model
• Crystalline gauge fields and quantized discrete geometric response for Abelian topological phases with lattice symmetry
• Anisotropic layer construction of anisotropic fracton models
• A simple anisotropic three-dimensional quantum spin liquid with fracton topological order
• Fracton-elasticity duality of two-dimensional superfluid vortex crystals: defect interactions and quantum melting
• Hidden quasiconservation laws in fracton hydrodynamics
• Goldstone bosons and fluctuating hydrodynamics with dipole and momentum conservation
• Emergent fractons and algebraic quantum liquid from plaquette melting transitions
• Spiral spin-liquid on a honeycomb lattice
• Dipole condensates in tilted Bose-Hubbard chains
• Fractons from confinement in one dimension
• Gauging permutation symmetries as a route to non-Abelian fractons
• Unifying Emergent Hydrodynamics and Lindbladian Low Energy Spectra across Symmetries, Constraints, and Long-Range Interactions
• Position-Dependent Excitations and UV/IR Mixing in the ${\mathbb{Z}}_N$ Rank-2 Toric Code and its Low-Energy Effective Field Theory
• On duality between Cosserat elasticity and fractons
• Jordan-Wigner Dualities for Translation-Invariant Hamiltonians in Any Dimension: Emergent Fermions in Fracton Topological Order
• Bifurcating entanglement-renormalization group flows of fracton stabilizer models
• Fracton hydrodynamics without time-reversal symmetry
• Fractonic superfluids. (II). Condensing subdimensional particles
• Hilbert space shattering and dynamical freezing in the quantum Ising model
• Hohenberg-Mermin-Wagner-type theorems and dipole symmetry
• Comments on Foliated Gauge Theories and Dualities in 3+1d
• Compactifying fracton stabilizer models
• Higher-Form Subsystem Symmetry Breaking: Subdimensional Criticality and Fracton Phase Transitions
• Rank-2 Toric Code in Two Dimensions
• Finite-Temperature Screening of U(1) Fractons
• Many-Body Non-Hermitian Skin Effect for Multipoles
• Fractons from polarons
• Fracton physics of spatially extended excitations
• $(k,n)$-fractonic Maxwell theory
• Generalized Symmetries of the Graviton
• 2+1d Compact Lifshitz Theory, Tensor Gauge Theory, and Fractons
• Classification of translation invariant topological Pauli stabilizer codes for prime dimensional qudits on two-dimensional lattices
• Quantum effects on unconventional pinch point singularities
• Mixed s-sourcery: Building many-body states using bubbles of Nothing
• Majorana Quantum Lego, a Route Towards Fracton Matter
• Entanglement Spectra of Stabilizer Codes: A Window into Gapped Quantum Phases of Matter
• Constructing Quantum Spin Liquids Using Combinatorial Gauge Symmetry
• Quantum robustness of fracton phases
• Hydrodynamics of dipole-conserving fluids
• Gauging modulated symmetries: Kramers-Wannier dualities and non-invertible reflections
• Exact solution for the filling-induced thermalization transition in a 1D fracton system
• Spontaneously Broken Subsystem Symmetries
• Searching for Fracton Orders via Symmetry Defect Condensation
• Classifying local fractal subsystem symmetry protected topological phases
• Foliated BF theories and Multipole symmetries
• Higher-form Gauge Symmetries in Multipole Topological Phases
• Maxwell theory of fractons
• Effective field theories for gapless phases with fractons via a coset construction
• Subdimensional criticality: condensation of lineons and planons in the X-cube model
• Coupled Hydrodynamics in Dipole-Conserving Quantum Systems
• Fractonic order in infinite-component Chern-Simons gauge theories
• Low energy structure of spiral spin liquids
• Hyperbolic Fracton Model, Subsystem Symmetry, and Holography II: The Dual Eight-Vertex Model
• Combined approach to analyze and classify families of classical spin liquids
• Hilbert space fragmentation produces a "fracton Casimir effect"
• Gapless edge modes in (4+1)-dimensional topologically massive tensor gauge theory and anomaly inflow for subsystem symmetry
• Gauging fractons and linearized gravity
• Lieb-Schultz-Mattis type constraints on Fractonic Matter
• Dual gauge theory formulation of planar quasicrystal elasticity and fractons
• Topological fracton quantum phase transitions by tuning exact tensor network states
• Higher-Rank Tensor Non-Abelian Field Theory: Higher-Moment or Subdimensional Polynomial Global Symmetry, Algebraic Variety, Noether's Theorem, and Gauging
• Emergent tracer dynamics in constrained quantum systems
• Boundary theory of the X-cube model in the continuum
• Lifshitz gauge duality
• Critically slow operator dynamics in constrained many-body systems
• Fracton Topological Order at Finite Temperature
• Foliated-Exotic Duality in Fractonic BF Theories
• 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
• Ideal fracton superfluids
• Height-conserving quantum dimer models
• Generalized $U(1)$ Gauge Field Theories and Fractal Dynamics
• Fracton superfluid hydrodynamics
• Spontaneously broken supersymmetric fracton phases with fermionic subsystem symmetries
• Effective Field Theory of Dipolar Braiding Statistics in Two Dimensions
• Emergent Dipole Gauge Fields and Fractons
• Fractal Quantum Phase Transitions: Critical Phenomena Beyond Renormalization
• Planar p-String Condensation: Chiral Fracton Phases from Fractional Quantum Hall Layers and Beyond
• Fracton magnetohydrodynamics
• Covariant fracton gauge theory with boundary
• Fractonic plaquette-dimer liquid beyond renormalization
• Distilling Fractons from Layered Subsystem-Symmetry Protected Phases
• A degeneracy bound for homogeneous topological order
• Non-Abelian Gauged Fracton Matter Field Theory: New Sigma Models, Superfluids and Vortices
• Deconfinement Dynamics of Fractons in Tilted Bose-Hubbard Chains
• Gapped boundaries of (3+1)d topological orders
• Emergent Fracton Dynamics in a Non-Planar Dimer Model
• Fracton Self-Statistics
• Lattice Clifford fractons and their Chern-Simons-like theory
• Hierarchical hydrodynamics in long-range multipole-conserving systems
• Evolution of Dynamical Signature in the X-cube Fracton Topological Order
• Exotic quantum liquids in Bose-Hubbard models with spatially-modulated symmetries
• Theory of Dipole Insulators
• Fractons, non-Riemannian Geometry, and Double Field Theory
• Renormalization group analysis on emergence of higher rank symmetry and higher moment conservation
• Tearing Fractons
• Fractons from frustration in hole-doped antiferromagnets
• Detecting Subsystem Symmetry Protected Topological Order Through Strange Correlators
• Realization of fractonic quantum phases in the breathing pyrochlore lattice
• Fractons on Graphs and Complexity
• Fracton gravity from spacetime dipole symmetry
• Statistical mechanics of dimers on quasiperiodic Ammann-Beenker tilings
• Note on Generalized Symmetries, Gapless Excitations, Generalized Symmetry Protected Topological states, and Anomaly
• Geodesic string condensation from symmetric tensor gauge theory: a unifying framework of holographic toy models
• Bose-Hubbard realization of fracton defects
• A Classical Chiral Spin-Liquid from Chiral Interactions on the Pyrochlore Lattice
• Topological Dipole Conserving Insulators and Multipolar Responses
• Noncommutative Field Theory of the Tkachenko Mode: Symmetries and Decay Rate
• Multipole groups and fracton phenomena on arbitrary crystalline lattices
• Fractonic topological phases from coupled wires
• Topological defect network representations of fracton stabilizer codes
• Odd Fracton Theories, Proximate Orders, and Parton Constructions
• Fractons from a liquid of singlet pairs
• Beyond the Freshman's Dream: Classical fractal spin liquids from matrix cellular automata in three-dimensional lattice models
• Non-Abelian defects in Fracton phase of matter
• Fracton excitations in classical frustrated kagome spin models
• Gapless Topological Order, Gravity, and Black Holes
• Fracton-like phases from subsystem symmetries
• Electric Circuit Realizations of Fracton Physics
• Systematic Constructions of Fracton Theories
• Holographic subdiffusion
• Spectroscopic fingerprints of gapless type-II fracton phases
• Boundary Modes in the Chamon Model
• Dynamical Spectral Response of Fractonic Quantum Matter
• Non-Fermi liquid induced by Bose metal with protected subsystem symmetries
• Screw dislocations in the X-cube fracton model
• Higher-Order Cellular Automata Generated Symmetry-Protected Topological Phases and Detection Through Multi-Point Strange Correlators
• Solving the quantum dimer and six vertex models one electric field line at a time
• Asymptotic symmetries and soft charges of fractons
• Glassy dynamics of the one-dimensional Mott insulator excited by a strong terahertz pulse
• Topological order and Fractons from Gauging Exponential Symmetries
• Hierarchical Proliferation of Higher-Rank Symmetry Defects in Fractonic Superfluids
• Hall-like behaviour of higher rank Chern-Simons theory of fractons
• Ferromagnets, a New Anomaly, Instantons, and (noninvertible) Continuous Translations
• Covariant Interacting Fractons
• Spiral spin liquid in a frustrated honeycomb antiferromagnet: A single-crystal study of GdZnPO
• Line-Graph Approach to Spiral Spin Liquids
• Quantum Hydrodynamics of Fractonic Superfluids with Lineon Condensate: from Navier-Stokes-like Equations to Landau-like Criterion
• Dynamical Signatures of Rank-2 $U(1)$ Spin Liquids
• Anomalous diffusion and Noether's second theorem
• Fractons in effective field theories for spontaneously broken translations
• Fractal Subsystem Symmetries, 't Hooft Anomalies, and UV/IR Mixing
• On quantum melting of superfluid vortex crystals: from Lifshitz scalar to dual gravity
• Observation of the spiral spin liquid in a triangular-lattice material
• Higher-Rank Spin Liquids and Spin Nematics from Competing Orders in Pyrochlore Magnets
• Hamiltonian Formulation of Higher Rank Symmetric Gauge Theories
• Anomaly inflow for CSS and fractonic lattice models and dualities via cluster state measurement
• Irrational moments and signatures of higher-rank gauge theories in diluted classical spin liquids
• Quasi-topological fractons: a 3D dipolar gauge theory
• MultiCarroll dynamics
• Magnetic properties of the spiral spin liquid and surrounding phases in the square lattice XY model
• Fractonic self-duality and covariant magnetic fractons
• Fractonic Berezinskii-Kosterlitz-Thouless transition from a renormalization group perspective
• 2-Form U(1) Spin Liquids: Classical Model and Quantum Aspects
• Human-machine collaboration: ordering mechanism of rank-2 spin liquid on breathing pyrochlore lattice
• Non-equilibrium dynamics of bosons with dipole symmetry: Large-$N$ Keldysh approach
• Bridging three-dimensional coupled-wire models and cellular topological states: Solvable models for topological and fracton orders
• The spin-orbital Kitaev model: from kagome spin ice to classical fractons
• Fracton and Non-Lorentzian Particle Duality: Gauge Field Couplings and Geometric Implications
• Fractons in curved space
• A New Model for Fractons, Fluxons, and Freeons
• Higgs Phases and Boundary Criticality
• Fractonic Coset Construction for Spontaneously Broken Translations
• Surface Operators in Superspace
• Nonlinear Lifshitz Photon Theory in Condensed Matter Systems
• Field Theories for type-II fractons
• Strings as Hyper-Fractons
• Fractonic superfluids. III. Hybridizing higher moments
• Dual Description of Gauge Theories from an Iterative Noether Approach
• Quadrupole gauge theory: anti-Higgs mechanism and elastic dual
• Fractons on the edge
• Topological dipoles of quantum skyrmions
• Supersymmetric quantum field theory with exotic symmetry in 3+1 dimensions and fermionic fracton phases
• Electric-Magnetic Duality for Symmetric Tensor Gauge Theories and Immobile $p$-branes
• Vortices in fracton type gauge theories
• Classical fracton spin liquid and Hilbert space fragmentation in a 2D spin-$1/2$ model
• Covariant field theory of 3D massive fractons
• Emergent Kalb-Ramond fields from a dimer model
• Weak symmetry breaking and topological order in a 3D compressible quantum liquid
• Galilei particles revisited
• Topological Dipole Insulator
• Domain coarsening in fractonic systems: a cascade of critical exponents
• Stress-stress correlations in two-dimensional amorphous and crystalline solids
• Infinite-component $BF$ field theory: Connection of fracton order, Toeplitz braiding, and non-Hermitian amplification
• Scaling Symmetry and Carrollian Gravity
• Itinerant and topological excitations in a honeycomb spiral spin liquid candidate
• Global shift symmetry on an ADM hypersurface: Toward emergent gravity
• A stabilizer code model with non-invertible symmetries: Strange fractons, confinement, and non-commutative and non-Abelian fusion rules
• Spontaneous layering and power-law order in the three-dimensional fully-packed hard-plate lattice gas
• Relaxation and fluctuations of a mass- and dipole-conserving stochastic lattice gas
• ${\mathbb{Z}}_N$ generalizations of three-dimensional stabilizer codes
• Resonant dynamics of dipole-conserving Bose-Hubbard model with time-dependent tensor electric fields
• Unidirectional subsystem symmetry in a hole-doped honeycomb-lattice Ising magnet
• Hollow Lattice Tensor Gauge Theories with Bosonic Matter
• Matrix product state classification of 1D multipole symmetry protected topological phases
• Tri-unitary quantum circuits
• Symmetry-enriched topological order and quasifractonic behavior in ${\mathbb{Z}}_N$ stabilizer codes
• Preparing Code States via Seed-Entangler-Enriched Sequential Quantum Circuits: Application to Tetra-Digit Topological Error-Correcting Codes
• Effective field theory for dissipative photons from higher-form symmetries
• Quantum Coulomb Liquids of Different Rank in the Breathing Pyrochlore Antiferromagnet
• Emergent fracton strings from covariant bi-form gauge field theory
• Covariant Fracton Electrodynamics in Six Dimensions
• Constrained motions and slow dynamics in one-dimensional bosons with double-well dispersion
• Mapping the Phase Diagram of a Frustrated Magnet: Degeneracies, Flat Bands, and Canting Cycles on the Pyrochlore Lattice
• Subsystem symmetries, critical Bose surface, and immobile excitations in an extended compass model