Fracton Topological Order from Nearest-Neighbor Two-Spin Interactions and Dualities
arXiv:1704.03870 · doi:10.1103/PhysRevB.96.165106
Abstract
Fracton topological order describes a remarkable phase of matter which can be characterized by fracton excitations with constrained dynamics and a ground state degeneracy that increases exponentially with the length of the system on a three-dimensional torus. However, previous models exhibiting this order require many-spin interactions which may be very difficult to realize in a real material or cold atom system. In this work, we present a more physically realistic model which has the so-called X-cube fracton topological order but only requires nearest-neighbor two-spin interactions. The model lives on a three-dimensional honeycomb-based lattice with one to two spin-1/2 degrees of freedom on each site and a unit cell of 6 sites. The model is constructed from two orthogonal stacks of topologically ordered Kitaev honeycomb layers, which are coupled together by a two-spin interaction. It is also shown that a four-spin interaction can be included to instead stabilize 3+1D topological order. We also find dual descriptions of four quantum phase transitions in our model, all of which appear to be discontinuous first order transitions.
15+11 pages, 13 figures
References in corpus (7)
- Local stabilizer codes in three dimensions without string logical operators
- Glassy quantum dynamics in translation invariant fracton models
- Fracton topological order via coupled layers
- Emergent Gravity of Fractons: Mach's Principle Revisited
- Gapless Bosonic Excitation without symmetry breaking: Novel Algebraic Spin liquid with soft Gravitons
- Resonating plaquette phases in large spin cold atom systems
- Fractons from Partons
Cited by in corpus (95)
- Fractons
- Fracton Phases of Matter
- Fracton-Elasticity Duality
- Fracton hydrodynamics
- Hilbert-Space Fragmentation from Strict Confinement
- Quantum Field Theory of X-Cube Fracton Topological Order and Robust Degeneracy from Geometry
- Subsystem symmetry protected topological order
- Foliated fracton order from gauging subsystem symmetries
- Fracton topological order from Higgs and partial confinement mechanisms of rank-two gauge theory
- Localization in fractonic random circuits
- Multiple topological transitions in twisted bilayer graphene near the first magic angle
- Higher-Spin Witten Effect and Two-Dimensional Fracton Phases
- Emergent Phases of Fractonic Matter
- Dynamical scar states in driven fracton systems
- Fracton topological phases from strongly coupled spin chains
- Topological Entanglement Entropy of Fracton Stabilizer Codes
- Foliated Quantum Field Theory of Fracton Order
- A classification of 3+1D bosonic topological orders (I): the case when point-like excitations are all bosons
- Fractional excitations in foliated fracton phases
- Fractal Symmetric Phases of Matter
- X-Cube Fracton Model on Generic Lattices: Phases and Geometric Order
- Foliated Field Theory and String-Membrane-Net Condensation Picture of Fracton Order
- Twisted Fracton Models in Three Dimensions
- Breakdown of hydrodynamics below four dimensions in a fracton fluid
- Cage-Net Fracton Models
- Fractonic Superfluids
- Fractons from Partons
- Rank-2 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
- Symmetric Tensor Gauge Theories on Curved Spaces
- Crystal-to-Fracton Tensor Gauge Theory Dualities
- Correlation function diagnostics for type-I fracton phases
- Topological Defect Networks for Fractons of all Types
- Fractonic line excitations : an inroad from 3d elasticity theory
- Fractons from vector gauge theory
- 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
- Twisted foliated fracton phases
- Universal entanglement signatures of foliated fracton phases
- Foliated fracton order in the checkerboard model
- Higher order topological superconductors as generators of quantum codes
- Sorting topological stabilizer models in three dimensions
- Higher Rank Deconfined Quantum Criticality at the Lifshitz Transition and the Exciton Bose Condensate
- Anisotropic layer construction of anisotropic fracton models
- Goldstone bosons and fluctuating hydrodynamics with dipole and momentum conservation
- A systematic construction of gapped non-liquid states
- Infinite families of fracton fluids with momentum conservation
- Gauging permutation symmetries as a route to non-Abelian fractons
- Fractons from confinement in one dimension
- On duality between Cosserat elasticity and fractons
- Bifurcating entanglement-renormalization group flows of fracton stabilizer models
- Fractonic superfluids. (II). Condensing subdimensional particles
- Floquet-engineering topological transitions in a twisted transition metal dichalcogenide homobilayer
- Compactifying fracton stabilizer models
- Finite-Temperature Screening of U(1) Fractons
- Fracton physics of spatially extended excitations
- Foliated fracton order in the Majorana checkerboard model
- Hybrid Fracton Phases: Parent Orders for Liquid and Non-Liquid Quantum Phases
- Majorana Quantum Lego, a Route Towards Fracton Matter
- Entanglement Spectra of Stabilizer Codes: A Window into Gapped Quantum Phases of Matter
- Quantum robustness of fracton phases
- Type-II fractons from coupled spin chains and layers
- Subdimensional criticality: condensation of lineons and planons in the X-cube model
- Hyperbolic Fracton Model, Subsystem Symmetry, and Holography II: The Dual Eight-Vertex Model
- Lieb-Schultz-Mattis type constraints on Fractonic Matter
- Topological fracton quantum phase transitions by tuning exact tensor network states
- Generalized Gauge Field Theories and Fractal Dynamics
- Fracton magnetohydrodynamics
- Towards Non-Invertible Anomalies from Generalized Ising Models
- Theory of Dipole Insulators
- Competing topological orders in three dimensions: X-cube versus toric code
- Renormalization group analysis on emergence of higher rank symmetry and higher moment conservation
- Quantum spin ice in three-dimensional Rydberg atom arrays
- Fractons from frustration in hole-doped antiferromagnets
- Realization of fractonic quantum phases in the breathing pyrochlore lattice
- Note on Generalized Symmetries, Gapless Excitations, Generalized Symmetry Protected Topological states, and Anomaly
- Designer non-Abelian fractons from topological layers
- Non-Abelian defects in Fracton phase of matter
- Electric Circuit Realizations of Fracton Physics
- Fracton excitations in classical frustrated kagome spin models
- Holographic subdiffusion
- Emergent fermionic gauge theory and foliated fracton order in the Chamon model
- Control of superexchange interactions with DC electric fields
- A Simple Mechanism for Unconventional Superconductivity in a Repulsive Fermion Model
- Field-induced dimer orders in quantum spin chains
- Gauge Field Dynamics in Multilayer Kitaev Spin Liquids
- Bridging three-dimensional coupled-wire models and cellular topological states: Solvable models for topological and fracton orders
- Non-Abelian fracton order from gauging a mixture of subsystem and global symmetries
- Pinch-line spin liquids as layered Coulomb phases and applications to cubic models
- Unidirectional subsystem symmetry in a hole-doped honeycomb-lattice Ising magnet
- Coupling quantum spin ice to matter on the centered pyrochlore lattice
- How quantum fluctuations freeze a classical liquid and then melt it into a topological one
- Covariant Fracton Electrodynamics in Six Dimensions