Unification of parton and coupled-wire approaches to quantum magnetism in two dimensions
arXiv:2006.16256 · doi:10.1103/PhysRevResearch.2.043437
Abstract
The fractionalization of microscopic degrees of freedom is a remarkable manifestation of strong interactions in quantum many-body systems. Analytical studies of this phenomenon are primarily based on two distinct frameworks: field theories of partons and emergent gauge fields, or coupled arrays of one-dimensional quantum wires. We unify these approaches for two-dimensional spin systems. Via exact manipulations, we demonstrate how parton gauge theories arise in microscopic wire arrays and explicitly relate spin operators to emergent quasiparticles and gauge-field monopoles. This correspondence allows us to compute physical correlation functions within both formulations and leads to a straightforward algorithm for constructing parent Hamiltonians for a wide range of exotic phases. We exemplify this technique for several chiral and non-chiral quantum spin liquids.
arXiv comment32 pages, 11 figures
References in corpus (100)
- Topological insulators and superconductors
- Fault-tolerant quantum computation by anyons
- Anyons in an exactly solved model and beyond
- Topological entanglement entropy
- Detecting topological order in a ground state wave function
- Quantum Spin Liquids
- Quantum Spin Liquid States
- "Deconfined" quantum critical points
- Bosonization and Strongly Correlated Systems
- Spin Liquid Ground State of the Kagome Heisenberg Model
- Fractionalized excitations in the spin liquid state of a kagomé lattice antiferromagnet
- Spin Liquid State in an Organic Mott Insulator with Triangular Lattice
- Quantum Spin Liquids
- Quantum Orders and Symmetric Spin Liquids
- Spin Dynamics of the Spin-1/2 Kagome Lattice Antiferromagnet ZnCu_3(OH)_6Cl_2
- Kitaev quantum spin liquid - concept and materialization
- Spin-lattice coupling in frustrated antiferromagnets
- Herbertsmithite and the Search for the Quantum Spin Liquid
- Theory and classification of interacting 'integer' topological phases in two dimensions: A Chern-Simons approach
- Variational study of triangular lattice spin-1/2 model with ring exchanges and spin liquid state in κ-(ET)_2 Cu_2 (CN)_3
- A Duality Web in 2+1 Dimensions and Condensed Matter Physics
- An exact chiral spin liquid with non-Abelian anyons
- Universal topological quantum computation from a superconductor/Abelian quantum Hall heterostructure
- Mott Transition from a Spin Liquid to a Fermi Liquid in the Spin-Frustrated Organic Conductor kappa-(ET)2Cu2(CN)3
- On the stability of U(1) spin liquids in two dimensions
- Quantum frustration in organic Mott insulators: from spin liquids to unconventional superconductors
- Bipartite entanglement and entropic boundary law in lattice spin systems
- Coulombic Quantum Liquids in Spin-1/2 Pyrochlores
- The Fractional Quantum Hall effect in an array of quantum wires
- Spin liquid phase of the Heisenberg model on the triangular lattice
- From Luttinger liquid to non-Abelian quantum Hall states
- Particle-Vortex Duality from 3d Bosonization
- Emergent Chiral Spin Liquid: Fractional Quantum Hall Effect in a Kagome Heisenberg Model
- Signatures of Dirac cones in a DMRG study of the Kagome Heisenberg model
- Unusual thermal Hall effect in a Kitaev spin liquid candidate -RuCl
- Competing Spin Liquid States in the Spin- Heisenberg Model On Triangular Lattice
- Chiral spin liquid in a frustrated anisotropic kagome Heisenberg model
- Incommensurate spin correlations in Heisenberg spin-1/2 zig-zag ladders
- Emergence of a Field-Driven U(1) Spin Liquid in the Kitaev Honeycomb Model
- Global Phase Diagram of Competing Ordered and Quantum Spin Liquid Phases on the Kagomé Lattice
- Explicit derivation of duality between a free Dirac cone and quantum electrodynamics in (2+1) dimensions
- Deconfined quantum criticality and Neel order via dimer disorder
- Wire deconstructionism of two-dimensional topological phases
- Spin Bose-Metal phase in a spin-1/2 model with ring exchange on a two-leg triangular strip
- Fractional Helical Liquids and Non-Abelian Anyons in Quantum Wires
- Duality between Quantum Critical Points
- Stability of the U(1) spin liquid with spinon Fermi surface in 2+1 dimensions
- Particle-vortex duality in topological insulators and superconductors
- Coupled wire construction of chiral spin liquids
- Ground states of quantum antiferromagnets in two dimensions
- Spinons in more than one dimension: Resonance Valence Bond state stabilized by frustration
- Theory of a competitive spin liquid state for weak Mott insulators on the triangular lattice
- Superconducting analogue of the parafermion fractional quantum Hall states
- Valence-bond crystal in the extended kagome spin-1/2 quantum Heisenberg antiferromagnet: A variational Monte Carlo approach
- Non-Abelian topological insulators from an array of quantum wires
- Chiral Spin Liquids in Arrays of Spin Chains
- Spin Bose-Metal and Valence Bond Solid phases in a spin-1/2 model with ring exchanges on a four-leg triangular ladder
- Quantum Spin Hall Effect in Strip of Stripes Model
- Topological Superconducting Phases of Weakly Coupled Quantum Wires
- Composite Dirac liquids: parent states for symmetric surface topological order
- Pairing in Luttinger Liquids and Quantum Hall States
- Exact Chiral Spin Liquid with Stable Spin Fermi Surface on the Kagome Lattice
- Variational Monte Carlo study of chiral spin liquid in quantum antiferromagnet on the triangular lattice
- Spin liquid phase in a quantum magnet on the kagome lattice
- Fractional Topological Superconductivity and Parafermion Corner States
- Assembling Fibonacci Anyons From a Parafermion Lattice Model
- Integer and Fractional Quantum Hall Effect in a Strip of Stripes
- Quantum Confinement Transition in a d-wave Superconductor
- Coupled Wire description of the Correlated Physics in Twisted Bilayer Graphene
- Symmetry and duality in bosonization of two-dimensional Dirac fermions
- Non-Abelian topological spin liquids from arrays of quantum wires or spin chains
- Fractional Topological Insulators: from sliding Luttinger Liquids to Chern-Simons theory
- Helical nuclear spin order in a strip of stripes in the Quantum Hall regime
- Wire constructions of Abelian topological phases in three or more dimensions
- Numerical study of fractionalization in an Easy-axis Kagome antiferromagnet
- From an array of quantum wires to three-dimensional fractional topological insulators
- Fractional topological phases in three-dimensional coupled-wire systems
- Coupled wire model of symmetric Majorana surfaces of topological superconductors
- Lattice spin models for non-Abelian Chiral Spin Liquids
- Time reversal symmetry broken fractional topological phases at zero magnetic field
- Imprint of topological degeneracy in quasi-one-dimensional fractional quantum Hall states
- Coupled-wire constructions: a Luttinger liquid approach to topology
- Theory of a 3+1D fractional chiral metal: interacting variant of the Weyl semimetal
- Quantum Hall hierarchy from coupled wires
- Fractional chiral superconductors
- Gapless chiral spin liquid from coupled chains on the kagome lattice
- Two dimensional spin liquids with topological order in an array of quantum wires
- Quantum spin liquid in a kagome lattice spin-1/2 XY model with four-site exchange
- Magnetic three states of matter: A quantum Monte Carlo study of spin liquids
- A model of chiral spin liquids with Abelian and non-Abelian topological phases
- Ground state degeneracy of non-Abelian topological phases from coupled wires
- Bridging coupled wires and lattice Hamiltonian for two-component bosonic quantum Hall states
- From Dirac semimetals to topological phases in three dimensions: a coupled wire construction
- From coupled-wire construction of quantum Hall states to wave functions and hydrodynamics
- Composite Weyl semimetal as a parent state for three dimensional topologically ordered phases
- From Quantum Wires to the Chern-Simons Description of the Fractional Quantum Hall Effect
- Coupled spin-1/2 ladders as microscopic models for non-Abelian chiral spin liquids
- Weyl Semimetal from the Honeycomb Array of Topological Insulator Nanowires
- Coupled Wire Models of Interacting Dirac Nodal Superconductors
- Model of spin liquids with and without time-reversal symmetry
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- Paired fermions in strong magnetic fields and daughters of even-denominator Hall plateaus
- Symmetry-resolved entanglement of 2D symmetry-protected topological states
- Bridging three-dimensional coupled-wire models and cellular topological states: Solvable models for topological and fracton orders
- Majorana Fermi surface state in a network of quantum spin chains
- Weak symmetry breaking and topological order in a 3D compressible quantum liquid
- Triangular lattice models of the Kalmeyer-Laughlin spin liquid from coupled wires
- Quantum criticality and confinement in weak Mott insulators
- Spin-charge separation in two dimensions: spinon-chargon gauge theories from duality
- Quantum spin liquids bootstrapped from Ising criticality in Rydberg arrays