Triangular lattice models of the Kalmeyer-Laughlin spin liquid from coupled wires

Abstract

Chiral spin liquids (CSLs) are exotic phases of interacting spins in two dimensions, characterized by long-range entanglement and fractional excitations. We construct a local Hamiltonian on the triangular lattice that stabilizes the Kalmeyer-Laughlin CSL without requiring fine-tuning. Our approach employs coupled-wire constructions and introduces a lattice duality to construct a solvable chiral sliding Luttinger liquid, which is driven toward the CSL phase by generic perturbations. By combining symmetry analysis and bosonization, we make sharp predictions for the ground states on quasi-one-dimensional cylinders and tori, which exhibit a fourfold periodicity in the circumference. Extensive tensor network simulations demonstrating ground-state degeneracies, fractional quasiparticles, nonvanishing long-range order parameters, and entanglement signatures confirm the emergence of the CSL in the lattice Hamiltonian.

25 pages, 27 figures. The new version has updated 2D results. Typos are also fixed in this version

References in corpus (56)

• Quantum Spin Liquids
• Entanglement Spectrum as a Generalization of Entanglement Entropy: Identification of Topological Order in Non-Abelian Fractional Quantum Hall Effect States
• Entanglement entropy and conformal field theory
• Quantum Spin Liquid States
• Quantum Spin Liquids
• The ITensor Software Library for Tensor Network Calculations
• Classification of Gapped Symmetric Phases in 1D Spin Systems
• Symmetry protection of topological order in one-dimensional quantum spin systems
• Classical simulation of infinite-size quantum lattice systems in two spatial dimensions
• Theory and classification of interacting 'integer' topological phases in two dimensions: A Chern-Simons approach
• Neel order in square and triangular lattice Heisenberg models
• Entanglement spectrum and boundary theories with projected entangled-pair states
• The Fractional Quantum Hall effect in an array of quantum wires
• Variational optimization algorithms for uniform matrix product states
• From Luttinger liquid to non-Abelian quantum Hall states
• Experimental identification of quantum spin liquids
• Differentiable Programming Tensor Networks
• Variational optimization with infinite projected entangled-pair states
• Integer quantum Hall effect for bosons: A physical realization
• Characterizing topological order by studying the ground states of an infinite cylinder
• Chiral spin liquid in a frustrated anisotropic kagome Heisenberg model
• Tangent-space methods for uniform matrix product states
• Chiral spin liquid phase of the triangular lattice Hubbard model: a density matrix renormalization group study
• Spin Hamiltonian for which the Chiral Spin Liquid is the Exact Ground State
• Explicit derivation of duality between a free Dirac cone and quantum electrodynamics in (2+1) dimensions
• Ordering in spatially anisotropic triangular antiferromagnets
• Global phase diagram and quantum spin liquids in spin-1/2 triangular antiferromagnet
• Fractional quantum Hall states in lattices: Local models and physical implementation
• Coupled wire construction of chiral spin liquids
• Laughlin spin liquid states on lattices obtained from conformal field theory
• Four-Spin Terms and the Origin of the Chiral Spin Liquid in Mott Insulators on the Triangular Lattice
• Chiral Spin Liquids in Arrays of Spin Chains
• Parent Hamiltonian for the Chiral Spin Liquid
• Bosonic Integer Quantum Hall effect in an interacting lattice model
• Integer Quantum Hall State in Two-Component Bose Gases in a Synthetic Magnetic Field
• Flux insertion, entanglement, and quantized responses
• Symmetry and duality in bosonization of two-dimensional Dirac fermions
• Non-Abelian topological spin liquids from arrays of quantum wires or spin chains
• Obtaining topological degenerate ground states by the density matrix renormalization group
• Exact realization of Integer and Fractional Quantum Hall Phases in U(1)xU(1) models in (2+1)d
• Weak symmetry breaking in two dimensional topological insulators
• Lattice spin models for non-Abelian Chiral Spin Liquids
• Two dimensional spin liquids with ${\mathbb{Z}}_2$ topological order in an array of quantum wires
• Bridging coupled wires and lattice Hamiltonian for two-component bosonic quantum Hall states
• Quantum Geometry and Stabilization of Fractional Chern Insulators Far from the Ideal Limit
• Fractional quantum Hall states with variational Projected Entangled-Pair States: a study of the bosonic Harper-Hofstadter model
• An introduction to infinite projected entangled-pair state methods for variational ground state simulations using automatic differentiation
• Coexistence of non-Abelian chiral spin liquid and magnetic order in a spin-1 antiferromagnet
• Coupled spin-1/2 ladders as microscopic models for non-Abelian chiral spin liquids
• Unification of parton and coupled-wire approaches to quantum magnetism in two dimensions
• Statistics tuned entanglement of the boundary modes in coupled Su-Schrieffer-Heeger chains
• Model of spin liquids with and without time-reversal symmetry
• Generalized Gibbs Ensemble Description of Real Space Entanglement Spectra of (2+1)-dimensional Chiral Topological Systems with $SU(2)$ Symmetry
• Variationally optimizing infinite projected entangled-pair states at large bond dimensions: A split corner transfer matrix renormalization group approach
• Global quantum phase diagram and non-Abelian chiral spin liquid in a spin-3/2 square lattice antiferromagnet
• The large $|U|$ expansion for a half-filled asymmetric Hubbard model on a triangular ladder in the presence of spin-dependent magnetic flux