Chiral Spin Liquids in Arrays of Spin Chains

Abstract

We describe a coupled-chain construction for chiral spin liquids in two-dimensional spin systems. Starting from a one-dimensional zigzag spin chain and imposing SU(2) symmetry in the framework of non-Abelian bosonization, we first show that our approach faithfully describes the low-energy physics of an exactly solvable model with a three-spin interaction. Generalizing the construction to the two-dimensional case, we obtain a theory that incorporates the universal properties of the chiral spin liquid predicted by Kalmeyer and Laughlin: charge-neutral edge states, gapped spin-1/2 bulk excitations, and ground state degeneracy on the torus signalling the topological order of this quantum state. In addition, we show that the chiral spin liquid phase is more easily stabilized in frustrated lattices containing corner-sharing triangles, such as the extended kagome lattice, than in the triangular lattice. Our field theoretical approach invites generalizations to more exotic chiral spin liquids and may be used to assess the existence of the chiral spin liquid as the ground state of specific lattice systems.

12 pages, 8 figures

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Cited by in corpus (25)

• Anyons in Multichannel Kondo Systems
• Non-Abelian SU(N-1)-singlet fractional quantum Hall states from coupled wires
• Pretopological fractional excitations in the two-leg flux ladder
• Fractional chiral superconductors
• Gapless chiral spin liquid from coupled chains on the kagome lattice
• Two dimensional spin liquids with ${\mathbb{Z}}_2$ topological order in an array of quantum wires
• Planar p-String Condensation: Chiral Fracton Phases from Fractional Quantum Hall Layers and Beyond
• A model of chiral spin liquids with Abelian and non-Abelian topological phases
• From Quantum Wires to the Chern-Simons Description of the Fractional Quantum Hall Effect
• From coupled wires to coupled layers: Model with three-dimensional fractional excitations
• Generalized parafermions and non-local Josephson effect in multi-layer systems
• Symmetry-resolved entanglement of 2D symmetry-protected topological states
• Network construction of non-Abelian chiral spin liquids
• Generalized Phase-Space Techniques to Explore Quantum Phase Transitions in Critical Quantum Spin Systems
• Exact ground state and elementary excitations of a competing spin chain with twisted boundary condition
• Bridging three-dimensional coupled-wire models and cellular topological states: Solvable models for topological and fracton orders
• Fractional Spin Quantum Hall Effect in Weakly Coupled Spin Chain Arrays
• Quantum Thermal Hall effect of chiral spinons on a Kagome strip
• Topological states constructed by two different trivial quantum wires
• Dihedral twist liquid models from emergent Majorana fermions
• Majorana Fermi surface state in a network of quantum spin chains
• Quantum wires, Chern-Simons theory, and dualities in the quantum Hall system
• Quantum criticality and confinement in weak Mott insulators
• Quantum spin liquids bootstrapped from Ising criticality in Rydberg arrays
• Triangular lattice models of the Kalmeyer-Laughlin spin liquid from coupled wires