Chiral spin liquid and emergent anyons in a Kagome lattice Mott insulator

Abstract

Topological phases in frustrated quantum spin systems have fascinated researchers for decades. One of the earliest proposals for such a phase was the chiral spin liquid put forward by Kalmeyer and Laughlin in 1987 as the bosonic analogue of the fractional quantum Hall effect. Elusive for many years, recent times have finally seen a number of models that realize this phase. However, these models are somewhat artificial and unlikely to be found in realistic materials. Here, we take an important step towards the goal of finding a chiral spin liquid in nature by examining a physically motivated model for a Mott insulator on the Kagome lattice with broken time-reversal symmetry. We first provide a theoretical justification for the emergent chiral spin liquid phase in terms of a network model perspective. We then present an unambiguous numerical identification and characterization of the universal topological properties of the phase, including ground state degeneracy, edge physics, and anyonic bulk excitations, by using a variety of powerful numerical probes, including the entanglement spectrum and modular transformations.

9 pages, 9 figures; partially supersedes arXiv:1303.6963

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Cited by in corpus (139)

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• Floquet Engineering of Quantum Materials
• Quantum entanglement in condensed matter systems
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• Signatures of Dirac cones in a DMRG study of the Kagome Heisenberg model
• A Short Introduction to Topological Quantum Computation
• Competing Spin Liquid States in the Spin-$1/2$ Heisenberg Model On Triangular Lattice
• Neural-Network Quantum States, String-Bond States, and Chiral Topological States
• Gapped spin liquid with ${\mathbb{Z}}_2$-topological order for kagome Heisenberg model
• Dynamical Time-Reversal Symmetry Breaking and Photo-Induced Chiral Spin Liquids in Frustrated Mott Insulators
• Chiral Spin Liquid and Quantum Criticality in Extended $S=1/2$ Heisenberg Models on the Triangular Lattice
• Unifying Description of Competing Orders in Two Dimensional Quantum Magnets
• Mott insulating states with competing orders in the triangular lattice Hubbard model
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• Global phase diagram and quantum spin liquids in spin-1/2 triangular antiferromagnet
• Projective symmetry group classification of chiral spin liquids
• Coupled wire construction of chiral spin liquids
• Nature of chiral spin liquids on the kagome lattice
• A Quantum Dipolar Spin Liquid
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• Four-Spin Terms and the Origin of the Chiral Spin Liquid in Mott Insulators on the Triangular Lattice
• Probing and controlling spin chirality in Mott insulators by circularly polarized laser
• SU(4) chiral spin liquid, exciton supersolid and electric detection in moiré bilayers
• Non-Abelian chiral spin liquid in a quantum antiferromagnet revealed by an iPEPS study
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• Spin Thermal Hall Conductivity of a Kagomé Antiferromagnet
• Numerical treatment of spin systems with unrestricted spin length $S$: A functional renormalization group study
• Haldane-Hubbard Mott Insulator: From Tetrahedral Spin Crystal to Chiral Spin Liquid
• Variational Monte Carlo study of chiral spin liquid in quantum antiferromagnet on the triangular lattice
• Extension of the standard Heisenberg Hamiltonian to multispin exchange interactions
• Chiral spin liquids in triangular lattice SU(N) fermionic Mott insulators with artificial gauge fields
• Quantum Spin Liquid with Emergent Chiral Order in the Triangular-lattice Hubbard Model
• Trimerized ground state of the spin-1 Heisenberg antiferromagnet on the kagome lattice
• Non-Abelian topological spin liquids from arrays of quantum wires or spin chains
• Chiral spin liquids on the kagome Lattice
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• Topological superconductivity in the doped chiral spin liquid on the triangular lattice
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• Spin dynamics of itinerant electrons: local magnetic moment formation and Berry phase
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• Chiral and Critical Spin Liquids in Spin-$1/2$ Kagome Antiferromagnet
• Lattice spin models for non-Abelian Chiral Spin Liquids
• SU(6) Heisenberg model on the honeycomb lattice: competition between plaquette and chiral order
• Topology by Dissipation: Transport properties
• Asymmetric Particle Transport and Light-Cone Dynamics Induced by Anyonic Statistics
• Competing Chiral Orders in the Topological Haldane-Hubbard Model of Spin-1/2 Fermions and Bosons
• Quantum Phase Diagram and Spontaneously Emergent Topological Chiral Superconductivity in Doped Triangular-Lattice Mott Insulators
• Abelian SU$(N{)}_1$ Chiral Spin Liquids on the Square Lattice
• Emergent Multi-flavor QED3 at the Plateau Transition between Fractional Chern Insulators: Applications to graphene heterostructures
• Topological chiral and nematic superconductivity by doping Mott insulators on triangular lattice
• Measuring space-group symmetry fractionalization in Z${}_2$ spin liquids
• Manipulating synthetic gauge fluxes via multicolor dressing of Rydberg-atom arrays
• Kagome chiral spin liquid as a gauged U(1) symmetry protected topological phase
• Detecting a $Z_2$ topologically ordered phase from unbiased infinite projected entangled-pair state simulations
• Clustering of Topological Charges in a Kagome Classical Spin Liquid
• Static and dynamical signatures of Dzyaloshinskii-Moriya interactions in the Heisenberg model on the kagome lattice
• Quantum spin liquid and cluster Mott insulator phases in the Mo${}_3$O${}_8$ magnets
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• Topological Magnetic Excitations on the Distorted Kagome Antiferromagnets: Applications to Volborthite, Vesignieite, and Edwardsite
• Emergent quasi-one-dimensionality in a kagomé magnet: A simple route to complexity
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• Emergent spin-1 trimerized valence bond crystal in the spin-1/2 Heisenberg model on the star lattice
• Topological Characterization of Non-Abelian Moore-Read State using Density-Matrix Renormailzation Group
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• Spin chain network construction of chiral spin liquids
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• The route to magnetic order in the spin-$1/2$ kagome Heisenberg antiferromagnet: The role of interlayer coupling
• Numerical evidence for a chiral spin liquid in the XXZ antiferromagnetic Heisenberg model on the kagome lattice at $m=\frac{2}{3}$ magnetization
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• Valence bond solid and possible deconfined quantum criticality in an extended kagome lattice Heisenberg antiferromagnet
• Quantum phase diagram and chiral spin liquid in the extended spin-$\frac{1}{2}$ honeycomb XY model
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• Deconfined criticalities and dualities between chiral spin liquid, topological superconductor and charge density wave Chern insulator
• Quantum spin circulator in Y junctions of Heisenberg chains
• Determining non-Abelian topological order from infinite projected entangled pair states
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• Chiral Broken Symmetry Descendants of the Kagomé Lattice Chiral Spin Liquid
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• Non-Abelian chiral spin liquid on spin-1 kagome lattice: truncation of an exact Hamiltonian and numerical optimization
• Topological Aspects of Antiferromagnets
• Rainbow chains and numerical renormalisation group for accurate chiral conformal spectra
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• Flux-driven quantum spin liquids in kagome optical lattices
• Effective Field Theory of Chiral Spin Liquid between Ordered Phases in Kagomé Antiferromagnet
• Fermi-Hubbard model on non-bipartite lattices: flux problem and emergent chirality
• Chiral spin liquid from magnetic Wannier states
• Chiral Bosonic Topological Insulator on the Honeycomb Lattice with Anisotropic Interactions
• Variational methods for characterizing matrix product operator symmetries
• Quantum Magnetism in Wannier-Obstructed Mott Insulators
• Entanglement gap in 1D long-range quantum spherical models
• Chiral Edge States Emerging on Anyon-Net
• Emergence of magnetic long-range order in kagome quantum antiferromagnets
• Waveguide QED toolboxes for universal quantum matter
• Schwinger-Boson mean-field study of spin-1/2 $J_1$-$J_2$-$J_{\chi }$ model in honeycomb lattice: thermal Hall signature