Chiral and Critical Spin Liquids in Spin-$1/2$ Kagome Antiferromagnet

Abstract

The topological quantum spin liquids (SL) and the nature of quantum phase transitions between them have attracted intensive attentions for the past twenty years. The extended kagome spin-1/2 antiferromagnet emerges as the primary candidate for hosting both time reversal symmetry (TRS) preserving and TRS breaking SLs based on density matrix renormalization group simulations. To uncover the nature of the novel quantum phase transition between the SL states, we study a minimum XY model with the nearest neighbor (NN) ($J_{xy}$), the second and third NN couplings ($J_{2xy}=J_{3xy}=J_{xy}^{\prime }$). We identify the TRS broken chiral SL (CSL) with the turn on of a small perturbation $J_{xy}^{\prime }\sim 0.06J_{xy}$, which is fully characterized by the fractionally quantized topological Chern number and the conformal edge spectrum as the $\nu =1/2$ fractional quantum Hall state. On the other hand, the NN XY model ($J_{xy}^{\prime }=0$) is shown to be a critical SL state adjacent to the CSL, characterized by the gapless spin singlet excitations and also vanishing small spin triplet excitations. The quantum phase transition from the CSL to the gapless critical SL is driven by the collapsing of the neutral (spin singlet) excitation gap. By following the evolution of entanglement spectrum, we find that the transition takes place through the coupling of the edge states with opposite chiralities, which merge into the bulk and become gapless neutral excitations. The effect of the NN spin-$z$ coupling $J_z$ is also studied, which leads to a quantum phase diagram with an extended regime for the gapless SL.

8 pages, 7 figures

References in corpus (21)

• Entanglement Spectrum as a Generalization of Entanglement Entropy: Identification of Topological Order in Non-Abelian Fractional Quantum Hall Effect States
• Spin Dynamics of the Spin-1/2 Kagome Lattice Antiferromagnet ZnCu_3(OH)_6Cl_2
• Identifying Topological Order by Entanglement Entropy
• Projected wavefunction study of Spin-1/2 Heisenberg model on the Kagome lattice
• Quantum magnetism in the paratacamite family: towards an ideal kagome lattice
• Mott Transition from a Spin Liquid to a Fermi Liquid in the Spin-Frustrated Organic Conductor kappa-(ET)2Cu2(CN)3
• Time-evolving a matrix product state with long-ranged interactions
• Plaquette Ordered Phase and Quantum Phase Diagram in the Spin-1/2 J1-J2 Square Heisenberg Model
• Chiral spin liquid and emergent anyons in a Kagome lattice Mott insulator
• Emergent Chiral Spin Liquid: Fractional Quantum Hall Effect in a Kagome Heisenberg Model
• Characterizing topological order by studying the ground states of an infinite cylinder
• Chiral spin liquid in a frustrated anisotropic kagome Heisenberg model
• Projected wave function study of Z2 spin liquids on the kagome lattice for the spin-1/2 quantum Heisenberg antiferromagnet
• Global Phase Diagram of Competing Ordered and Quantum Spin Liquid Phases on the Kagomé Lattice
• Spin Hamiltonian for which the Chiral Spin Liquid is the Exact Ground State
• Weak plaquette valence bond order in the $S=1/2$ honeycomb $J_1-J_2$ Heisenberg model
• Distinct Spin Liquids and their Transitions in Spin-1/2 XXZ Kagome Antiferromagnets
• $Z_2$ spin liquid and chiral antiferromagnetic phase in Hubbard model on the honeycomb lattice: duality between Schwinger-fermion and Schwinger-boson representations
• Spin liquids on a honeycomb lattice: Projective Symmetry Group study of Schwinger fermion mean-field theory
• Algebraic vortex liquid theory of a quantum antiferromagnet on the kagome lattice
• Fractionalized gapless quantum vortex liquids

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• Universal Entanglement Spectra of Gapped One-dimensional Field Theories
• A Kagome Map of Spin Liquids: from XXZ to Dzyaloshinskii-Moriya Ferromagnet
• Generic nearest-neighbour kagome model: XYZ & Dzyaloshinskii-Moriya, and comparison to pyrochlore
• Doping quantum spin liquids on the Kagome lattice
• Emergent quasi-one-dimensionality in a kagomé magnet: A simple route to complexity
• Gapless chiral spin liquid from coupled chains on the kagome lattice
• Topological Characterization of Non-Abelian Moore-Read State using Density-Matrix Renormailzation Group
• Anomalous dimensions of monopole operators at the transitions between Dirac and topological spin liquids
• Spin ordered ground state and thermodynamic behaviors of the spin-3/2 kagome Heisenberg antiferromagnet
• Chiral liquid phase of simple quantum magnets
• The route to magnetic order in the spin-$1/2$ kagome Heisenberg antiferromagnet: The role of interlayer coupling
• Quantum phase diagram and chiral spin liquid in the extended spin-$\frac{1}{2}$ honeycomb XY model
• Antiferromagnetic magnons from fractionalized excitations
• Infrared phonons as a probe of a spin-liquid states in herbertsmithite ZnCu3(OH)6Cl2
• Determining non-Abelian topological order from infinite projected entangled pair states
• Determining topological order from infinite projected entangled pair states
• Bosonic fractional Chern insulating state at integer fillings in multi-band system
• Fermionic spinon and holon statistics in the pyrochlore quantum spin liquid
• Piercing the Dirac spin liquid: From a single monopole to chiral states
• Engineering frustrated Rydberg spin models by graphical Floquet modulation
• Variational Monte Carlo study of gapless spin liquid in the spin-$1/2$ XXZ antiferromagnetic model on the kagome lattice
• Loop-gas description of the localized-magnon states on the kagome lattice with open boundary conditions
• Crystal chemistry criteria of the existence of spin liquids on the kagome lattice
• Chiral spin liquid from magnetic Wannier states
• Variational methods for characterizing matrix product operator symmetries
• Emergence of magnetic long-range order in kagome quantum antiferromagnets
• Schwinger-Boson mean-field study of spin-1/2 $J_1$-$J_2$-$J_{\chi }$ model in honeycomb lattice: thermal Hall signature