Chiral spin liquids on the kagome Lattice

Abstract

We study the nearest neighbor $XXZ$ Heisenberg quantum antiferromagnet on the kagome lattice. Here we consider the effects of several perturbations: a) a chirality term, b) a Dzyaloshinski-Moriya term, and c) a ring-exchange type term on the bowties of the kagome lattice, and inquire if they can suppport chiral spin liquids as ground states. The method used to study these Hamiltonians is a flux attachment transformation that maps the spins on the lattice to fermions coupled to a Chern-Simons gauge field on the kagome lattice. This transformation requires us to consistently define a Chern-Simons term on the kagome lattice. We find that the chirality term leads to a chiral spin liquid even in the absence of an uniform magnetic field, with an effective spin Hall conductance of $\sxy = \frac{1}{2}$ in the regime of $XY$ anisotropy. The Dzyaloshinkii-Moriya term also leads a similar chiral spin liquid but only when this term is not too strong. An external magnetic field also has the possibility of giving rise to additional plateaus which also behave like chiral spin liquids in the $XY$ regime. Finally, we consider the effects of a ring-exchange term and find that, provided its coupling constant is large enough, it may trigger a phase transition into a chiral spin liquid by the spontaneous breaking of time-reversal invariance.

essentially the publsihed version, 19 pages, 3 tables, 9 figures and 58 references (18 are new) (Ref. 2 has been changed)

References in corpus (13)

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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
• Chiral Spin Order in Kondo-Heisenberg systems
• Correlated spin liquids in the quantum kagome antiferromagnet at finite field: a renormalisation group analysis
• Antiferromagnetism in kagome $\alpha$-Cu${}_3$Mg(OH)${}_6$Br${}_2$
• Modified spin-wave theory and spin liquid behavior of cold bosons on an inhomogeneous triangular lattice
• Evidence for a Parity Broken Monoclinic Ground State in the S = 1/2 Kagomé Antiferromagnet Herbertsmithite
• Spinon quantum spin Hall state in the kagome antiferromagnet with a Dzyaloshinskii-Moriya interaction
• Piercing the Dirac spin liquid: From a single monopole to chiral states
• Non-perturbative approach to quantum liquid ground states on geometrically frustrated Heisenberg antiferromagnets
• Unveiling chiral states in the XXZ chain: Finite-size scaling probing symmetry-enriched $c=1$ conformal field theories
• Cavity-Vacuum-Induced Chiral Spin Liquids in Kagome Lattices: Tuning and Probing Topological Quantum Phases via Cavity Quantum Electrodynamics
• Reactivity of ultra-thin Kagome Metal FeSn towards Oxygen and Water
• Thermal Hall response of an abelian chiral spin liquid at finite temperatures
• Recent progress in quantum spin liquids, fractional magnetization plateaus, and unconventional superconductivity in kagome lattices
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• Density Matrix Renormalization Group simulations of the SU(N) Fermi-Hubbard chain implementing the full SU(N) symmetry via Semi-Standard Young Tableaux and Unitary Group Subduction Coefficients
• Emergence of magnetic long-range order in kagome quantum antiferromagnets
• Waveguide QED toolboxes for universal quantum matter