Nature of the 1/9-magnetization plateau in the spin-1/2 kagome Heisenberg antiferromagnet

Abstract

The nature of the 1/9-magnetization plateau of the spin-1/2 kagome Heisenberg antiferromagnet remains controversial due to the exotic physical properties and high complexity induced by the geometrical frustration. Instead of a Z3 quantum spin liquid revealed on a cylinder, we show on an infinite-size lattice that the 1/9 plateau can be described by a valence bond crystal (VBC) that breaks spatial translational invariance. Consistent results are achieved by two accurate tensor network methods, namely the full-update infinite projected-entangled pair states and the projected-entangled simplex states. The VBC exhibits an hourglass pattern with $\sqrt{3}\times \sqrt{3}$ spatial symmetry, demonstrated by magnetizations, bond energies, and three-body correlators. The spatial inversion symmetry in the $\sqrt{3}\times \sqrt{3}$ VBC is instantly broken with the presence of the difference between the coupling strengths in the up and down triangles, suggesting the existence of gapless excitations. The gapless nature of the 1/9 plateau is further indicated by the scaling behaviors of the entanglement entropy and the correlation length, which indicate a c=1 conformal field theory.

arXiv comment6 pages, 5 figures, Supplemental Material at http://link.aps.org/supplemental/10.1103/PhysRevB.107.L220401

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• Unconventional Magnetic Oscillations in Kagome Mott Insulators
• Variational Monte Carlo Study of the 1/9 Magnetization Plateau in Kagome Antiferromagnets
• Thermodynamic evidence of fermionic behavior in the vicinity of one-ninth plateau in a kagome antiferromagnet
• Valence Bond Crystal Ground State of the 1/9 Magnetization Plateau in the Spin-1/2 Kagome Lattice
• Six magnetization plateau phases in a spin-1/2 distorted kagome antiferromagnet: application to ${\mathrm{Y}}_3{\mathrm{Cu}}_9(\mathrm{OH}{)}_{19}{\mathrm{Cl}}_8$
• Nature of the 1/3 Magnetization Plateau in Spin-1/2 Kagome Antiferromagnets
• Recent progress in quantum spin liquids, fractional magnetization plateaus, and unconventional superconductivity in kagome lattices
• Magnetic anisotropy effect on stabilizing magnetization plateaus of kagome strip chain Heisenberg antiferromagnets
• Dirac node pinning from Dzyaloshinskii-Moriya interactions in a Kagome spin liquid
• Robust semiclassical magnetization plateau in the kagome lattice