Spin Triplet Excitations for a Valence Bond Solid on the Kagome Lattice

Abstract

One of the most promising candidate ground states for the quantum antiferromagnetic Heisenberg model on the Kagome lattice is the valence bond solid (VBS) with a 36-site unit cell. We present a theory of triplet excitation spectra about this ground state using bond operator formalism. In particular we obtain dispersions of all 18 triplet modes in the reduced Brillouin zone. In the bond operator mean-field theory, it is found that a large number of triplet modes are non-dispersive. In particular, the lowest triplet excitation is non-dispersive and degenerate with a dispersive mode at the zone center. Away from the zone center, the lowest triplet is separated from two other flat modes by a small energy gap. Quantum fluctuations are considered by taking into account scattering processes of two triplets and their bound state formation, which leads to a downward renormalization of the lowest spin triplet gap. The dispersion of the lowest triplet excitation in the VBS state is compared with the dispersive lower bound of the triplet continuum expected in competing spin liquid phases. Implications to future neutron scattering experiments are discussed.

11 pages, 8 figures, 1 table

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• Valence Bond Glass Phase in the Diluted Kagome Antiferromagnets
• Magnetic susceptibilities in a family of S=1/2 Kagome antiferromagnet
• Competing quantum paramagnetic ground states of the Heisenberg antiferromagnet on the star lattice
• Spin cluster operator theory for the Kagome lattice antiferromagnet
• ${\mathbb{Z}}_2$ gauge theory for valence bond solids on the kagome lattice
• Valence Bond Solid Phases on Deformed Kagome Lattices: Application to Rb2Cu3SnF12
• Classification of quantum phases for the star-lattice antiferromagnet via a projective symmetry group analysis
• Structures of magnetic excitations in the spin-1/2 kagome-lattice antiferromagnets Cs${}_2$Cu${}_3$SnF${}_{12}$ and Rb${}_2$Cu${}_3$SnF${}_{12}$
• Ghost modes and continuum scattering in the dimerized distorted kagome lattice antiferromagnet Rb${}_2$Cu${}_3$SnF${}_{12}$
• Influence of Dzyaloshinskii-Moriya interactions on magnetic structure of a spin-1/2 deformed kagome lattice antiferromagnet
• Partial ferromagnetic ordering and indirect exchange interaction in spatially anisotropic kagome antiferromagnet Cs_2Cu_3CeF_{12}
• Signatures of spin-triplet excitations in optical conductivity of valence bond solids
• Ferromagnetism induced in anisotropic stacked kagome-lattice antiferromagnet Cs${}_2$Cu${}_3$CeF${}_{12}$
• Mean-field theory of interacting triplons in a two-dimensional valence-bond solid: stability and properties of many-triplon states
• Thermal features of Heisenberg antiferromagnets on edge- versus corner-sharing triangular-based lattices: A message from spin waves