Spin cluster operator theory for the Kagome lattice antiferromagnet

Abstract

The spin-1/2 quantum antiferromagnet on the Kagome lattice provides a quintessential example in the strongly correlated electron physics where both effects of geometric frustration and quantum fluctuation are pushed to their limit. Among possible non-magnetic ground states, the valence bond solid (VBS) with a 36-site unit cell is one of the most promising candidates. A natural theoretical framework for the analysis of such VBS order is to consider quantum states on a bond connecting the nearest-neighboring sites as fundamental quantum modes of the system and treat them as effectively independent "bond particles." While correctly describing the VBS order in the ground state, this approach, known as the bond operator theory, significantly overestimates the lowest spin excitation energy. To overcome this problem, we take a next logical step in this paper to improve the bond operator theory and consider extended spin clusters as fundamental building blocks of the system. Depending on two possible configurations of the VBS order, various spin clusters are considered: (i) in the VBS order with staggered hexagonal resonance, we consider one spin cluster for a David star and two spin clusters with each composed of a perfect hexagon and three attached dimers, and (ii) in the VBS order with uniform hexagonal resonance, one spin cluster composed of a David star and three attached dimers. It is shown that the majority of low-energy spin excitations are nearly or perfectly flat in energy. With most of its weight coming from the David star, the lowest spin excitation has a gap much lower than the previous value obtained by the bond operator theory, narrowing the difference against exact diagonalization results.

24 pages, 10 figures, 6 tables

References in corpus (21)

• Spin Liquid Ground State of the $S=1/2$ Kagome Heisenberg Model
• Spin Dynamics of the Spin-1/2 Kagome Lattice Antiferromagnet ZnCu_3(OH)_6Cl_2
• Projected wavefunction study of Spin-1/2 Heisenberg model on the Kagome lattice
• Quantum magnetism in the paratacamite family: towards an ideal kagome lattice
• Exact dimer ground state of the two dimensional Heisenberg spin system SrCu_2(BO_3)_2
• First excitations of the spin 1/2 Heisenberg antiferromagnet on the kagomé lattice
• Ground State of the Kagome Lattice Heisenberg Antiferromagnet
• Low-energy sector of the S=1/2 Kagome antiferromagnet
• Dirac, Anderson, and Goldstone on the Kagome
• Frustrated antiferromagnets with entanglement renormalization: ground state of the spin-1/2 Heisenberg model on a kagome lattice
• Projected wave function study of Z2 spin liquids on the kagome lattice for the spin-1/2 quantum Heisenberg antiferromagnet
• Physics of low energy singlet states of the Kagome lattice quantum Heisenberg antiferromagnet
• Magneto-thermodynamics of the spin-1/2 Kagome antiferromagnet
• Numerical-Diagonalization Study of Spin Gap Issue of the Kagome Lattice Heisenberg Antiferromagnet
• Ground-State Energy and Spin Gap of Spin-1/2 Kagome Heisenberg Antiferromagnetic Clusters: Large Scale Exact Diagonalization Results
• Low energy excitations of the kagome antiferromagnet and the spin gap issue
• Triplet and Singlet Excitations in the Valence Bond Crystal Phase of Kagome Lattice Heisenberg Model
• Valence-bond crystal in the extended kagome spin-1/2 quantum Heisenberg antiferromagnet: A variational Monte Carlo approach
• Effective Quantum Dimer Model for the Kagome Heisenberg Antiferromagnet: Nearby Quantum Critical Point and Hidden Degeneracy
• Fermionic spin excitations in two and three-dimensional antiferromagnets
• Spin Triplet Excitations for a Valence Bond Solid on the Kagome Lattice

Cited by in corpus (18)

• Gapless spin-liquid phase in the kagome spin-1/2 Heisenberg antiferromagnet
• Vanishing spin gap in a competing spin-liquid phase in the kagome Heisenberg antiferromagnet
• Finite-temperature properties of the Kitaev-Heisenberg models on kagome and triangular lattices studied by improved finite-temperature Lanczos methods
• Valence-Bond-Glass State with Singlet Gap in the Spin-1/2 Square-Lattice Random $J_1$-$J_2$ Heisenberg Antiferromagnet Sr${}_2$CuTe${}_{1-x}$W${}_x$O${}_6$
• Large Negative Quantum Renormalization of Excitation Energies in the Spin-1/2 Kagome Lattice Antiferromagnet Cs${}_2$Cu${}_3$SnF${}_{12}$
• Ground-state phase diagram of the Kitaev-Heisenberg model on a kagome lattice
• ${\mathbb{Z}}_2$ gauge theory for valence bond solids on the kagome lattice
• Magnetization plateaus in the spin-1/2 antiferromagnetic Heisenberg model on a kagome-strip chain
• Plaquette-triplon analysis of magnetic disorder and order in a trimerized spin-1 Kagomé antiferromagnet
• Structures of magnetic excitations in the spin-1/2 kagome-lattice antiferromagnets Cs${}_2$Cu${}_3$SnF${}_{12}$ and Rb${}_2$Cu${}_3$SnF${}_{12}$
• Spin-1/2 kagome Heisenberg antiferromagnet: Machine learning discovery of the spinon pair density wave ground state
• Influence of Dzyaloshinskii-Moriya interactions on magnetic structure of a spin-1/2 deformed kagome lattice antiferromagnet
• Resonating dimer-monomer liquid state in a magnetization plateau of a spin-$\frac{1}{2}$ kagome-strip Heisenberg chain
• Stability of the 1/3 magnetization plateau of the $J_1-J_2$ kagome Heisenberg model
• Signatures of spin-triplet excitations in optical conductivity of valence bond solids
• 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 ${\mathrm{Y}}_3{\mathrm{Cu}}_9(\mathrm{OH}{)}_{19}{\mathrm{Cl}}_8$
• Magnetic anisotropy effect on stabilizing magnetization plateaus of kagome strip chain Heisenberg antiferromagnets