Microscopic theory of the nearest-neighbor valence bond sector of the spin-1/2 kagome antiferromagnet

Abstract

The spin-1/2 Heisenberg model on the kagome lattice, which is closely realized in layered Mott insulators such as ZnCu${}_3$(OH)${}_6$Cl${}_2$, is one of the oldest and most enigmatic spin-1/2 lattice model. While the numerical evidence has accumulated in favor of a quantum spin liquid, the debate is still open as to whether it is a $Z_2$ spin liquid with very short-range correlations (some kind of Resonating Valence Bond spin liquid), or an algebraic spin-liquid with power-law correlations. To address this issue, we have pushed the program started by Rokhsar and Kivelson in their derivation of the effective quantum dimer model description of Heisenberg models to unprecedented accuracy for the spin-1/2 kagome, by including all the most important virtual singlet contributions on top of the orthogonalization of the nearest-neighbor valence bond singlet basis. Quite remarkably, the resulting picture is a competition between a $Z_2$ spin liquid and a diamond valence bond crystal with a 12-site unit cell, as in the DMRG simulations of Yan, Huse and White. Furthermore, we found that, on cylinders of finite diameter $d$, there is a transition between the $Z_2$ spin liquid at small $d$ and the diamond valence bond crystal at large $d$, the prediction of the present microscopic description for the 2D lattice. These results show that, if the ground state of the spin-1/2 kagome antiferromagnet can be described by nearest-neighbor singlet dimers, it is a diamond valence bond crystal, and, a contrario, that, if the system is a quantum spin liquid, it has to involve long-range singlets, consistent with the algebraic spin liquid scenario.

11 pages, 14 figures. Revised and extended version. Results are untouched, implications have been clarified and better put in context

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Cited by in corpus (22)

• The $S=1/2$ Kagome Heisenberg Antiferromagnet Revisited
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• Characterization of quantum spin liquids and their spinon band structures via functional renormalization
• Quantum spin liquid in the semiclassical regime
• Finite-temperature properties of the Kitaev-Heisenberg models on kagome and triangular lattices studied by improved finite-temperature Lanczos methods
• Effect of perturbations on the kagome $S=1/2$ antiferromagnet at all temperatures
• Topological Nematic Spin Liquid on the Square-Kagome Lattice
• Quantum paramagnetism and magnetization plateaus in a kagome-honeycomb Heisenberg antiferromagnet
• Nature of the 1/9-magnetization plateau in the spin-1/2 kagome Heisenberg antiferromagnet
• Resonating quantum three-coloring wavefunctions for the kagome quantum antiferromagnet
• Ground-state phase diagram of the Kitaev-Heisenberg model on a kagome lattice
• How correlations change the magnetic structure factor of the kagome Hubbard model
• Valence bond solid and possible deconfined quantum criticality in an extended kagome lattice Heisenberg antiferromagnet
• Correlated spin liquids in the quantum kagome antiferromagnet at finite field: a renormalisation group analysis
• Valence bond phases of herbertsmithite and related copper kagome materials
• Schwinger boson theory of the J1,J2=J3 kagome antiferromagnet
• Resonating dimer-monomer liquid state in a magnetization plateau of a spin-$\frac{1}{2}$ kagome-strip Heisenberg chain
• Quantum-classical crossover in the spin-1/2 Heisenberg-Kitaev kagome magnet
• Frustration relief and reorientation transition in the kagome-like dolerophanite Cu${}_2$OSO${}_4$
• Geometric frustration and Dzyaloshinskii-Moriya interactions in a quantum star lattice hybrid copper sulfate
• Is Herbertsmithite far from an ideal antiferromagnet? Ab-initio answer including in-plane Dzyaloshinskii-Moriya interactions and coupling with extra-plane impurities
• Vison condensation and spinon confinement in a kagome-lattice ${\mathbb{Z}}_2$ spin liquid: A numerical study of a quantum dimer model