Hexagon-singlet solid ansatz for the spin-1 kagome antiferromagnet

Abstract

We perform a systematic investigation on the hexagon-singlet solid (HSS) states, which are a class of spin liquid candidates for the spin-1 kagome antiferromagnet. With the Schwinger boson representation, we show that all HSS states have exponentially decaying correlations and can be interpreted as a (special) subset of the resonating Affleck-Kennedy-Lieb-Tasaki (AKLT) loop states. We provide a compact tensor network representation of the HSS states, with which we are able to calculate physical observables efficiently. We find that the HSS states have vanishing topological entanglement entropy, suggesting the absence of intrinsic topological order. We also employ the HSS states to perform a variational study of the spin-1 kagome Heisenberg antiferromagnetic model. When we use a restricted HSS ansatz preserving lattice symmetry, the best variational energy per site is found to be $e_0=-1.3600$. In contrast, when allowing lattice symmetry breaking, we find a trimerized simplex valence bond crystal with a lower energy, $e_0=-1.3871$.

arXiv comment14 pages, 12 figures, published version

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• The route to magnetic order in the spin-$1/2$ kagome Heisenberg antiferromagnet: The role of interlayer coupling
• Non-perturbative linked-cluster expansions for the trimerized ground state of the spin-one Kagome Heisenberg model
• Benchmarking global $SU(2)$ symmetry in 2d tensor network algorithms
• Quantum criticality on a chiral ladder: an $SU(2)$ iDMRG study
• Non-perturbative linked-cluster expansions in long-range ordered quantum systems
• Absence of long-range order in a general spin-$S$ kagome lattice Ising antiferromagnet
• Survival of magnetic correlations above ordering temperature in a ferromagnetically ordered classical kagomé magnet: Li9Cr3(P2O7)3(PO4)2
• Ferrichiral skyrmions with sublattice-resolved chirality in extended Kitaev model in triangular lattice
• Emergence of magnetic long-range order in kagome quantum antiferromagnets