The spin-half Heisenberg antiferromagnet on two Archimedian lattices: From the bounce lattice to the maple-leaf lattice and beyond

Abstract

We investigate the ground state of the two-dimensional Heisenberg antiferromagnet on two Archimedean lattices, namely, the maple-leaf and bounce lattices as well as a generalized $J$-$J^{\prime }$ model interpolating between both systems by varying $J^{\prime }/J$ from $J^{\prime }/J=0$ (bounce limit) to $J^{\prime }/J=1$ (maple-leaf limit) and beyond. We use the coupled cluster method to high orders of approximation and also exact diagonalization of finite-sized lattices to discuss the ground-state magnetic long-range order based on data for the ground-state energy, the magnetic order parameter, the spin-spin correlation functions as well as the pitch angle between neighboring spins. Our results indicate that the "pure" bounce ($J^{\prime }/J=0$) and maple-leaf ($J^{\prime }/J=1$) Heisenberg antiferromagnets are magnetically ordered, however, with a sublattice magnetization drastically reduced by frustration and quantum fluctuations. We found that magnetic long-range order is present in a wide parameter range $0\le J^{\prime }/J\lesssim J_c^{\prime }/J$ and that the magnetic order parameter varies only weakly with $J^{\prime }/J$. At $J_c^{\prime }\approx 1.45J$ a direct first-order transition to a quantum orthogonal-dimer singlet ground state without magnetic long-range order takes place. The orthogonal-dimer state is the exact ground state in this large-$J^{\prime }$ regime, and so our model has similarities to the Shastry-Sutherland model. Finally, we use the exact diagonalization to investigate the magnetization curve. We a find a 1/3 magnetization plateau for $J^{\prime }/J\gtrsim 1.07$ and another one at 2/3 of saturation emerging only at large $J^{\prime }/J\gtrsim 3$.

9 pages, 10 figures

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• Magnetization plateaus in frustrated antiferromagnetic quantum spin models
• Absence of magnetic order for the spin-half Heisenberg antiferromagnet on the star lattice
• Coupled Cluster Treatment of the Shastry-Sutherland Antiferromagnet
• Spangolite: an s=1/2 maple leaf lattice antiferromagnet?

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