Complete phase diagram of the spin-1/2 $J_1$-$J_2$-$J_3$ model (with $J_3=J_2$) on the honeycomb lattice

Abstract

We use the coupled cluster method to investigate the ground-state (GS) properties of the frustrated spin-1/2 $J_1$-$J_2$-$J_3$ model on the honeycomb lattice, with nearest-neighbor exchange coupling $J_1$ plus next-nearest-neighbor ($J_2$) and next-next-nearest-neighbor ($J_3$) exchanges of equal strength. In particular we find a direct first-order phase transition between the Néel-ordered antiferromagnetic phase and the ferromagnetic phase at a value $J_2/J_1=-1.17\pm 0.01$ when $J_1>0$, compared to the corresponding classical value of -1. We find no evidence for any intermediate phase. From this and our previous CCM studies of the model we present its full zero-temperature GS phase diagram.

arXiv comment4 pages, 4 figures

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• Frustrated Heisenberg antiferromagnet on the honeycomb lattice: Spin gap and low-energy parameters
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• A frustrated honeycomb-bilayer Heisenberg antiferromagnet: The spin-$\frac{1}{2}$ $J_1$--$J_2$--$J_1^{\perp }$ model
• Ground-state phases of the spin-1 $J_1$--$J_2$ Heisenberg antiferromagnet on the honeycomb lattice
• A high-order study of the quantum critical behavior of a frustrated spin-$\frac{1}{2}$ antiferromagnet on a stacked honeycomb bilayer
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• Spin-1/2 $J_1$-$J_2$ Heisenberg model on a cross-striped square lattice
• Spin excitations and thermodynamics of the antiferromagnetic Heisenberg model on the layered honeycomb lattice
• Frustrated magnetic interactions in an S=3/2 bilayer honeycomb lattice compound Bi3Mn4O12(NO3)
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• Ground-state phase structure of the spin-$\frac{1}{2}$ anisotropic planar pyrochlore
• Collinear antiferromagnetic phases of a frustrated spin-$\frac{1}{2}$ $J_1$--$J_2$--$J_1^{\perp }$ Heisenberg model on an $AA$-stacked bilayer honeycomb lattice
• Coupled Cluster Treatment of the Alternating Bond Diamond Chain
• Low-energy parameters and spin gap of a frustrated spin-$s$ Heisenberg antiferromagnet with $s\le \frac{3}{2}$ on the honeycomb lattice
• Frustrated spin-$\frac{1}{2}$ Heisenberg magnet on an $AA$-stacked honeycomb bilayer: High-order study of the collinear magnetic phases of the $J_1$--$J_2$--$J_1^{\perp }$ model
• Transverse Magnetic Susceptibility of a Frustrated Spin-$\frac{1}{2}$ $J_1$--$J_2$--$J_1^{\perp }$ Heisenberg Antiferromagnet on a Bilayer Honeycomb Lattice
• A frustrated spin-1 $J_1$--$J_2$ Heisenberg antiferromagnet: An anisotropic planar pyrochlore model