Large-$s$ expansions for the low-energy parameters of the honeycomb-lattice Heisenberg antiferromagnet with spin quantum number $s$

Abstract

The coupled cluster method (CCM) is employed to very high orders of approximation to study the ground-state (GS) properties of the spin-$s$ Heisenberg antiferromagnet (with isotropic interactions, all of equal strength, between nearest-neighbour pairs only) on the honeycomb lattice. We calculate with high accuracy the complete set of GS parameters that fully describes the low-energy behaviour of the system, in terms of an effective magnon field theory, viz., the energy per spin, the magnetic order parameter (i.e., the sublattie magnetization), the spin stiffness and the zero-field (uniform, transverse) magnetic susceptibility, for all values of the spin quantum number $s$ in the range $\frac{1}{2}\le s\le \frac{9}{2}$. The CCM data points are used to calculate the leading quantum corrections to the classical ($s\to \infty$) values of these low-energy parameters, considered as large-$s$ asymptotic expansions.

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• Comparing quantum fluctuations in the spin-$\frac{1}{2}$ and spin-$1$ XXZ Heisenberg models on square and honeycomb lattices
• 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
• Low-energy parameters and spin gap of a frustrated spin-$s$ Heisenberg antiferromagnet with $s\le \frac{3}{2}$ on the honeycomb lattice
• Transverse Magnetic Susceptibility of a Frustrated Spin-$\frac{1}{2}$ $J_1$--$J_2$--$J_1^{\perp }$ Heisenberg Antiferromagnet on a Bilayer 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