The Spin-Half {\it XXZ} Antiferromagnet on the Square Lattice Revisited: A High-Order Coupled Cluster Treatment

Abstract

We use the coupled cluster method (CCM) to study the ground-state properties and lowest-lying triplet excited state of the spin-half {\it XXZ} antiferromagnet on the square lattice. The CCM is applied to it to high orders of approximation by using an efficient computer code that has been written by us and which has been implemented to run on massively parallelized computer platforms. We are able therefore to present precise data for the basic quantities of this model over a wide range of values for the anisotropy parameter $\Delta$ in the range $-1\le \Delta <\infty$ of interest, including both the easy-plane $(-1<\Delta <1)$ and easy-axis $(\Delta >1)$ regimes, where $\Delta \to \infty$ represents the Ising limit. We present results for the ground-state energy, the sublattice magnetization, the zero-field transverse magnetic susceptibility, the spin stiffness, and the triplet spin gap. Our results provide a useful yardstick against which other approximate methods and/or experimental studies of relevant antiferromagnetic square-lattice compounds may now compare their own results. We also focus particular attention on the behaviour of these parameters for the easy-axis system in the vicinity of the isotropic Heisenberg point ($\Delta =1$), where the model undergoes a phase transition from a gapped state (for $\Delta >1$) to a gapless state (for $\Delta \le 1$), and compare our results there with those from spin-wave theory (SWT). Interestingly, the nature of the criticality at $\Delta =1$ for the present model with spins of spin quantum number $s=\frac{1}{2}$ that is revealed by our CCM results seems to differ qualitatively from that predicted by SWT, which becomes exact only for its near-classical large-$s$ counterpart.

References in corpus (11)

• Ground-state phases of the spin-1/2 J_1-J_2 Heisenberg antiferromagnet on the square lattice: A high-order coupled cluster treatment
• Coupled Cluster Treatment of the Shastry-Sutherland Antiferromagnet
• Effect of anisotropy on the ground-state magnetic ordering of the spin-half quantum $J_1^{XXZ}$--$J_2^{XXZ}$ model on the square lattice
• The spin-1/2 square-lattice J_1-J_2 model: The spin-gap issue
• The frustrated Heisenberg antiferromagnet on the honeycomb lattice: A candidate for deconfined quantum criticality
• The frustrated Heisenberg antiferromagnet on the checkerboard lattice: the $J_1$--$J_2$ model
• The ground-state phase diagram of the XXZ spin-s kagome antiferromagnet: A coupled-cluster study
• Analytical and numerical studies of the one-dimensional sawtooth chain
• Frustrated Quantum Antiferromagnets: Application of High-Order Coupled Cluster Method
• The Coupled Cluster Method Applied to Quantum Magnets: A New LPSUB$m$ Approximation Scheme for Lattice Models
• Hydrodynamic relation in 2D Heisenberg antiferromagnet in a field

Cited by in corpus (9)

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• One-dimensional projection of two-dimensional systems using spiral boundary conditions
• Quantum phases of hardcore bosons with repulsive dipolar density-density interactions on two-dimensional lattices
• Study of Staggered Magnetization in the Spin-$S$ Square-Lattice Heisenberg Model Using Spiral Boundary Conditions
• Comparing quantum fluctuations in the spin-$\frac{1}{2}$ and spin-$1$ XXZ Heisenberg models on square and honeycomb lattices
• Charge pumps, boundary modes, and the necessity of unnecessary criticality
• Anomalous enhancement of Neel order in the $S=1/2$ square lattice Heisenberg model under fictitious magnetic field
• Deconfined classical criticality in the anisotropic quantum spin-$\frac{1}{2}$ XY model on the square lattice