High-Order Coupled Cluster Method Study of Frustrated and Unfrustrated Quantum Magnets in External Magnetic Fields

Abstract

We apply the coupled cluster method (CCM) in order to study the ground-state properties of the (unfrustrated) square-lattice and (frustrated) triangular-lattice spin-half Heisenberg antiferromagnets in the presence of external magnetic fields. Here we determine and solve the basic CCM equations by using the localised approximation scheme commonly referred to as the `LSUB$m$' approximation scheme and we carry out high-order calculations by using intensive computational methods. We calculate the ground-state energy, the uniform susceptibility, the total (lattice) magnetisation and the local (sublattice) magnetisations as a function of the magnetic field strength. Our results for the lattice magnetisation of the square-lattice case compare well to those results of QMC for all values of the applied external magnetic field. We find a value for magnetic susceptibility of $\chi =0.070$ for the square-lattice antiferromagnet, which is also in agreement with the results of other approximate methods (e.g., $\chi =0.0669$ via QMC). Our estimate for the range of the extent of the ($M/M_s=$)$\frac{1}{3}$ magnetisation plateau for the triangular-lattice antiferromagnet is $1.37<\lambda <2.15$, which is in good agreement with results of spin-wave theory ($1.248<\lambda <2.145$) and exact diagonalisations ($1.38<\lambda <2.16$). The CCM value for the in-plane magnetic susceptibility per site is $\chi =0.065$, which is below the result of the spin-wave theory (evaluated to order 1/S) of ${\chi }_{SWT}=0.0794$.

30 pages, 13 figures, 1 Table

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