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

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 $χ=0.070$ for the square-lattice antiferromagnet, which is also in agreement with the results of other approximate methods (e.g., $χ=0.0669$ via QMC). Our estimate for the range of the extent of the ($M/M_s=$)$\frac 13$ magnetisation plateau for the triangular-lattice antiferromagnet is $1.37< λ< 2.15$, which is in good agreement with results of spin-wave theory ($1.248 < λ< 2.145$) and exact diagonalisations ($1.38 < λ< 2.16$). The CCM value for the in-plane magnetic susceptibility per site is $χ=0.065$, which is below the result of the spin-wave theory (evaluated to order 1/S) of $χ_{SWT}=0.0794$.