High-order coupled cluster method study of frustrated and unfrustrated quantum magnetsin external magnetic fields

Abstract

We apply the coupled cluster method (CCM) in order to study the ground-state propertiesof the (unfrustrated) square-lattice and (frustrated) triangular-lattice spin-half Heisenbergantiferromagnets in the presence of external magnetic fields. Approximate methods aredifficult to apply to the triangular-lattice antiferromagnet because of frustration, and so,for example, the quantum Monte Carlo (QMC) method suffers from the ‘signproblem’. Results for this model in the presence of magnetic field are rarer thanthose for the square-lattice system. Here we determine and solve the basic CCMequations by using the localized approximation scheme commonly referred to as the ‘LSUBm’ approximation scheme and we carry out high-order calculations by using intensivecomputational methods. We calculate the ground-state energy, the uniform susceptibility,the total (lattice) magnetization and the local (sublattice) magnetizations as a functionof the magnetic field strength. Our results for the lattice magnetization of thesquare-lattice case compare well to the results from QMC approaches for all values of theapplied external magnetic field. We find a value for the magnetic susceptibility ofχ = 0.070 for thesquare-lattice antiferromagnet, which is also in agreement with the results from other approximate methods(e.g., χ = 0.0669 obtained via the QMC approach). Our estimate for the range of the extent of the (M/Ms =) magnetization plateau for the triangular-lattice antiferromagnet is1.37<λ<2.15, which is in good agreement with results from spin-wave theory (1.248<λ<2.145) and exactdiagonalizations (1.38<λ<2.16). Our results therefore support those from exact diagonalizationsthat indicate that the plateau begins at a higher value ofλ thanthat suggested by spin-wave theory (SWT). The CCM value for the in-plane magnetic susceptibility persite is χ = 0.065, which is below the result of SWT (evaluated to order1/S)of χSWT = 0.0794. Higher-order calculations are thus suggested for both SWT and CCMLSUBm calculations in order to determine the value ofχ for the triangular lattice conclusively.