Farnell D J J, Zinke R, Schulenburg J, Richter J
Academic Department of Radiation Oncology, Faculty of Medical and Human Science, University of Manchester, c/o The Christie NHS Foundation Trust, Manchester M20 4BX, UK.
J Phys Condens Matter. 2009 Oct 7;21(40):406002. doi: 10.1088/0953-8984/21/40/406002. Epub 2009 Sep 8.
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. Approximate methods are difficult to apply to the triangular-lattice antiferromagnet because of frustration, and so, for example, the quantum Monte Carlo (QMC) method suffers from the 'sign problem'. Results for this model in the presence of magnetic field are rarer than those for the square-lattice system. Here we determine and solve the basic CCM equations by using the localized approximation scheme commonly referred to as the 'LSUBm' 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) magnetization and the local (sublattice) magnetizations as a function of the magnetic field strength. Our results for the lattice magnetization of the square-lattice case compare well to the results from QMC approaches for all values of the applied external magnetic field. We find a value for the magnetic susceptibility of χ = 0.070 for the square-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/M(s) =) [Formula: see text] magnetization plateau for the triangular-lattice antiferromagnet is 1.37<λ<2.15, which is in good agreement with results from spin-wave theory (1.248<λ<2.145) and exact diagonalizations (1.38<λ<2.16). Our results therefore support those from exact diagonalizations that indicate that the plateau begins at a higher value of λ than that suggested by spin-wave theory (SWT). The CCM value for the in-plane magnetic susceptibility per site is χ = 0.065, which is below the result of SWT (evaluated to order 1/S) of χ(SWT) = 0.0794. Higher-order calculations are thus suggested for both SWT and CCM LSUBm calculations in order to determine the value of χ for the triangular lattice conclusively.
为了研究在外加磁场存在下（无挫折的）正方晶格和（有挫折的）三角晶格自旋 - 1/2海森堡反铁磁体的基态性质，我们应用耦合簇方法（CCM）。由于挫折效应，近似方法难以应用于三角晶格反铁磁体，例如，量子蒙特卡罗（QMC）方法存在“符号问题”。该模型在磁场存在下的结果比正方晶格系统的结果更为罕见。在这里，我们使用通常称为“LSUBm”近似方案的局域近似方法来确定并求解基本的CCM方程，并使用密集计算方法进行高阶计算。我们计算基态能量、均匀磁化率、总（晶格）磁化强度和局部（亚晶格）磁化强度作为磁场强度的函数。对于正方晶格情况，我们关于晶格磁化强度的结果与所有外加磁场值下QMC方法的结果相当吻合。我们发现正方晶格反铁磁体的磁化率值为χ = 0.070，这也与其他近似方法的结果一致（例如，通过QMC方法得到χ = 0.0669）。我们对三角晶格反铁磁体的（M/M(s) =）[公式：见正文]磁化平台范围的估计是1.37 < λ < 2.15，这与自旋波理论的结果（1.248 < λ < 2.145）和精确对角化的结果（1.38 < λ < 2.16）非常吻合。因此，我们的结果支持精确对角化的结果，即平台开始时的λ值高于自旋波理论（SWT）所建议的值。每个位点平面内磁化率的CCM值为χ = 0.065，低于SWT（按1/S阶次评估）的结果χ(SWT) = 0.0794。因此，为了最终确定三角晶格的χ值，建议对SWT和CCM LSUBm计算都进行高阶计算。
