With the commutation relations of the spin operators, we first write out the equations of motion of the spin susceptibility and related correlation functions that have a hierarchical structure, then under the “soft cut-off” approximation, we give a set of equations of motion of spin susceptibilities for a spin [Formula: see text] antiferromagnetic Heisenberg model that is independent of whether or not the system has a long-range order in the low energy/temperature limit. Applying for a chain, a square lattice and a honeycomb lattice, respectively, we obtain the upper and the lowest boundaries of the low-lying excitations by solving this set of equations. For a chain, the upper and the lowest boundaries of the low-lying excitations are the same as that of the exact ones obtained by the Bethe ansatz, where the elementary excitations are the spinon pairs. For a square lattice, the spin wave excitation (magnons) resides in the region close to the lowest boundary of the low-lying excitations, and the multispinon excitations take place in the high-energy region close to the upper boundary of the low-lying excitations. For a honeycomb lattice, we have one kind of “mode” of the low-lying excitation. The present results obey the Lieb–Schultz–Mattis theorem, and they are also consistent with recent neutron scattering observations and numerical simulations for a square lattice.

中文翻译：

---

自旋 S = 1/2 反铁磁 Heisenberg 模型中的多自旋子激发

利用自旋算子的对易关系，我们首先写出具有层次结构的自旋磁化率的运动方程和相关的相关函数，然后在“软截止”近似下，给出一组运动方程自旋的自旋磁化率 [公式：见正文] 反铁磁海森堡模型，该模型与系统在低能量/温度极限内是否具有长程有序无关。分别应用链、方格和蜂窝格，通过求解这组方程得到低位激发的上边界和下边界。对于一条链，低位激发的上下边界与 Bethe ansatz 获得的确切激发相同，其中基本激发是自旋子对。对于方形晶格，自旋波激发（磁振子）位于靠近低洼激发的最低边界的区域，而多自旋子激发发生在靠近低洼激发的上边界的高能区域激发。对于蜂窝晶格，我们有一种低位激发的“模式”。目前的结果遵循 Lieb-Schultz-Mattis 定理，并且它们也与最近的中子散射观测和方形晶格的数值模拟一致。对于蜂窝晶格，我们有一种低位激发的“模式”。目前的结果遵循 Lieb-Schultz-Mattis 定理，并且它们也与最近的中子散射观测和方形晶格的数值模拟一致。对于蜂窝晶格，我们有一种低位激发的“模式”。目前的结果遵循 Lieb-Schultz-Mattis 定理，并且它们也与最近的中子散射观测和方形晶格的数值模拟一致。