标题： 自旋铁模型的精确四自旋子动力学关联函数 显示英文标题

标题： Exact four-spinon dynamical correlation function of the Heisenberg model

摘要： 本文我们推导出自旋为 S = 1/2 的各向异性（XXZ）海森堡模型在反铁磁区域的动力学相关函数的四自旋子贡献的确切表达式。我们广泛研究了它的各向同性（XXX）极限，并通过微扰方法得到了伊辛模型的结果。我们的方法依赖于该模型的量子仿射对称性，这使得我们在热力学极限下能够系统地对哈密顿量进行对角化，并精确计算局域自旋算符的矩阵元。实际上，我们认为针对此方法的常见批评——即这些矩阵元的复杂性——是没有根据的。首先，我们以轮廓积分的形式给出了 n 自旋子贡献的确切表达式。在整理了最近发现的关于两自旋子贡献的结果后，我们将 n 自旋子公式专门用于新的情况 n = 4。然后，我们在各向同性极限下给出了此贡献的一个明确的级数表示。最后，在证明了这种表示没有发散之后，我们讨论了在各向异性参数一阶展开时简单表达式的伊辛极限。 显示英文摘要

摘要： In this paper we derive the exact expression of the four-spinon contribution to the dynamical correlation function of the spin S= 1/2 anisotropic (XXZ) Heisenberg model in the antiferromagnetic regime. We extensively study its isotropic (XXX) limit and derive perturbatively the Ising one. Our method relies on the quantum affine symmetry of the model, which allows for a systematic diagonalization of the Hamiltonian in the thermodynamic limit and for an exact calculation of matrix elements of local spin operators. In fact, we argue that the familiar criticism of this method related to the complication of these matrix elements is not justified. First, we give, in the form of contour integrals, an exact expression for the n-spinon contribution. After we compile recently found results concerning the two-spinon contribution, we specialize the n-spinon formula to the new case n=4. Then we give an explicit series representation of this contribution in the isotropic limit. Finally, after we show that this representation is free of divergences, we discuss the Ising limit in which a simple expression is found up to first order in the anisotropy parameter.