论文标题

各向异性XXZ模型的确切两翼纵向动力学结构因子

The exact two-spinon longitudinal dynamical structure factor of the anisotropic XXZ model

论文作者

Castillo, Isaac Pérez

论文摘要

非弹性中子散射实验通常用于揭示海森堡自旋模型上的激发如何在动态相关功能中发挥作用。对于某种类别的材料,例如CSCOCL $ _3 $或CSCOBR $ _3 $盐,事实证明,Quasi-One Dimensional XXZ型号的磁性非常近似,这些XXZ模型享受了量子集成性的属性。在这些情况下,原则上可以使用其潜在的代数结构来确切地描述激发,即所谓的纺纱子如何参与动态相关功能。即使可用的理论(代数Bethe Ansatz或量子组方法)提供了所有所需的物理数量,例如形式因素,完整的本征局体和光谱集,但通常这是一项相当艰巨的任务,但是要获得足够简单的分析表达式,以实现基于参数的数据,以计算动态结构因子(DSFS),以实验估算。 XXZ模型的纵向DSF尤其如此,到目前为止,该模型已经避免了一种形式的数学处理。使用量子组方法,我们在这里介绍了2-Spinon纵向DSF的精确而简单的表达,并显示我们的结果与预期的总和规则以及各向同性和ISING抗fiferromagnet限制案例一致。

Inelastic neutron scattering experiments are commonly used to unveil how excitations on Heisenberg spin models play a role in dynamical correlations functions. For a certain class of materials, like CsCoCl$_3$ or CsCoBr$_3$ salts, it turns out that their magnetic properties are fairly well approximated by quasi-one dimensional XXZ models, which enjoy the property of quantum integrability. In these instances, one can in principle use their underlying algebraic structure to describe very precisely how excitations, the so-called spinons, participate in dynamical correlations functions. Even though the available theories (either algebraic Bethe ansatz or quantum group approach) provide all the needed physical quantities such as form factors, complete set of eigenstates and spectrum, it is typically a rather daunting task, however, to obtain sufficiently simple analytical expressions for computing Dynamical Structure Factors (DSFs), valuable, e.g., for parameters estimation based on experimental data. This is particularly the case for the longitudinal DSF of the XXZ model, which has eluded a formal mathematical treatment thus far. Using the quantum group approach, we present here an exact and simple expression of the 2-spinon longitudinal DSF and show our results to be consistent with the expected sum rules and the isotropic and Ising antiferromagnet limiting cases.

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