标题： 哈德纳分数统计用于一维海森堡 XXX 自旋链 显示英文标题

标题： Haldane Fractional Statistics for 1D Heisenberg Spin XXX Chain

摘要： 哈德纳的分数排斥统计（FES）描述了一种广义的泡利排斥统计，可以视为由内在动力学相互作用引起的涌现量子统计。在二维（2D）相互作用玻色气体的量子临界性中已识别出一种非互惠的FES [Nat. Sci. Rev. 9, nwac027 (2022)]。自然地会问，这种非互惠的FES是否可以通过反铁磁自旋-1/2 XXX链中的自旋-自旋相互作用产生？在本文中，我们首先将自旋字符串的贝特假设方程用不同种类的FES方程表示。然后我们表明，1D自旋XXX链在临界区域显著地具有非互惠的FES。我们观察到，以FES表示的状态方程产生了模型在量子临界性下的完整统计性质，这与从模型的热力学贝特假设方程（TBA）得到的结果高度一致。从非互惠的FES出发，我们还精确地确定了量子标度函数，这些函数进一步与之前的TBA结果 [Phys. Rev. B 96, 220401(R) (2017)] 非常吻合。最后，我们还建立了Lieb-Liniger模型和自旋海森堡自旋链在量子临界性下的标度函数之间的精确映射。我们的方法从量子FES的角度为物质的临界相提供了深刻的见解。 显示英文摘要

摘要： Haldane's fractional exclusion statistics (FES) describes a generalized Pauli exclusion statistics, which can be regarded as an emergent quantum statistics induced by the intrinsic dynamical interaction. A non-mutual FES has been identified at the quantum criticality of the one-dimensional (1D) and 2D interacting Bose Gas [Nat. Sci. Rev. 9, nwac027 (2022)]. It is naturally asked if such a non-mutual FES can be induced by the spin-spin interaction in the antiferromagnetic spin-1/2 XXX chain? In this article, we first represent the Bethe ansatz equations of spin strings in terms of the FES equations of different species. Then we show that the 1D spin XXX chain remarkably possesses the non-mutual FES in the critical region. We observe that the equation of state in terms of the FES gives rises to full statistical properties of the model at quantum criticality, which are in good agreement with the results obtained from the thermodynamic Bethe ansatz (TBA) equations of the model. From the non-mutual FES, we also precisely determine the quantum scaling functions, which further agree well with the previous TBA results [Phys. Rev. B 96, 220401(R) (2017)]. Finally, we also build up an exact mapping between the scaling functions of the Lieb-Liniger model and the spin Heisenberg spin chain at quantum criticality. Our method provides deep insights into the critical phase of matter from quantum FES point of view.