XXZ链的四邻域两点函数和费米基方法
Fourth-neighbour two-point functions of the XXZ chain and the Fermionic basis approach
摘要：
本文对XXZ量子自旋链的关联函数理论的费米基方法作了一个描述性的评述。重点是明确的短距离关联函数，这将是在一种方式，允许其直接在计算机上实现的公式。在费米子基方法中，与模型的可积结构相容的一大类固定约化密度矩阵假定为因子分解形式。这意味着，局部算子的所有期望值和所有两点函数，特别地，可以被表示为仅两个函数$ρ$和$ω$及其导数中的多变量多项式，其系数在模型的变形参数$q$中是有理的。这些系数是“代数的起源”。它们不依赖于密度矩阵的选择，密度矩阵仅影响$ρ$和$ω$的形式。作为一个例子，我们详细计算了温度为$T$，磁场为$h$时，$q$处于临界区的巨正则系综。我们比较我们的精确结果的第四个邻居两点函数的渐近公式为$h, T = 0$和有限的$h$和$T$。
英文摘要：
We give a descriptive review of the Fermionic basis approach to the theory of correlation functions of the XXZ quantum spin chain. The emphasis is on explicit formulae for short-range correlation functions which will be presented in a way that allows for their direct implementation on a computer. Within the Fermionic basis approach a huge class of stationary reduced density matrices, compatible with the integrable structure of the model, assumes a factorized form. This means that all expectation values of local operators and all two-point functions, in particular, can be represented as multivariate polynomials in only two functions $ρ$ and $ω$ and their derivatives with coefficients that are rational in the deformation parameter $q$ of the model. These coefficients are of `algebraic origin'. They do not depend on the choice of the density matrix, which only impacts the form of $ρ$ and $ω$. As an example we work out in detail the case of the grand canonical ensemble at temperature $T$ and magnetic field $h$ for $q$ in the critical regime. We compare our exact results for the fourth-neighbour two-point functions with asymptotic formulae for $h, T = 0$ and for finite $h$ and $T$.
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