论文标题
海森堡 - 旋转1/2链中的域壁
Domain Walls in the Heisenberg-Ising Spin-1/2 Chain
论文作者
论文摘要
在本文中，我们获得了公式，用于在Heisenberg-asision Spin-1/2链中具有各向异性参数$δ$（也称为XXZ Spin-1/2链），在一维晶格$ \ Mathbb {Z} $带有域壁初始条件上。我们使用Bethe Ansatz解决Cantini，Colomo和Pronko（Arxiv：1906.07636）的最新反对称身份，以简化左上旋转的边际分布。在$δ= 0 $ case中，出现了分布$ f_2 $。在$δ\ neq 0 $ case中，我们提出了一个基于鞍点分析的猜想系列扩展类型公式。猜想的公式原来是$δ\ rightarrow 0 $限制的弗雷德姆系列扩展，并以$δ= 0 $恢复结果。
In this paper we obtain formulas for the distribution of the left-most up-spin in the Heisenberg-Ising spin-1/2 chain with anisotropy parameter $Δ$, also known as the XXZ spin-1/2 chain, on the one-dimensional lattice $\mathbb{Z}$ with domain wall initial conditions. We use the Bethe Ansatz to solve the Schr$ö$dinger equation and a recent antisymmetrization identity of Cantini, Colomo, and Pronko (arXiv:1906.07636) to simplify the marginal distribution of the left-most up-spin. In the $Δ=0$ case, the distribution $F_2$ arises. In the $Δ\neq 0$ case, we propose a conjectural series expansion type formula based on a saddle point analysis. The conjectural formula turns out to be a Fredholm series expansion in the $Δ\rightarrow 0$ limit and recovers the result for $Δ= 0$.
