This script is based on the notes the author prepared to give a set of six lectures at the Les Houches School "Integrability in Atomic and Condensed Matter Physics" in the summer of 2018. The school had its focus on the application of integrability based methods to problems in non-equilibrium statistical mechanics. The lectures were meant to complement this subject with background material on the equilibrium statistical mechanics of quantum spin chains from a vertex model perspective. The author was asked to provide a minimal introduction to quantum spin systems including notions like the reduced density matrix and correlation functions of local observables. He was further asked to explain the graphical language of vertex models and to introduce the concepts of the Trotter decomposition and the quantum transfer matrix. This was basically the contents of the first four lectures presented at the school. In the remaining two lectures these notions were filled with life by deriving an integral representation of the free energy per lattice site for the Heisenberg-Ising chain (alias XXZ model) using techniques based on non-linear integral equations.

中文翻译：

---

可积量子自旋系统的统计力学

该脚本基于作者准备在2018年夏季在莱克斯·休斯学校（Les Houches School）举行的六次讲座“原子和凝聚态物理的可集成性”中的注释。该学校专注于将基于可集成性的方法应用于非平衡统计力学中的问题。这些讲座旨在通过从顶点模型的角度对量子自旋链的平衡统计力学的背景材料进行补充。要求作者提供有关量子自旋系统的最小介绍，其中包括诸如密度降低矩阵和局部可观察物的相关函数之类​​的概念。他还被要求解释顶点模型的图形语言，并介绍Trotter分解和量子转移矩阵的概念。这基本上是该学校前四次讲座的内容。在剩下的两个讲座中，这些概念通过使用基于非线性积分方程的技术推导海森堡-伊辛链（又称XXZ模型）的每个晶格位点的自由能的积分表示而充满了生命。