Title: Canonical formulation for the thermodynamics of $sl_n$-invariant integrable spin chains Show Chinese title

Title: 具有$sl_n$不变量的可积自旋链的热力学的规范表述

Abstract: Integrable quantum spin chains display distinctive physical properties making them a laboratory to test and assess different states of matter. The study of the finite temperature properties is possible by use of the thermodynamic Bethe ansatz, however at the expense of dealing with non-linear integral equations for, in general, infinitely many auxiliary functions. The definition of an alternative finite set of auxiliary functions allowing for the complete description of their thermodynamic properties at finite temperature and fields has been elusive. Indeed, in the context of $sl_n$-invariant models satisfactory auxiliary functions have been established only for $n \leq 4$. In this paper we take a step further by proposing a systematic approach to generate finite sets of auxiliary functions for $sl_n$-invariant models. We refer to this construction as the canonical formulation. The numerical efficiency is illustrated for $n=5$, for which we present some of the thermodynamic properties of the corresponding spin chain. Show Chinese abstract

Abstract: 可积量子自旋链表现出独特的物理性质，使其成为测试和评估不同物质状态的实验室。 通过使用热力学Bethe假设可以研究有限温度的特性，但需要处理非线性积分方程，通常涉及无限多个辅助函数。 定义一种替代的有限辅助函数集，以完全描述其在有限温度和场下的热力学性质一直是一个难题。 事实上，在$sl_n$不变模型的背景下，仅对$n \leq 4$建立了令人满意的辅助函数。 在本文中，我们通过提出一种系统的方法，为$sl_n$不变模型生成有限的辅助函数集，更进一步地推进了这一领域。 我们将这种构造称为规范形式。 对于$n=5$，我们展示了其对应的自旋链的一些热力学性质，以说明数值效率。