Title: Root patterns and energy spectra of quantum integrable systems without $U(1)$ symmetry: antiperiodic $XXZ$ spin chain Show Chinese title

Title: 根模式和无$U(1)$对称性的量子可积系统的能量谱：反对周期$XXZ$自旋链

Abstract: Finding out root patterns of quantum integrable models is an important step to study their physical properties in the thermodynamic limit. Especially for models without $U(1)$ symmetry, their spectra are usually given by inhomogeneous $T-Q$ relations and the Bethe root patterns are still unclear. In this paper with the antiperiodic $XXZ$ spin chain as an example, an analytic method to derive both the Bethe root patterns and the transfer-matrix root patterns in the thermodynamic limit is proposed. Based on them the ground state energy and elementary excitations in the gapped regime are derived. The present method provides an universal procedure to compute physical properties of quantum integrable models in the thermodynamic limit. Show Chinese abstract

Abstract: 找出量子可积模型的根模式是研究其热力学极限下物理性质的重要步骤。 特别是对于没有$U(1)$对称性的模型，它们的光谱通常由非均匀的$T-Q$关系给出，而贝斯根模式仍然不清晰。 在本文中，以反对称$XXZ$自旋链为例，提出了一种解析方法，在热力学极限下推导出贝斯根模式和转移矩阵根模式。 基于此，得到了间隙区间的基态能量和基本激发。 目前的方法为计算量子可积模型在热力学极限下的物理性质提供了一个通用的程序。