具有任意非对角边界场的XXZ自旋链的精确表面能和螺旋自旋子
Exact surface energy and helical spinons in the XXZ spin chain with arbitrary non-diagonal boundary fields
摘要：
本文提出了一种计算具有一般非对角边界场的XXZ自旋链的表面能和元激发的解析方法。对于有间隙的情况，在某些边界参数区域，两个边界场对表面能的贡献是非加性的。即使在热力学极限$N\to\infty$中，两个边界之间的这种相关效应也取决于位点数$N$的宇称。对于无间隙的情况下，两个边界场的贡献的表面能是添加剂由于在散装的长程相关的情况下。虽然系统的$U(1)$对称性被破坏，但观察到明显不携带自旋- $\frac12$的类自旋激发。本方法提供了一个处理具有或不具有$U(1)$对称性的量子可积系统的通用方法。
英文摘要：
An analytic method is proposed to compute the surface energy and elementary excitations of the XXZ spin chain with generic non-diagonal boundary fields. For the gapped case, in some boundary parameter regimes the contributions of the two boundary fields to the surface energy are non-additive. Such a correlation effect between the two boundaries also depends on the parity of the site number $N$ even in the thermodynamic limit $N\to\infty$. For the gapless case, contributions of the two boundary fields to the surface energy are additive due to the absence of long-range correlation in the bulk. Although the $U(1)$ symmetry of the system is broken, exact spinon-like excitations, which obviously do not carry spin-$\frac12$, are observed. The present method provides an universal procedure to deal with quantum integrable systems either with or without $U(1)$ symmetry.
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