拓扑自旋链的精确基态和元激发
Exact ground state and elementary excitations of a topological spin chain
摘要：
提出了一种新的Bethe Answer方案来计算不具有$U(1)$对称性的量子可积系统的物理性质。作为一个例子，反周期XXZ自旋链，一个典型的相关多体系统嵌入在一个拓扑流形，检查。尽管没有平移不变性和$U(1)$对称性，守恒的“动量”和“电荷”算子被构造。精确地导出了体系的基态能量和基元激发。结果表明，在本征态中存在两个本征分数（一半）零模，这两个本征分数零模是双简并模。基元激发显示出与周期链完全不同的图像。该方法也适用于其它具有或不具有$U(1)$对称性的量子可积模型。
英文摘要：
A novel Bethe Ansatz scheme is proposed to calculate physical properties of quantum integrable systems without $U(1)$ symmetry. As an example, the anti-periodic XXZ spin chain, a typical correlated many-body system embedded in a topological manifold, is examined. Conserved "momentum" and "charge" operators are constructed despite the absence of translational invariance and $U(1)$ symmetry. The ground state energy and elementary excitations are derived exactly. It is found that two intrinsic fractional (one half) zero modes accounting for the double degeneracy exist in the eigenstates. The elementary excitations show quite a different picture from that of a periodic chain. This method can be applied to other quantum integrable models either with or without $U(1)$ symmetry.
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