可积周期和开自旋链中的Phantom Bethe激发和自旋螺旋本征态
Phantom Bethe excitations and spin helix eigenstates in integrable periodic and open spin chains
摘要：
以$XXZ$海森堡自旋链为例，证明了开放和周期封闭可积系统中特殊幻影激发的存在性。幻影激发不贡献于贝特态的能量，并且对应于具有无限“幻影”贝特根的贝特方程的特解。幻影贝特根导致不同的磁化扇区之间的周期性的情况下，并出现自旋螺旋状态（SHS），即周期性调制状态的手性性质在开放和封闭的系统。对于周期链，幻影贝特根（PBR）的解决方案出现的各向异性$\De=\coshη$与$\exp(η)$是一个根的单位，从而限制了该现象的关键区域$|\De|<1$。对于开链，PBR解决方案出现的任何值的各向异性，在临界和非临界区域，提供边界场满足一个标准，我们在本文中推导。存在所有Bethe根都是幻影的PBR解，以及由幻影根和常规（有限）根组成的PBR解。我们的实验结果的影响进行了讨论。
英文摘要：
We demonstrate the existence of special phantom excitations for open and periodically closed integrable systems at the example of the $XXZ$ Heisenberg spin chain. The phantom excitations do not contribute to the energy of the Bethe state and correspond to special solutions to the Bethe Ansatz equations with infinite "phantom" Bethe roots. The phantom Bethe roots lead to degeneracies between different magnetization sectors in the periodic case and to the appearance of spin helix states (SHS), i.e. periodically modulated states of chiral nature in both open and closed systems. For the periodic chain, phantom Bethe root (PBR) solutions appear for anisotropies $\De=\coshη$ with $\exp(η)$ being a root of unity, thus restricting the phenomenon to the critical region $|\De|<1$. For the open chain, PBR solutions appear for any value of anisotropy, both in the critical and in the non-critical region, provided that the boundary fields satisfy a criterion which we derive in this paper. There exist PBR solutions with all Bethe roots being phantom, and PBR solutions that consist of phantom roots as well as regular (finite) roots. Implications of our results for an experiment are discussed.
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