可积自旋链中的周期轨道与量子多体伤疤
Periodic orbits and quantum many-body scars in integrable spin chains
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中文总结 AI 辅助
研究可积自旋链中量子多体伤疤与周期轨道的关系，应用周期轨道框架及能量分辨方法，通过贝塞耳假设解析相关本征态和塔间距，建立二者联系，揭示伤疤动力学关键特征可在该框架内理解。
中文摘要 AI 辅助
量子多体伤疤是一般热化动力学的一个例外，但其与可积性的关系仍不明确。本文将周期轨道框架应用于可积的XYZ/XXZ自旋-1/2链，开发了一种能量分辨方法来定位和跟踪整个谱中的周期轨道。识别出伤疤轨道族并根据贝塞耳假设量子数解析其支持的本征态，揭示了由零动量磁振子对修饰的共同弦核。这使得能在贝塞耳假设内直接重建伤疤本征态和相关塔状结构，并从贝塞耳方程中零动量磁振子对的解耦解析地解释等距塔间距，在可积设置中提供了伤疤现象学的微观实现。还表明在有横向场打破可积性时该结构仍然存在，周期轨道继续支配动力学。结果建立了量子伤疤的周期轨道图景与可积模型代数结构之间的直接联系，表明伤疤动力学的关键特征可在贝塞耳假设框架内解析理解。
英文摘要
Quantum many-body scars provide an exception to generic thermalising dynamics, but their relation to integrability remains unclear. Here we apply the periodic-orbit framework to the integrable XYZ/XXZ spin-1/2 chain, developing an energy-resolved approach that enables us to locate and track periodic orbits across the spectrum. We identify families of scarred orbits and resolve their supporting eigenstates in terms of Bethe-ansatz quantum numbers, revealing a common string core dressed by zero-momentum magnon pairs. This allows us to reconstruct both the scarred eigenstates and the associated towers directly within the Bethe ansatz, and explain the equidistant tower spacing analytically from the decoupling of zero-momentum magnon pairs in the Bethe equations, providing a microscopic realisation of scar phenomenology in an integrable setting. We further show that this structure persists upon breaking integrability with a transverse field, with the periodic orbits continuing to govern the dynamics. Our results establish a direct connection between the periodic-orbit picture of quantum scarring and the algebraic structure of integrable models, showing that key features of scar dynamics can be understood analytically within the Bethe ansatz framework.
