发表机构
Institute for Mathematics and Fundamental Physics; Hefei National Laboratory; School of Science, Constructor University（数学与基础物理研究所; 合肥国家实验室; 康斯坦茨大学理学院）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
本文在有序量子磁体中展示了离散标度不变性可由复合激发的内部运动涌现，通过长程Ising链中的反平方吸引力确定标度反常指数，实现量子极限环物理的微观多体实现。
AI 中文摘要
离散标度不变性通常源于共振少体或奇异标度不变动力学。我们表明，它可以在有序量子磁体中复合激发的内部运动中涌现。在边缘$1/r^4$横向场Ising链中，长程键在 dressed 畴壁之间产生渐近反平方吸引力，其强度由自发磁化固定。dressed 双扭结阈值曲率设定了相对动能标度。这些独立可访问的量共同决定了标度反常指数，从而决定了介子层级。在超临界区域，同一指数控制几何结合能与尺寸比、对数能级累积以及对数周期阈值散射。全自旋精确对角化和四阶弱场哈密顿量支持在核心与环效应之间的有限窗口内的耦合能量-尺寸标度。这为量子极限环物理提供了微观多体实现，其普适标度由磁序和扭结迁移率固定。
英文摘要
Discrete scale invariance often arises from resonant few-body or singular scale-invariant dynamics. We show that it can instead emerge in the internal motion of a composite excitation in an ordered quantum magnet. In the marginal $1/r^4$ transverse-field Ising chain, long-range bonds generate an asymptotic inverse-square attraction between dressed domain walls, with strength fixed by the spontaneous magnetization. The dressed two-kink threshold curvature sets the relative kinetic scale. Together, these independently accessible quantities determine the scale-anomaly exponent and hence the meson hierarchy. In the supercritical regime, the same exponent governs geometric binding-energy and size ratios, logarithmic level accumulation, and log-periodic threshold scattering. Full-spin exact diagonalization and a fourth-order weak-field Hamiltonian support the coupled energy--size scaling in the finite window between core and ring effects. This provides a microscopic many-body realization of quantum limit-cycle physics, with its universal scaling fixed by magnetic order and kink mobility.
Comments26 pages, 8 figures
