可积三态链中的精确弹道能量输运与涌现XXZ动力学

中文摘要 AI 辅助

我们研究了一个可积厄米三态链中弹道能量输运的耦合依赖性以及涌现的自旋动力学，该链将时钟相互作用连接到一个高度简并的旗极限。通过构造正则$R$-矩阵来建立全局守恒的能量流，我们解析地评估了其完全方差，从而获得了热Drude权重的高温前导系数的精确严格正值，以及能量关联二阶矩的弹道增长率。在强耦合极限下，简并被一个离域的第三色旁观者态的虚跃迁所解除，这产生了一个各向异性为$\Delta = -1/2$的有效自旋-$1/2$ XXZ哈密顿量，并从根本上选择全活跃的双色扇区作为真正的基态。对于周期性边界条件，这种虚旁观者运动引入了一个正的改变长度的XXZ超荷平方，对于$L\ge4$，它严格湮灭了基态之上有限且与长度无关的能量区间内的所有态。因此，我们严格证明了完整的周期性有效理论完美地再现了精确的低能XXZ谱，包括所有态多重性，以及其宏观体自由能密度。

英文摘要

We investigate the coupling dependence of ballistic energy transport and the emergent spin dynamics in an integrable Hermitian three-state chain that connects a clock interaction to a highly degenerate flag limit. By constructing a regular $R$-matrix to establish a globally conserved energy current, we analytically evaluate its full variance to obtain the exact, strictly positive leading high-temperature coefficient of the thermal Drude weight and the ballistic growth rate of the energy-correlation second moment. In the strong-coupling limit, the degeneracy is lifted by virtual transitions of a delocalized third-color spectator state, which generates an effective spin-$1/2$ XXZ Hamiltonian with anisotropy $Δ= -1/2$ and fundamentally selects the all-active two-color sector as the true ground state. For periodic boundaries, this virtual spectator motion introduces a positive length-changing XXZ supercharge squared that, for $L\ge4$, strictly annihilates all states within a finite, length-independent energy interval above the ground state. Consequently, we rigorously prove that the full periodic effective theory perfectly replicates the exact low-energy XXZ spectrum, including all state multiplicities, as well as its macroscopic bulk free-energy density.

发表机构

• Nanophotonics and Biophotonics Key Laboratory of Jilin Province, School of Physics, Changchun University of Science and Technology（吉林省纳米光子学与生物光子学重点实验室，长春理工大学物理学院）

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23 pages, 2 figures; exact symbolic verification code included as arXiv ancillary files