发表机构
International Centre for Theoretical Sciences, Tata Institute of Fundamental Research（国际理论科学中心，塔塔基础研究所）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
本文研究可积Landau-Lifshitz自旋链中畴壁波前动力学，推导磁振子色散关系，揭示各向同性点的扩散展宽与易平面区的弹道传播，并发现临界各向异性$\Delta_c=1/7$处三次色散项符号反转导致波前尾迹方向改变。
AI 中文摘要
我们研究了可积晶格Landau-Lifshitz自旋链中畴壁初态的远离平衡动力学。基于畴壁扩展的线性自旋波描述，我们直接从微观可积哈密顿量推导出长波磁振子色散关系，并利用它来表征由此产生的波前的传播和展宽。该色散关系在各向同性点处为二次型，在易平面区域为线性型，两者之间连续过渡。在各向同性极限下，二次色散导致扩散展宽，而在易平面区域，畴壁前沿以弹道方式传播。保留线性色散的首阶非线性修正项，得到一个三次色散项，它产生弹道前沿的特征性$t^{1/3}$展宽。我们进一步证明，该三次修正项的符号在临界各向异性处发生改变，导致色散尾迹从滞后转变为超前。由此产生的临界点出现在$\Delta_c=1/7$，对应$\gamma_c\simeq 1.047$。完整非线性自旋动力学的数值模拟证实了上述解析标度律，并展示了与振幅无关的自旋波前沿和与振幅相关的非线性孤子传播的共存。
英文摘要
We study the far-from-equilibrium dynamics of domain-wall initial states in the integrable lattice Landau--Lifshitz spin chain. Building on the linear spin-wave description of domain-wall spreading, we derive the long-wavelength magnon dispersion directly from the microscopic integrable Hamiltonian and use it to characterize the propagation and broadening of the resulting wavefronts. The dispersion interpolates between a quadratic form at the isotropic point and a linear form in the easy-plane regime. In the isotropic limit, the quadratic dispersion leads to diffusive broadening, whereas in the easy-plane regime the domain-wall front propagates ballistically. Keeping the leading nonlinear correction to the linear dispersion gives a cubic dispersive term, which produces a characteristic $t^{1/3}$ broadening of the ballistic front. We further show that the sign of this cubic correction changes at a critical anisotropy, leading to a reversal of the dispersive wake from trailing to advancing. The resulting critical point occurs at $Δ_c=1/7$, corresponding to $γ_c\simeq 1.047$. Numerical simulations of the full nonlinear spin dynamics confirm the analytical scaling and demonstrate the coexistence of the amplitude-independent spin-wave front with amplitude-dependent nonlinear soliton propagation.
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