AI 中文总结
研究无限一维横向场伊辛链全局量子猝灭后的子系统距离衰减，用布雷斯距离量化偏差，发现后期衰减遵循离散幂律，指数由多种因素共同决定，揭示了可积量子系统局部平衡动力学的通用离散结构。
AI 中文摘要
我们对无限一维横向场伊辛链中的全局量子猝灭后的子系统距离衰减进行了数值研究，使用数学上严格的布雷斯距离\(B_A(t)\)来量化时间演化的约化密度矩阵与其平稳广义吉布斯系综状态的偏差。我们表明，后期衰减遵循离散幂律\(B_A(t) \sim t^{-\lambda}\)，其中指数\(\lambda\)限于离散值：\(1\)、\(5/4\)、\(3/2\)、\(7/4\)、\(2\)、\(5/2\)以及可能的更多值。特定指数由猝灭前后的横向场以及在\(\varphi\in[0,\pi]\)上定义的对称激发分数函数\(m_S(\varphi)\)的性质共同决定，该函数用于表征猝灭前哈密顿量的本征态，包括连续性、边界值和一阶导数边界值等。先前为猝灭前哈密顿量的初始基态建立的\(t^{-3/2}\)衰减自然地作为这种一般分类的特殊情况被恢复。我们的结果揭示了控制可积量子系统中局部平衡动力学的通用离散结构。
英文摘要
We present a numerical study of subsystem distance decay following a global quantum quench in the infinite one-dimensional transverse-field Ising chain, using the mathematically rigorous Bures distance $B_A(t)$ to quantify the deviation of the time-evolved reduced density matrix from its stationary generalized Gibbs ensemble state. We show that the late-time decay follows a discrete power law $B_A(t) \sim t^{-λ}$, with the exponent $λ$ confined to discrete values: $1$, $5/4$, $3/2$, $7/4$, $2$, $5/2$, and potentially further values. The specific exponent is jointly determined by the pre- and post-quench transverse fields, as well as by properties of the symmetric excitation-fraction function $m_S(φ)$, defined on $φ\in[0,π]$ to characterize the pre-quench Hamiltonian eigenstates, including continuity, boundary values, and first-derivative boundary values, among others. The previously established $t^{-3/2}$ decay for the initial ground state of the pre-quench Hamiltonian is naturally recovered as a special case of this general classification. Our results reveal a universal discrete structure governing local equilibration dynamics in integrable quantum systems.
Comments10 pages, 4 figures
