AI 中文总结
本研究推导了二元Floquet驱动下的分段解析MT表达式，应用于无序Floquet伊辛链，证实重标MT泛函可表征有限尺寸周期2动力学的回几何并关联锁定自旋响应。
AI 中文摘要
对于纯态幺正动力学，Mandelstam Tamm（MT）下界泛函将终点Fubini-Study回角与路径平均能量色散进行比较。它们不同的尺寸和时间依赖性，模糊了类离散时间晶体（DTC）动力学中周期为2的MT结构的起源及其与自旋响应的关系。对于二元Floquet驱动，我们在不假设分段哈密顿量可交换的情况下，推导了精确的分段解析MT表达式，并将其应用于无序Floquet伊辛链。局部能量项的连通协方差具有绝对且一致的可求和性，这意味着路径平均能量色散的上界为O(√L)（L为系统尺寸）。四个系统尺寸的终点数据与该主导行为一致，支持对MT泛函进行相应重标。在具有锁定自旋响应的有限尺寸区域的一个代表点，奇数和偶数重标MT分支在10²个周期的观测窗口内始终分离；回角交替剧烈，而尺寸归一化的路径平均能量色散几乎无明显奇偶依赖性，表明终点几何是分支分裂的主要来源。在相互作用参数网格上，控制脉冲误差和相互作用强度后，周期为2的MT分量与锁定自旋响应具有强偏斯皮尔曼秩相关性。重标MT泛函可表征有限尺寸周期为2动力学的全局回几何，并量化其与锁定自旋响应的关联。
英文摘要
For pure state unitary dynamics, the Mandelstam Tamm (MT) lower-bound functional compares the endpoint Fubini Study return angle with path averaged energy dispersion. Their distinct size and temporal dependences obscure the origin of period two MT structure in discrete time crystal (DTC) like dynamics and its relation to the spin response. For binary Floquet drives, we derive an exact segment resolved MT expression without assuming commuting segment Hamiltonians and apply it to a disordered Floquet Ising chain. Absolute and uniform summability of connected covariances of local energy terms implies an $O(\sqrt{L})$ upper bound on the path-averaged energy dispersion. Endpoint data for four system sizes are consistent with this leading behavior and support the corresponding rescaling of the MT functional. At a representative point in the finite-size region with a locked spin response, odd and even rescaled MT branches remain separated throughout the $10^2$ period observation window. The return angle alternates strongly, whereas the size-normalized path-averaged energy dispersion shows little discernible parity dependence, indicating that endpoint geometry is the main source of the branch splitting. Across the interacting parameter grid, the period-two MT component has a strong partial Spearman rank correlation with the locked spin response after controlling for pulse error and interaction strength. The rescaled MT functional characterizes the global return geometry of finite-size period-two dynamics and quantifies its association with the locked spin response.
Comments21 pages, 9 figs
