一维自旋1/2 XY链各态历经可能性的猝灭动力学探讨
Probing the Possibilities of Ergodicity in the 1D Spin-1/2 XY Chain with Quench Dynamics
摘要：
遍历性是物理系统的统计力学和动力学之间联系的核心。通过将系统的初态固定为零温时哈密顿量的基态，并调节控制参数，我们研究了横向磁场中一维自旋1/2 XY模型的各态历经性和猝灭动力学.基态相图由两个铁磁相和顺磁相组成。已知该自旋系统中的磁化强度是非遍历的。我们建立了两个不同的实验，因为我们称之为单，双淬火和测试的动态磁化沿$Z$轴和自旋-自旋关联函数沿$X$轴，这是序参量的零温度相。我们的精确结果表明，对于零温单次猝灭，遍历性依赖于初始状态和序参量。有趣的是，在另一个设置中，循环路径上的双猝灭，遍历性被完全打破，从对应于序参量的相位开始。否则，它取决于第一个猝灭点，以及当模型在返回的路上第二次猝灭之前花费的猝灭时间$T$，这给出了控制系统中遍历性的能力。因此，与预期相反，在所提到的模型中，遍历性可以通过探测零温度下的淬火动力学来观察。我们的结果提供了进一步的洞察量子系统的零温度动力学行为及其遍历现象的连接。
英文摘要：
Ergodicity sits at the heart of the connection between statistical mechanics and dynamics of a physical system. By fixing the initial state of the system into the ground state of the Hamiltonian at zero temperature and tuning a control parameter, we consider the occurrence of the ergodicity with quench dynamics in the one-dimensional (1D) spin-1/2 XY model in a transverse magnetic field. The ground-state phase diagram consists of two ferromagnetic and paramagnetic phases. It is known the magnetization in this spin system is non-ergodic. We set up two different experiments as we call them single and double quenches and test the dynamics of the magnetization along the $Z$-axis and the spin-spin correlation function along the $X$-axis which are the order parameters of the zero-temperature phases . Our exact results reveal that for single quenches at zero-temperature, the ergodicity depends on the initial state and the order parameter. Interestingly on the other setup, a double quench on a cyclic path, ergodicity is completely broken for starting from the phase corresponding to the order parameter. Otherwise, it depends on the first quenched point, and the quench time $T$ when the model spent before a second quench in the way back which gives an ability to controlling the ergodicity in the system. Therefore, and contrary to expectations, in the mentioned model the ergodicity can be observed with probing quench dynamics at zero-temperature. Our results provide further insight into the zero-temperature dynamical behavior of quantum systems and their connections to the ergodicity phenomenon.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
