在无序有限自旋链中延长离散时间晶体寿命的途径
Route to Extend the Lifetime of a Discrete Time Crystal in a Finite Spin Chain Without Disorder
AI总结：
本文提出在无平移不变Ising自旋链中通过将最近邻相互作用强度调至最优值 $JT=π$，利用量子干涉机制抑制激发产生，从而显著延长离散时间晶体寿命，并在偶数尺寸系统中实现永久周期倍化振荡。
摘要：
周期性驱动（Floquet）系统由具有离散时间平移对称性的含时哈密顿量描述。这种对称性的自发破缺导致了一种新型非平衡物质相——离散时间晶体（DTC）的出现。在本文中，我们提出了一种方案，以在典范模型中延长DTC的寿命——该模型为具有最近邻相互作用 $J$ 的平移不变 Ising 自旋链，受频率为 $\frac{2 π}{T}$ 的横向磁场周期性驱动。该系统在广泛的参数范围内表现出DTC的标志特征——频率为 $\fracπ{T}$ 的持续次谐波振荡。通过解析论证和精确对角化计算，我们证明当相互作用强度被调节至最优值 $JT = π$ 时，DTC的寿命达到最大。我们的方案本质上依赖于一种由相互作用诱导的量子干涉机制，该机制抑制了激发的产生，从而延长了DTC的寿命。有趣的是，我们发现在偶数尺寸系统中，周期倍化振荡可以永久持续。这种异常长的寿命可归因于在 $JT=π$ 时出现的时间反演对称性。我们的工作为在各种量子模拟器平台中实现稳健的DTC提供了一条有前景的途径。
英文摘要：
Periodically driven (Floquet) systems are described by time dependent Hamiltonians that possess discrete time translation symmetry. The spontaneous breaking of this symmetry leads to the emergence of a novel non-equilibrium phase of matter - the Discrete Time Crystal (DTC). In this paper, we propose a scheme to extend the lifetime of a DTC in a paradigmatic model - a translation invariant Ising spin chain with nearest-neighbor interaction $J$, subjected to a periodic kick by a transverse magnetic field with frequency $\frac{2 π}{T}$. This system exhibits the hallmark signature of a DTC - persistent subharmonic oscillations with frequency $\fracπ{T}$ - for a wide parameter regime. Employing both analytical arguments as well as exact diagonalization calculations, we demonstrate that the lifetime of the DTC is maximized, when the interaction strength is tuned to an optimal value, $JT = π$. Our proposal essentially relies on an interaction induced quantum interference mechanism that suppresses the creation of excitations, and thereby enhances the DTC lifetime. Intriguingly, we find that the period doubling oscillations can last eternally in even size systems. This anomalously long lifetime can be attributed to a time reflection symmetry that emerges at $JT=π$. Our work provides a promising avenue for realizing a robust DTC in various quantum emulator platforms.
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