论文标题
高斯近似中浮标时间晶体的临界特性
Critical properties of the Floquet time crystal within the Gaussian approximation
论文作者
论文摘要
周期性驱动的O（n）模型在临界线附近进行了研究，该模型将无序的顺磁性相位与周期倍增相分开，后者是浮力时间晶体的一个例子。单点和两点相关函数的时间演变是在高斯近似值内获得的，在驱动幅度中触及触及。发现相关性不仅表现出一倍增加一倍，而且在很大的空间距离上腐烂。这些特征与非元素O（n）模型相提并论，在顺磁性铁磁临界点附近。在驱动和未发动的情况下，空间中的代数衰减在质量上有所不同。特别是，浮标时间晶体的时空顺序导致位置摩托车和动量摩肌相关函数，在驱动的范围内比未经启动的模型更长。与相关函数相关的轻锥动力学在质量上也有所不同，因为Floquet Time Crystal的临界线显示了一个具有两个不同速度的轻锥，这两个速度的比例是缩放的比例，作为无尺寸驱动幅度的正方形。与驱动频率相比，为驱动器的完整周期构建了由于驱动器的完整循环而导致的时间演变的Floquet Unitar，但与驱动频率相比，但与驱动振幅的平方根有一般关系。在与驱动振幅的平方根相比，在中间动量上很大，发现Floquet Unity只是简单地旋转模式。另一方面，与驱动振幅的平方根相比，在动量很小的时候，发现Floquet Unity主要挤压模式，在增加模式的波长时增加了模式，并且对其进行了巨型依赖。
The periodically driven O(N) model is studied near the critical line separating a disordered paramagnetic phase from a period doubled phase, the latter being an example of a Floquet time crystal. The time evolution of one-point and two-point correlation functions are obtained within the Gaussian approximation and perturbatively in the drive amplitude. The correlations are found to show not only period doubling, but also power-law decays at large spatial distances. These features are compared with the undriven O(N) model, in the vicinity of the paramagnetic-ferromagnetic critical point. The algebraic decays in space are found to be qualitatively different in the driven and the undriven cases. In particular, the spatio-temporal order of the Floquet time crystal leads to position-momentum and momentum-momentum correlation functions which are more long-ranged in the driven than in the undriven model. The light-cone dynamics associated with the correlation functions is also qualitatively different as the critical line of the Floquet time crystal shows a light-cone with two distinct velocities, with the ratio of these two velocities scaling as the square-root of the dimensionless drive amplitude. The Floquet unitary, which describes the time evolution due to a complete cycle of the drive, is constructed for modes with small momenta compared to the drive frequency, but having a generic relationship with the square-root of the drive amplitude. At intermediate momenta, which are large compared to the square-root of the drive amplitude, the Floquet unitary is found to simply rotate the modes. On the other hand, at momenta which are small compared to the square-root of the drive amplitude, the Floquet unitary is found to primarily squeeze the modes, to an extent which increases upon increasing the wavelength of the modes, with a power-law dependence on it.
