标题： 量子 XY 自旋-1/2 链在相关噪声磁场和各向异性驱动下的反基普尔-祖雷克行为 显示英文标题

标题： Anti Kibble-Zurek behavior in the quantum XY spin-1/2 chain driven by correlated noisy magnetic field and anisotropy

摘要： 在量子相变过程中的非绝热动力学中，Kibble-Zurek范式描述了拓扑缺陷的平均数量随着淬火时间尺度以普遍幂律形式被抑制。在一些研究中，报道了一种与之矛盾的观察结果，称为反Kibble-Zurek动力学，特别是在具有不相关随机（白）噪声的驱动系统中。在这里，我们研究了在存在相关（彩色）高斯噪声的情况下，驱动横向场/各向异性量子$XY$模型中的缺陷生成。我们提出了一个通用假设，能够正确捕捉噪声引起的激发特征，该假设与数值模拟结果有很好的一致性。我们表明，通过改变噪声相关时间，缺陷密度的动力学特征会发生变化。我们的数值模拟证实，对于快速噪声，缺陷密度的动力学与不相关（白）噪声的情况相同，这是预期的结果。然而，噪声相关时间与退火时间的较大比值会导致更大的缺陷密度形成，并重新形成普遍的动力学特征。我们的发现表明，对于快速噪声，噪声引起的缺陷与退火时间成线性比例，而在存在慢速噪声的情况下，噪声引起的缺陷与退火时间的平方成线性比例。数值模拟证实，缺陷密度最小的最优退火时间，在对数尺度上与总噪声功率成线性比例，对于快速和慢速噪声有不同的指数。 显示英文摘要

摘要： In the non-adiabatic dynamics across a quantum phase transition, the Kibble-Zurek paradigm describes that the average number of topological defects is suppressed as a universal power law with the quench time scale. A conflicting observation, which termed anti-Kibble-Zurek dynamics has been reported in several studies, specifically in the driven systems with an uncorrelated stochastic (white) noise. Here, we study the defect generation in the driven transverse field/anisotropy quantum $XY$ model in the presence of a correlated (colored) Gaussian noise. We propose a generic conjecture that properly capture the noise-induced excitation features, which shows good agreement with the numerical simulations. We show that, the dynamical features of defect density are modified by varying the noise correlation time. Our numerical simulations confirm that, for fast noises, the dynamics of the defect density is the same as that of the uncorrelated (white) noise, as is expected. However, the larger ratio of noise correlation time to the annealing time results in larger defects density formation and reforms the universal dynamical features. Our finding reveals that, the noise-induced defects scale linearly with the annealing time for fast noises, while in the presence of the slow noises, the noise-induced defects scale linearly with the square of the annealing time. The numerical simulations confirm that, the optimal annealing time, at which the defects density is minimum, scales linearly in logarithmic scale with the total noise power having different exponents for the fast and slow noises.