用自适应含时密度矩阵重整化群方法实时研究自旋1/2链中的扩散输运和弹道输运
A real-time study of diffusive and ballistic transport in spin-1/2 chains using the adaptive time-dependent density matrix renormalization group method
摘要：
利用自适应含时密度矩阵重整化群方法，数值研究了零温下一维自旋1/2系统的自旋动力学和输运。而不是从线性响应理论计算输运系数，我们研究了从空间不均匀的初始状态的磁化的实时演变。特别是，我们能够分析系统远离平衡与此设置。通过计算磁化方差的时间依赖性，我们可以区分扩散弹道制度，这取决于模型参数。对于自旋为1/2的各向异性链和半填充的例子，我们发现预期的弹道行为在易平面相，而在大量的制度的动态磁化是扩散。我们的方法允许我们调整初始状态的偏离从基态和定性行为的动力学证明是有效的，即使是高度扰动的初始状态的情况下，易平面交换各向异性。我们进一步介绍了不可积模型的两个例子，阻挫链和两条腿的自旋梯，我们遇到了扩散输运在所有的大规模阶段。在前一个系统中，我们的结果表明在临界阶段的弹道行为。我们讨论了我们的研究结果，鉴于准一维量子磁体的实验，我们提出的粒子密度的空间方差的时间依赖性的研究可能有助于在光晶格以及超冷原子的膨胀的表征。
英文摘要：
Using the adaptive time-dependent density matrix renormalization group method, we numerically study the spin dynamics and transport in one-dimensional spin-1/2 systems at zero temperature. Instead of computing transport coefficients from linear response theory, we study the real-time evolution of the magnetization starting from spatially inhomogeneous initial states. In particular, we are able to analyze systems far away from equilibrium with this set-up. By computing the time-dependence of the variance of the magnetization, we can distinguish diffusive from ballistic regimes, depending on model parameters. For the example of the anisotropic spin-1/2 chain and at half filling, we find the expected ballistic behavior in the easy-plane phase, while in the massive regime the dynamics of the magnetization is diffusive. Our approach allows us to tune the deviation of the initial state from the ground state and the qualitative behavior of the dynamics turns out to be valid even for highly perturbed initial states in the case of easy-plane exchange anisotropies. We further cover two examples of nonintegrable models, the frustrated chain and the two-leg spin ladder, and we encounter diffusive transport in all massive phases. In the former system, our results indicate ballistic behavior in the critical phase. We discuss our findings in view of experiments on quasi-one dimensional quantum magnets and we propose that the study of the time-dependence of the spatial variance of particle densities could be instrumental in the characterization of the expansion of ultracold atoms in optical lattices as well.
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