正弦变化交错势一维模型中的最大群速度
Maximum group velocity in a one-dimensional model with a sinusoidally varying staggered potential
摘要：
本文利用Floquet理论研究了一维紧束缚模型中的频闪群速度的最大值，该模型中的势场是按正弦函数变化的。通过数值对角化的Floquet算子得到的结果进行了分析，使用各种分析方案。在低频极限，我们使用绝热理论，而在高频极限的Floquet哈密顿量的马格纳斯展开证明是适当的。当交错势的大小远大于或远小于跳跃时，我们使用简并Floquet微扰理论，我们发现在前一种情况下，当最大群速度为零时，动力学局部化发生。最后，从一个“工程”的初始状态，粒子（采取硬核玻色子）是本地化的链的一部分，我们证明了最大频闪群速度的存在，体现在光锥一样的粒子在真实空间中的传播。
英文摘要：
We use Floquet theory to study the maximum value of the stroboscopic group velocity in a one-dimensional tight-binding model subjected to an on-site staggered potential varying sinusoidally in time. The results obtained by numerically diagonalizing the Floquet operator are analyzed using a variety of analytical schemes. In the low frequency limit we use adiabatic theory, while in the high frequency limit the Magnus expansion of the Floquet Hamiltonian turns out to be appropriate. When the magnitude of the staggered potential is much greater or much less than the hopping, we use degenerate Floquet perturbation theory; we find that dynamical localization occurs in the former case when the maximum group velocity vanishes. Finally, starting from an "engineered" initial state where the particles (taken to be hard core bosons) are localized in one part of the chain, we demonstrate that the existence of a maximum stroboscopic group velocity manifests in a light cone like spreading of the particles in real space.
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