周期驱动的长程对势可积系统
Periodically driven integrable systems with long-range pair potentials
摘要：
我们研究周期驱动的封闭系统与长程哈密顿考虑广义Kitaev链与配对项的衰减与距离的幂律指数$α$。从一个初始的非纠缠态，我们表明，所有的本地量放松到定义良好的稳态值的热力学极限和$n \gg 1$驱动周期后，任何$α$和驱动频率$ω$。我们引入了一个距离测度，$\mathcal{D}_l(n)$，它表征了$l$站点的子系统的约化密度矩阵到其最终稳态的方法。我们绘制出的$n$依赖的${\mathcal D}_l(n)$，并确定一个临界值$α=α_c$低于他们一般衰减为零的$(ω/n)^{1/2}$。相比之下，对于$α> α_c$，对于$ω\to \infty [0]$，${\mathcal D}_l(n) \sim (ω/n)^{3/2}[(ω/n)^{1/2}]$具有至少一个中间动力学转变。我们还研究了互信息的传播，以了解这种系统的纠缠在空间中传播的性质，随着$n$的增加。我们指出了$ω< ω^{(1)}_c$互信息的时空依赖性中存在定性的新特征，其中$ω^{(1)}_c$是给定$α$动力学跃迁的最大临界频率。一个这样的特征是存在{\it multiple}光锥状结构，其即使在$α$大时也持续存在。我们还表明，与$α\le 2$的长程哈密顿的互信息的时空依赖性的性质定性不同，从他们的短程同行与$α> 2$的任何驱动频率，并将这种差异的行为的Floquet群速度的驱动系统。
英文摘要：
We study periodically driven closed systems with a long-ranged Hamiltonian by considering a generalized Kitaev chain with pairing terms which decay with distance as a power law characterized by exponent $α$. Starting from an initial unentangled state, we show that all local quantities relax to well-defined steady state values in the thermodynamic limit and after $n \gg 1$ drive cycles for any $α$ and driving frequency $ω$. We introduce a distance measure, $\mathcal{D}_l(n)$, that characterizes the approach of the reduced density matrix of a subsystem of $l$ sites to its final steady state. We chart out the $n$ dependence of ${\mathcal D}_l(n)$ and identify a critical value $α=α_c$ below which they generically decay to zero as $(ω/n)^{1/2}$. For $α> α_c$, in contrast, ${\mathcal D}_l(n) \sim (ω/n)^{3/2}[(ω/n)^{1/2}]$ for $ω\to \infty [0]$ with at least one intermediate dynamical transition. We also study the mutual information propagation to understand the nature of the entanglement spreading in space with increasing $n$ for such systems. We point out existence of qualitatively new features in the space-time dependence of mutual information for $ω< ω^{(1)}_c$, where $ω^{(1)}_c$ is the largest critical frequency for the dynamical transition for a given $α$. One such feature is the presence of {\it multiple} light cone-like structures which persists even when $α$ is large. We also show that the nature of space-time dependence of the mutual information of long-ranged Hamiltonians with $α\le 2$ differs qualitatively from their short-ranged counterparts with $α> 2$ for any drive frequency and relate this difference to the behavior of the Floquet group velocity of such driven system.
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