We consider a one-dimensional interacting spinless fermion model, which displays the well-known Luttinger liquid (LL) to charge density wave (CDW) transition as a function of the ratio between the strength of the interaction $U$ and the hopping $J$. We subject this system to a spatially uniform drive which is ramped up over a finite time interval and becomes time periodic in the long-time limit. We show that by using a density matrix renormalization group approach formulated for infinite system sizes, we can access the large-time limit even when the drive induces finite heating. When both the initial and long-time states are in the gapless (LL) phase, the final state has power-law correlations for all ramp speeds. However, when the initial and final state are gapped (CDW phase), we find a pseudothermal state with an effective temperature that depends on the ramp rate, both for the Magnus regime in which the drive frequency is very large compared to other scales in the system and in the opposite limit where the drive frequency is less than the gap. Remarkably, quantum defects (instantons) appear when the drive tunes the system through the quantum critical point, in a realization of the Kibble-Zurek mechanism.

中文翻译：

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量子链中的浮球工程

我们考虑一维相互作用的无旋费米子模型，该模型显示了众所周知的Luttinger液体（LL）到电荷密度波（CDW）的跃迁，它是相互作用强度之间的比率的函数 $ü$ 和跳跃 $Ĵ$。我们对该系统进行空间上均匀的驱动，该驱动在有限的时间间隔内逐渐增大，并在长时间限制内成为时间周期性的驱动。我们表明，通过使用为无限系统尺寸制定的密度矩阵重归一化组方法，即使驱动器引起有限的加热，我们也可以访问较大的时间限制。当初始状态和长时间状态均处于无间隙（LL）阶段时，最终状态对所有斜坡速度都具有幂律相关性。但是，当初始状态和最终状态（CDW相）处于空白时，我们发现在有效温度下，假热状态取决于斜率，对于马格努斯状态而言，其驱动频率与其他比例相比非常大。系统并处于相反的极限（驱动频率小于间隙）。值得注意的是