标题： 周期驱动的无相互作用费米子系统中的测量诱导相变 显示英文标题

标题： Measurement-induced phase transition in periodically driven free-fermionic systems

摘要： 众所周知，幺正演化倾向于增加纠缠，而连续监测通过将波函数轨迹固定在测量算符的本征态上来抵消这种增长。 在本工作中，我们研究了在周期性驱动的自由费米量子系统中，测量引起的相变的命运，其中跳跃幅值通过方波脉冲在时间上周期性调制。 在高频极限下，对非厄米量子正弦-戈登模型的重整化群分析[如{物理评论X 11, 041004 (2021)}中所提出]表明，如果跳跃幅值对零对称变化，系统总是倾向于面积律相，其中稳态纠缠熵与子系统大小无关。 相比之下，驱动幅值的不对称性倾向于促进纠缠的增长。 此外，对于我们可以访问的系统尺寸，数值证据表明，降低驱动频率通常会促进纠缠的增长。 对于这样的驱动系统，在合理的小频率范围内，作为测量强度的函数，我们观察到一个可能的贝瑞金-科尔特斯-托斯勒（Berezinskii-Kosterlitz-Thouless）（BKT）相变的特征，该相变发生在无能隙临界相（其纠缠熵随子系统大小对数增长）和有能隙面积律相之间。 然而，几乎不可能排除这里观察到的相变不是真正的热力学相变，而是对数增长到面积律纠缠相之间的有限尺寸交叉。 即使在这种情况下，面积律相占优的临界长度尺度随着驱动周期的增加而增加。 另一方面，对于对称驱动，无论驱动频率如何，系统始终表现出面积律相。 显示英文摘要

摘要： It is well known that unitary evolution tends to increase entanglement, whereas continuous monitoring counteracts this growth by pinning the wavefunction trajectories to the eigenstates of the measurement operators. In this work, we investigate the fate of the measurement-induced phase transition in a periodically driven free-fermionic quantum system, where the hopping amplitude is modulated periodically in time using a square pulse. In the high-frequency limit, a renormalization group analysis of the non-Hermitian quantum sine-Gordon model [as proposed in {Phys. Rev. X 11, 041004 (2021)}] reveals that if the hopping amplitude is varied symmetrically around zero, the system always favors the area-law phase, where the steady-state entanglement entropy is independent of subsystem size. In contrast, asymmetry in the drive amplitudes tends to promote entanglement growth. Furthermore, numerical evidence for the system sizes accessible to us suggests that decreasing the drive frequency typically favors entanglement growth. For such driven systems, at least for reasonably small frequency regimes, as a function of measurement strength, we observe a potential signature of a Berezinskii-Kosterlitz-Thouless (BKT) phase transition between a gapless critical phase, characterized by logarithmic growth of entanglement entropy with subsystem size, and a gapped area-law phase. However, it is almost impossible to rule out the possibility that the transition observed here is not an actual thermodynamic transition, but a finite-size crossover between logarithmic to area law entanglement phase. Even in that scenario, the critical length scale beyond which the area law phase prevails increases with the increasing time period of driving. On the other hand, for a symmetric drive, the system consistently exhibits an area-law phase, regardless of the driving frequency.