AI 中文总结
研究周期驱动下受局域粒子密度监测的一维自由费米子系统，用NLSM和维纳-霍普夫方法解析结合数值模拟，揭示驱动不改变普适类及耦合常数重整化等规律，为相关研究提供统一框架。
AI 中文摘要
我们通过解析和数值方法研究了一维周期驱动的自由费米子系统，该系统会受到局域粒子密度的监测。基于用非线性σ模型（NLSM）以场论语言描述含时哈密顿量长波物理的解析方法，我们发现驱动不会改变该问题的普适类，因此系统在热力学极限下仍保持面积定律行为；当监测速率较小时，中间扩散区会导致纠缠熵出现对数增长。与此同时，驱动会对NLSM的裸耦合常数进行重整化，该常数控制着扩散区的时空“电导率”。我们推导了这种重整化的解析形式，当驱动为“最大对称”驱动且驱动周期足够短时，重整化效应尤为显著。此外，我们采用维纳-霍普夫方法研究弹道-扩散 crossover（交叉）。这些解析预测通过冯·诺依曼纠缠熵和密度关联函数的数值模拟得到验证。我们的数值结果清晰表明，随着系统尺寸增大，会依次出现从弹道行为到扩散行为，最终到局域化的交叉；在扩散区，我们观测到弱局域化修正，与NLSM的解析预测一致。总体而言，我们的结果为理解时间调制费米子系统中的监测效应提供了统一的解析和数值框架，为更广泛地研究驱动量子物质铺平了道路。
英文摘要
We investigate analytically and numerically a one-dimensional periodically driven free-fermionic system subjected to monitoring of the local particle density. Based on the analytical approach that describes the long-wavelength physics of the time-dependent Hamiltonian in the field-theoretical language using the nonlinear sigma-model (NLSM), we reveal that driving does not alter the universality class of the problem. As a consequence, the system retains the area-law behavior in the thermodynamic limit, with an intermediate diffusive regime giving rise to logarithmic growth of entanglement entropy for a small monitoring rate. At the same time, driving leads to a renormalization of the bare coupling constant of the NLSM, which controls the space-time ``conductivity'' in the diffusive regime. We derive the analytic form of this renormalization, which becomes particularly strong in the case of a ``maximally symmetric'' drive and sufficiently short driving period. In addition, we employ the Wiener-Hopf method to investigate the ballistic-diffusive crossover. These analytical predictions are corroborated by numerical simulations of the von-Neumann entanglement entropy and the density correlation function. Our numerical results clearly demonstrate that, with an increase in the system size, there are successive crossovers from ballistic to diffusive behavior and ultimately to localization. Furthermore, in the diffusive regime, we observe weak-localization corrections that are in agreement with the analytical predictions of the NLSM. Overall, our results provide a unified analytical and numerical framework for understanding the effects of monitoring in time-modulated fermionic systems, paving a way for broader investigations of driven quantum matter.
Comments18 pages, 11 figures
