标题： 监控非相互作用费米子在图形处理单元上的纠缠动力学 显示英文标题

标题： Entanglement dynamics of monitored non-interacting fermions on Graphic-Processing-Units

摘要： 监控非相互作用费米子的纠缠动力学描述，包括测量诱导相变（MIPT）的存在，是一个具有文献中矛盾结果的挑战性问题。 将该问题映射到非线性σ模型（NLSM）表明，在热力学极限下确定纠缠熵（EE）的性质需要相对较大的晶格尺寸。 在这里，我们数值地研究了具有$U(1)$对称性的监控非相互作用费米子问题。 使用图形处理单元（GPU）技术，即使使用过时的硬件，也可以达到比之前研究更大的晶格尺寸（1维（1d）和2维（2d）中分别为$L = 16384$和$160\times160$），这使我们能够定量地表征纠缠动力学。 在1维中，我们表明为了确认NLSM预测的无MIPT的存在，无论是投影测量还是同相测量，都需要达到$L \sim 10000$。 在2维中，正如NLSM所预测的那样，对于两种协议，在有限监控速率下观察到由尺度不变互信息表征的MIPT。 临界监控强度取决于协议，而控制接近MIPT的临界指数$\nu \approx 1.3$在两种情况下相似。 这些特征未被NLSM正确预测。 我们的结果为对监控量子系统的纠缠动力学进行完全定量描述铺平了道路。 显示英文摘要

摘要： The description of the entanglement dynamics of monitored non-interacting fermions, including the existence of measurement-induced phase transitions (MIPT), is a challenging problem with conflicting results in the literature. The mapping of the problem onto a non-linear sigma model (NLSM) indicates that relatively large lattice sizes are required to determine the nature of the entanglement entropy (EE) in the thermodynamics limit. Here we address this problem numerically for monitored non-interacting fermions with $U(1)$ symmetry. The use of Graphic-Processing-Unit (GPU) techniques, even with outdated hardware, makes possible to reach much larger lattice sizes ($L = 16384$ and $160\times160$ in one (1d) and two (2d) dimensions respectively) than in previous studies which enables us to characterize quantitatively the entanglement dynamics. In 1d, we show that in order to confirm the absence of a MIPT, for both projective and homodyne measurements, predicted by the NLSM it is necessary to reach $L \sim 10000$. In 2d, also as predicted by the NLSM, we observe for both protocols a MIPT at finite monitoring rate characterized by a scale invariant mutual information. The critical monitoring strength depends on the protocol while the critical exponent $\nu \approx 1.3$ governing the approach to the MIPT is similar in both cases. These features are not correctly predicted by the NLSM. Our results paves the way for a fully quantitative description of the entanglement dynamics of monitoring quantum systems.