标题： 受监控费米子系统中的纠缠行为和局域化特性 显示英文标题

标题： Entanglement behavior and localization properties in monitored fermion systems

摘要： 我们研究了监测费米子的各种可积和不可积模型中的渐近双部分纠缠。 我们发现，在可积情况下，纠缠与系统大小的关系在超过一个数量级的范围内，可以通过在线性行为和幂律行为之间插值的函数很好地拟合。 在我们能够达到的尺寸范围内，相同的拟合也可以捕捉到纠缠的对数增长，此时幂律指数非常小。 因此，我们使用拟合参数来表征各种纠缠相。 对于不可积情况，如交错 t-V 模型和 Sachdev-Ye-Kitaev (SYK) 模型，数值计算使我们无法在尺寸上跨越不同的数量级，因此我们拟合渐近纠缠与测量强度的关系，然后观察拟合参数随尺寸的标度。 我们发现两种不同的行为：在 SYK 模型中，我们观察到体积律增长，而在 t-V 模型中则出现了一些纠缠相变的迹象。 在后一种模型中，我们通过反参与比研究了希尔伯特空间中的局域化性质，发现了一种与纠缠性质无关的异常扩展。 最后，我们展示了我们的函数能够很好地拟合阶梯几何中具有周期性投影测量的二次模型的费米子对数否定性。 显示英文摘要

摘要： We study the asymptotic bipartite entanglement in various integrable and nonintegrable models of monitored fermions. We find that, for the integrable cases, the entanglement versus the system size is well fitted, over more than one order of magnitude, by a function interpolating between a linear and a power-law behavior. Up to the sizes we are able to reach, a logarithmic growth of the entanglement can be also captured by the same fit with a very small power-law exponent. We thus propose a characterization of the various entanglement phases using the fitting parameters. For the nonintegrable cases, as the staggered t-V and the Sachdev-Ye-Kitaev (SYK) models, the numerics prevents us from spanning different orders of magnitude in the size, therefore we fit the asymptotic entanglement versus the measurement strength and then look at the scaling with the size of the fitting parameters. We find two different behaviors: for the SYK we observe a volume-law growth, while for the t-V model some traces of an entanglement transition emerge. In the latter models, we study the localization properties in the Hilbert space through the inverse participation ratio, finding an anomalous delocalization with no relation with the entanglement properties. Finally, we show that our function fits very well the fermionic logarithmic negativity of a quadratic model in ladder geometry with stroboscopic projective measurements.