具有守恒$\n\thrm{U}(1)$电荷的受监测费米子
Monitored fermions with conserved $\mathrm{U}(1)$ charge
AI总结：
该研究针对带U(1)对称性的自由费米子系统的测量诱导相，通过复制技巧推导耦合涨落流体动力学的SU(N) NL$σ$M有效场论，发现二分纠缠熵满足面积律且大关联长度下有非平凡标度，并给出数值验证与高维推广讨论。
摘要：
我们研究具有U(1)对称性的自由费米子系统的测量诱导相。沿用近期针对马约拉纳链开发的方法，我们推导了大空间和时间尺度下纯度与二分纠缠的场论描述。我们聚焦于具有随机复跃迁、且对局部费米子密度进行连续监测的多味一维链。借助复制技巧，并以味数作为控制近似的大参数，我们推导出一种有效场论，该理论由耦合到涨落流体动力学的SU(N)非线性σ模型（NL$σ$M）构成。与不具有U(1)对称性的无相互作用马约拉纳费米子情况相反，我们发现二分纠缠熵在所有监测速率下均满足面积律，但当关联长度较大时，纠缠呈现非平凡标度行为。我们提供了支持上述结论的数值证据。我们简要说明了对跃迁施加实性条件会如何改变NL$σ$M，还讨论了高维推广情形。
英文摘要：
We study measurement-induced phases of free fermion systems with U(1) symmetry. Following a recent approach developed for Majorana chains, we derive a field theory description for the purity and bipartite entanglement at large space and time scales. We focus on a multi-flavor one-dimensional chain with random complex hoppings and continuous monitoring of the local fermion density. By means of the replica trick, and using the number of flavors as a large parameter controlling our approximations, we derive an effective field theory made up of a SU(N) non-linear sigma model (NL$σ$M) coupled to fluctuating hydrodynamics. Contrary to the case of non-interacting Majorana fermions, displaying no U(1) symmetry, we find that the bipartite entanglement entropy satisfies an area law for all monitoring rates, but with a nontrivial scaling of entanglement when the correlation length is large. We provide numerical evidence supporting our claims. We briefly show how imposing a reality condition on the hoppings can change the NL$σ$M and also discuss higher dimensional generalizations.
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