We formulate a new “Wigner characteristics”-based method to calculate entanglement entropies of subsystems of Fermions using Keldysh field theory. This bypasses the requirements of working with complicated manifolds for calculating Rényi entropies for many-body systems. We provide an exact analytic formula for Rényi and von Neumann entanglement entropies of noninteracting open quantum systems, which are initialized in arbitrary Fock states. We use this formalism to look at entanglement entropies of momentum Fock states of one-dimensional Fermions. We show that the entanglement entropy of a Fock state can scale either logarithmically or linearly with subsystem size, depending on whether the number of discontinuities in the momentum distribution is smaller or larger than the subsystem size. We also use this formalism to describe entanglement dynamics of an open quantum system starting with a single domain wall at the center of the system. Using entanglement entropy and mutual information, we understand the dynamics in terms of coherent motion of the domain wall wavefronts, creation and annihilation of domain walls, and incoherent exchange of particles with the bath.

中文翻译：

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Wigner函数的费米子的纠缠熵：激发态和开放量子系统

我们制定了一种新的基于“维格纳特性”的方法，利用凯尔迪什场论来计算费米子子系统的纠缠熵。这绕开了使用复杂流形来计算多体系统的Rényi熵的要求。我们为非相互作用的开放量子系统的Rényi和von Neumann纠缠熵提供了一个精确的解析公式，这些熵在任意的Fock状态下初始化。我们使用这种形式主义来研究一维费米子的动量福克状态的纠缠熵。我们表明，Fock状态的纠缠熵可以与子系统大小成对数或线性比例，这取决于动量分布中的不连续数小于还是大于子系统大小。我们还使用这种形式主义来描述从系统中心的单个畴壁开始的开放量子系统的纠缠动力学。利用纠缠熵和互信息，我们了解了畴壁波前的相干运动，畴壁的产生和an灭以及粒子与熔池的不相干交换方面的动力学。