论文标题
Wigner函数的费米子的纠缠熵：激发态和开放量子系统
Entanglement Entropy of Fermions from Wigner Functions: Excited States and Open Quantum Systems
论文作者
论文摘要
我们使用Keldysh Field理论制定了一种新的``Wigner特征''方法来计算费米子子系统的纠缠熵。这绕开了使用复杂的歧管来计算许多身体系统的Rényi熵的要求。我们为非相互作用开放量子系统的Rényi和Von-Neumann纠缠熵提供了一个精确的分析公式，这些量子系统是在任意Fock状态下初始化的。我们使用这种形式主义来研究一维费米子的动量状态的纠缠熵。我们表明，Fock状态的纠缠熵可以与子系统大小进行对数或线性扩展，具体取决于动量分布中的不连续性数量是否比子系统大小更小还是更大。这种状态分类用占领力的块数量术语，使我们能够在分析特定子系统大小上分析估计关键和非关键的Fock状态的数量。我们还使用这种形式主义来描述开放量子系统的纠缠动态，从系统中心的单个域壁开始。使用纠缠熵和共同信息，我们从域壁波前的连贯运动，域壁的创建和an灭以及颗粒与浴室的不一致交换方面了解动力学。
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 non-interacting open quantum systems, which are initialised 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. This classification of states in terms number of blocks of occupied momenta allows us to analytically estimate the number of critical and non-critical Fock states for a particular 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.
