论文标题
耗时自由屈服系统中的对数纠缠缩放
Logarithmic entanglement scaling in dissipative free-fermion systems
论文作者
论文摘要
我们研究在存在局部热浴的情况下，在一维自由铁系统中扩散的量子信息。我们采用非本地的Lindblad主方程来描述系统浴的相互作用，从某种意义上说，Lindblad运算符是根据封闭系统的Bogoliubov操作员编写的，因此在太空中是非本地的。描述稳态的统计合奏是根据浴室的费米 - 迪拉克分布的凸组合而写的。由于自由屈服分散体的奇异性，稳态相互信息表现出奇异性作为系统参数的函数。虽然相互信息一致满足了区域定律，但在单数点，它表现出对数缩放的缩放，这是子系统大小的函数。通过采用Fisher-hartwig定理，我们得出对数缩放的预将因子，这取决于浴室的参数并扮演有效的“中央电荷”的作用。这是由中央电荷管理地面纠缠缩放缩放的上限。我们在范式的紧密结合链和Kitaev链中提供数值检查。
We study the quantum information spreading in one-dimensional free-fermion systems in the presence of localized thermal baths. We employ a nonlocal Lindblad master equation to describe the system-bath interaction, in the sense that the Lindblad operators are written in terms of the Bogoliubov operators of the closed system, and hence are nonlocal in space. The statistical ensemble describing the steady state is written in terms of a convex combination of the Fermi-Dirac distributions of the baths. Due to the singularity of the free-fermion dispersion, the steady-state mutual information exhibits singularities as a function of the system parameters. While the mutual information generically satisfies an area law, at the singular points it exhibits logarithmic scaling as a function of subsystem size. By employing the Fisher-Hartwig theorem, we derive the prefactor of the logarithmic scaling, which depends on the parameters of the baths and plays the role of an effective "central charge". This is upper bounded by the central charge governing ground-state entanglement scaling. We provide numerical checks of our results in the paradigmatic tight-binding chain and the Kitaev chain.
