论文标题
kolmogorov的复杂性是纯状态的内在熵：自由费米恩系统中的纠缠镜头
Kolmogorov complexity as intrinsic entropy of a pure state: Perspective from entanglement in free fermion systems
论文作者
论文摘要
我们将自由费用系统视为任意维度，并将每个特征态的职业模式表示为经典的二进制字符串。我们发现字符串的Kolmogorov复杂性正确捕获了其纠缠熵（EE）的缩放行为。特别是，复制了基态的EE的对数增强区域定律和在典型高度激发状态下的EE的体积定律。由于我们的方法不需要对系统进行两分化，因此它使我们能够通过其内在复杂性直接区分典型和非典型的本征态。我们揭示了不在自由费疗法系统中热量化的非典型本征菌的比例在热力学极限下呈指数呈指数消失。我们的结果明确说明了量子系统中各个纯状态的复杂性与EE之间的联系。
We consider free fermion systems in arbitrary dimensions and represent the occupation pattern of each eigenstate as a classical binary string. We find that the Kolmogorov complexity of the string correctly captures the scaling behavior of its entanglement entropy (EE). In particular, the logarithmically-enhanced area law for EE in the ground state and the volume law for EE in typical highly excited states are reproduced. Since our approach does not require bipartitioning the system, it allows us to distinguish typical and atypical eigenstates directly by their intrinsic complexity. We reveal that the fraction of atypical eigenstates which do not thermalize in the free fermion system vanishes exponentially in the thermodynamic limit. Our results illustrate explicitly the connection between complexity and EE of individual pure states in quantum systems.
