论文标题
几何状态的纠缠光谱
Entanglement spectrum of geometric states
论文作者
论文摘要
给定子系统的降低密度矩阵（由$ρ_a$表示）包含全息理论中的子区域二元性的信息。我们可以使用本文中称为纠缠谱的矩阵谱的光谱（特征值）提取信息。我们评估了与特征义的$ρ_{a，m} $在与特征值$λ$相关的微型典型集合状态$ρ_{a，m} $中的特征状态，单点和两点相关函数的密度，包括单个示例，包括单个间隔和两个间隔的2D cfts真空状态。我们发现有一个微型典型的集合状态，具有$λ_0$，可以看作是$ρ_A$的大约状态。参数$λ_0$在两个示例中获得。对于一般的几何状态，也存在近似的微型典型集合状态。参数$λ_0$与$ a $ a $ andrényi熵的纠缠熵相关联，限制为$ n \ to \ infty $。作为上述结论的应用，我们改革了2D CFT的真空状态的纠缠熵的Araki-Lieb不平等的平等案例，作为孔隙信息的条件。我们在本征态上显示了约束。最后，我们指出了一些未解决的问题及其对理解几何状态的意义。
The reduced density matrix of a given subsystem, denoted by $ρ_A$, contains the information on subregion duality in a holographic theory. We may extract the information by using the spectrum (eigenvalue) of the matrix, called entanglement spectrum in this paper. We evaluate the density of eigenstates, one-point and two-point correlation functions in the microcanonical ensemble state $ρ_{A,m}$ associated with an eigenvalue $λ$ for some examples, including a single interval and two intervals in vacuum state of 2D CFTs. We find there exists a microcanonical ensemble state with $λ_0$ which can be seen as an approximate state of $ρ_A$. The parameter $λ_0$ is obtained in the two examples. For a general geometric state, the approximate microcanonical ensemble state also exists. The parameter $λ_0$ is associated with the entanglement entropy of $A$ and Rényi entropy in the limit $n\to \infty$. As an application of the above conclusion we reform the equality case of the Araki-Lieb inequality of the entanglement entropies of two intervals in vacuum state of 2D CFTs as conditions of Holevo information. We show the constraints on the eigenstates. Finally, we point out some unsolved problems and their significance on understanding the geometric states.
