论文标题
全球淬火后三方信息中的普遍性
Universality in the tripartite information after global quenches
论文作者
论文摘要
我们认为宏观上的大型3部分$（a，b，c）$连接的子系统$ a \ cup b \ cup b \ cup c $ in Infinite量子旋转链中并研究了rényi-$α$α$ tripartite信息$ i_3^^{（α）}（α）}（a，b，c）$。在干净的1D系统中，与当地的哈密顿量的平衡通常消失。共形关键系统的基础状态是一个值得注意的例外，其中$ i_3^{（α）}（a，b，c）$ $是交叉比率$ x = | a | a | a | a | a | |/[（| a |+| b |）的通用函数（| c |+| b | b | b |）]我们确定了不同类别的状态，这些状态在随时间演化下，通过翻译不变的汉密尔顿人在本地放松，以非零（rényi）三方信息，此外，该信息还表现出对$ x $的普遍依赖性。我们报告了$ i_3^{（α）} $的数值研究，该系统是双重释放费米子，提出现场理论描述，并在系统子类中以$α= 2 $的渐近行为进行渐近行为。这使我们可以在缩放限制$ x \ rightarrow 1^ - $中推断$ i_3^{（α）} $的值，我们称``剩余的三方信息''。如果非零，我们的分析指出了独立于rényi索引$α$的通用残差$ - \ log 2 $，因此也适用于真实的（von Neumann）三方信息。
We consider macroscopically large 3-partitions $(A,B,C)$ of connected subsystems $A\cup B \cup C$ in infinite quantum spin chains and study the Rényi-$α$ tripartite information $I_3^{(α)}(A,B,C)$. At equilibrium in clean 1D systems with local Hamiltonians it generally vanishes. A notable exception is the ground state of conformal critical systems, in which $I_3^{(α)}(A,B,C)$ is known to be a universal function of the cross ratio $x=|A||C|/[(|A|+|B|)(|C|+|B|)]$, where $|A|$ denotes $A$'s length. We identify different classes of states that, under time evolution with translationally invariant Hamiltonians, locally relax to states with a nonzero (Rényi) tripartite information, which furthermore exhibits a universal dependency on $x$. We report a numerical study of $I_3^{(α)}$ in systems that are dual to free fermions, propose a field-theory description, and work out their asymptotic behaviour for $α=2$ in general and for generic $α$ in a subclass of systems. This allows us to infer the value of $I_3^{(α)}$ in the scaling limit $x\rightarrow 1^-$, which we call ``residual tripartite information''. If nonzero, our analysis points to a universal residual value $-\log 2$ independently of the Rényi index $α$, and hence applies also to the genuine (von Neumann) tripartite information.
