论文标题
二维形成式场理论中的普遍纠缠和相关度量
Universal entanglement and correlation measure in two-dimensional conformal field theories
论文作者
论文摘要
我们根据基于可计算的交叉标准（CCNR）标准的纠缠度量$ \ MATHCAL {E} $量化的纠缠量（CFT）的基础状态，以两个间隔分别计算出两次间隔的纠缠量。与负面信息或互信息不同，我们表明$ \ Mathcal {e} $即使对于两个不相交的间隔，它也仅取决于几何，中央电荷C和CFT的热分区函数。我们在复制方法中证明了这种通用表达式，其中用于计算$ \ MATHCAL {e} $的Riemann表面在每个顺序n始终是拓扑的。通过分析延续，n = 1/2的结果给出了$ \ Mathcal {e} $的值。此外，n的其他值的结果还得出有意义的结论：n = 1的结果给出了两间隔纯度的一般公式，这使我们能够为n <= 4个间隔计算renyi-2 n-partite信息；而$ n = \ infty $结果限制了两个间隔的相关函数。我们在Spin-1/2 XXZ链中进行数值验证我们的发现，其基态由Luttinger液体描述。
We calculate the amount of entanglement shared by two intervals in the ground state of a (1+1)-dimensional conformal field theory (CFT), quantified by an entanglement measure $\mathcal{E}$ based on the computable cross norm (CCNR) criterion. Unlike negativity or mutual information, we show that $\mathcal{E}$ has a universal expression even for two disjoint intervals, which depends only on the geometry, the central charge c, and the thermal partition function of the CFT. We prove this universal expression in the replica approach, where the Riemann surface for calculating $\mathcal{E}$ at each order n is always a torus topologically. By analytic continuation, result of n=1/2 gives the value of $\mathcal{E}$. Furthermore, the results of other values of n also yield meaningful conclusions: The n=1 result gives a general formula for the two-interval purity, which enables us to calculate the Renyi-2 N-partite information for N<=4 intervals; while the $n=\infty$ result bounds the correlation function of the two intervals. We verify our findings numerically in the spin-1/2 XXZ chain, whose ground state is described by the Luttinger liquid.
