Critical and noncritical long-range entanglement in Klein-Gordon fields
Critical and noncritical long-range entanglement in Klein-Gordon fields
复制标题
DOI：
10.1103/physreva.80.012325
复制
发表时间：
2008-11
影响因子：
2.9
通讯作者：
S. Marcovitch;A. Retzker;M. Plenio;B. Reznik
中科院分区：
文献类型：
--
作者：
S. Marcovitch;A. Retzker;M. Plenio;B. Reznik
通过在线性谐振链连续极限下的显式计算，研究了一维自由Klein-Gordon场真空态中两个空间分离区间之间的纠缠.我们证明了纠缠，我们量化的对数负，是有限的，没有进一步的重整化需要。我们发现，在临界区，量子关联是标度不变的，因为它们只依赖于距离与长度的比值。它们的衰减速度比经典关联快得多，因为在临界极限下，长程纠缠在大于块大小的间隔下呈指数衰减，而经典关联遵循幂律衰减。随着块体间距离的减小，纠缠度在距离上呈幂律发散。非临界状态表现出更丰富的行为，因为纠缠既取决于块的大小，也取决于它们的分离。与冯诺依曼熵相对应，长程纠缠也区分了临界系统和非临界系统。
We investigate the entanglement between two spatially separated intervals in the vacuum state of a free one-dimensional Klein-Gordon field by means of explicit computations in the continuum limit of the linear harmonic chain. We demonstrate that the entanglement, which we quantify by the logarithmic negativity, is finite with no further need for renormalization. We find that in the critical regime, the quantum correlations are scale invariant as they depend only on the ratio of distance to length. They decay much faster than the classical correlations as in the critical limit long-range entanglement decays exponentially for separations larger than the size of the blocks, while classical correlations follow a power-law decay. With decreasing distance of the blocks, the entanglement diverges as a power law in the distance. The noncritical regime manifests richer behavior, as the entanglement depends both on the size of the blocks and on their separation. In correspondence with the von Neumann entropy also long-range entanglement distinguishes critical from noncritical systems.