Entanglement and boundary critical phenomena
Entanglement and boundary critical phenomena
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DOI：
10.1103/physreva.74.050305
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发表时间：
2005-11
影响因子：
2.9
通讯作者：
Huan-Qiang Zhou;T. Barthel;J. O. Fjaerestad;U. Schollwoeck
中科院分区：
文献类型：
--
作者：
Huan-Qiang Zhou;T. Barthel;J. O. Fjaerestad;U. Schollwoeck
我们从量子信息的角度研究边界临界现象。利用Renyi熵S-α量化了一维量子系统基态中的二体纠缠，其中包括von Neumann熵(α-gt；1)和单拷贝纠缠(α-gt；无穷)作为特例。我们确定了边界对Renyi熵的贡献，并证明了沿边界重整化群(RG)流存在纠缠损失。这一性质与Affleck-Ludwig定理密切相关，它是沿边界RG流的约化密度矩阵的谱之间的优超关系的结果。我们还指出，对单拷贝纠缠的整体贡献是冯诺依曼熵的一半，而边界贡献是相同的。
We investigate boundary critical phenomena from a quantum-information perspective. Bipartite entanglement in the ground state of one-dimensional quantum systems is quantified using the Renyi entropy S-alpha, which includes the von Neumann entropy (alpha -> 1) and the single-copy entanglement (alpha ->infinity) as special cases. We identify the contribution of the boundaries to the Renyi entropy, and show that there is an entanglement loss along boundary renormalization group (RG) flows. This property, which is intimately related to the Affleck-Ludwig g theorem, is a consequence of majorization relations between the spectra of the reduced density matrix along the boundary RG flows. We also point out that the bulk contribution to the single-copy entanglement is half of that to the von Neumann entropy, whereas the boundary contribution is the same.