Momentum-space analysis of multipartite entanglement at quantum phase transitions
Momentum-space analysis of multipartite entanglement at quantum phase transitions
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DOI：
10.1103/physrevb.78.144519
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发表时间：
2008-06
影响因子：
3.7
通讯作者：
A. Anfossi;P. Giorda;A. Montorsi
中科院分区：
文献类型：
--
作者：
A. Anfossi;P. Giorda;A. Montorsi
我们研究了动量空间表示中可积扩展哈伯德模型的量子相变的纠缠性质。识别了两个基本子系统：电子的单模和模对（通过 eta 配对机制耦合的电子）。我们首先通过冯诺依曼熵和量子互信息的奇点的比较研究来检测每个量子相变的二元/多元性质。我们建立了动量表示中的相关性与互补图中显示的相关性之间的现有关系：直接晶格表示。然后通过 Q 测量（即 Meyer-Wallach 纠缠测量的推广）详细研究多部分纠缠的存在。这种测量对多部分性质的相关性变得越来越敏感，增加了约化密度矩阵的大小。在动量空间中，我们成功地为我们的系统获得了任意大小的后者，并将其行为与各种 QPT 的性质联系起来。
We investigate entanglement properties at quantum phase transitions of an integrable extended Hubbard model in the momentum space representation. Two elementary subsystems are recognized: the single mode of an electron, and the pair of modes (electrons coupled through the eta-pairing mechanism). We first detect the two/multi-partite nature of each quantum phase transition by a comparative study of the singularities of Von Neumann entropy and quantum mutual information. We establish the existing relations between the correlations in the momentum representation and those exhibited in the complementary picture: the direct lattice representation. The presence of multipartite entanglement is then investigated in detail through the Q-measure, namely a generalization of the Meyer-Wallach measure of entanglement. Such a measure becomes increasingly sensitive to correlations of a multipartite nature increasing the size of the reduced density matrix. In momentum space, we succeed in obtaining the latter for our system at arbitrary size and we relate its behaviour to the nature of the various QPTs.