Institut für Theoretische Physik, Universität Duisburg-Essen, D-47048, Duisburg, Germany.
Sci Rep. 2017 Jun 16;7(1):3634. doi: 10.1038/s41598-017-03402-8.
We study the ground-state entanglement in the quantum Ising model with nearest neighbor ferromagnetic coupling J and find a sequential increase of entanglement depth d with growing J. This entanglement avalanche starts with two-point entanglement, as measured by the concurrence, and continues via the three-tangle and four-tangle, until finally, deep in the ferromagnetic phase for J = ∞, arriving at a pure L-partite (GHZ type) entanglement of all L spins. Comparison with the two, three, and four-point correlations reveals a similar sequence and shows strong ties to the above entanglement measures for small J. However, we also find a partial inversion of the hierarchy, where the four-point correlation exceeds the three- and two-point correlations, well before the critical point is reached. Qualitatively similar behavior is also found for the Bose-Hubbard model, suggesting that this is a general feature of a quantum phase transition. This should be taken into account in the approximations starting from a mean-field limit.
我们研究了具有最近邻铁磁耦合 J 的量子伊辛模型中的基态纠缠，并发现随着 J 的增加，纠缠深度 d 呈顺序增加。这种纠缠雪崩从两点纠缠开始，由关联函数测量，然后通过三纠缠和四纠缠继续，直到最终，在 J=∞的铁磁相中，所有 L 个自旋达到纯 L 部分（GHZ 类型）纠缠。与两点、三点和四点相关的比较显示出类似的顺序，并与小 J 时的上述纠缠测量值有很强的联系。然而，我们也发现了层次结构的部分倒置，其中四点相关超过了三点和两点相关，远在临界点之前。玻色-哈伯德模型也表现出类似的定性行为，表明这是量子相变的一个普遍特征。在从平均场极限开始的近似中应该考虑到这一点。
