具有非对角长程序的η对态的纠缠
Entanglement of eta-pairing state with off-diagonal long-range order
摘要：
非对角长程序（ODLRO）是一种无法用经典力学术语描述的量子现象。它被认为是超导性的一个特征。证明ODLRO的η对构成的量子态是三维哈伯德模型的本征态。纠缠是量子信息处理中的一个关键概念，没有经典的对应概念。研究了η-配对量子态的纠缠特性。量子纠缠度是衡量量子纠缠的一个重要指标。我们证明了在热力学极限下，单格点与其余格点之间的纠缠纠缠度正好是η对态ODLRO的关联函数。因此，当η对态纠缠时，它表现为ODLRO，因此处于超导相，如果它是可分态，则不存在ODLRO。在热力学极限下，m-位与η-对态其他位之间的纠缠不为零。还介绍了其他类型的eta配对状态ODLRO。我们证明了ODLRO关联函数的行为等价于η对态的纠缠行为。研究了η-配对态纠缠熵的标度性。
英文摘要：
Off-diagonal long-range order (ODLRO) is a quantum phenomenon not describable in classical mechanical terms. It is believed to be one characteristic of superconductivity. The quantum state constructed by eta-pairing which demonstrates ODLRO is an eigenstate of the three-dimensional Hubbard model. Entanglement is a key concept of the quantum information processing and has no classical counterpart. We study the entanglement property of eta-pairing quantum state. The concurrence is a well-known measure of quantum entanglement. We show that the concurrence of entanglement between one-site and the rest sites is exactly the correlation function of the ODLRO for the eta-pairing state in the thermodynamic limit. So, when the eta-pairing state is entangled, it demonstrates ODLRO and is thus in superconducting phase, if it is a separable state, there is no ODLRO. In the thermodynamic limit, the entanglement between M-site and other sites of the eta-pairing state does not vanish. Other types of ODLRO of eta-pairing state are presented. We show that the behavior of the ODLRO correlation functions is equivalent to that of the entanglement of the eta-pairing state. The scaling of the entropy of the entanglement for the eta-pairing state is studied.
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