两杂质Kondo模型中的量子纠缠
Quantum Entanglement in the Two Impurity Kondo Model
摘要：
为了量化两个杂质近藤系统中的量子纠缠，我们计算了系统的纠缠度、负纠缠度和冯诺伊曼熵.两个近藤杂质的纠缠被证明是由两个竞争的多体效应，近藤效应和Ruderman-Kittel-Kasuya-Yosida（RKKY）相互作用，$I$。由于基态的自旋-转动不变性，杂质之间的自旋-自旋关联唯一地决定了共存性和负性。发现杂质自旋之间存在一个临界的最小反铁磁关联，这是两个杂质自旋纠缠所必需的。讨论了双杂质Kondo问题的临界值与不稳定不动点的关系。具体地说，在固定点处，杂质自旋之间没有纠缠。只有当RKKY相互作用交换能$I$至少比近藤温度$T_K$大几倍时，才会产生纠缠（量子信息处理（QIP）是可能的）。根据杂质自旋-自旋关联给出了准等离子体的定量判据。
英文摘要：
In order to quantify quantum entanglement in two impurity Kondo systems, we calculate the concurrence, negativity, and von Neumann entropy. The entanglement of the two Kondo impurities is shown to be determined by two competing many-body effects, the Kondo effect and the Ruderman-Kittel-Kasuya-Yosida (RKKY) interaction, $I$. Due to the spin-rotational invariance of the ground state, the concurrence and negativity are uniquely determined by the spin-spin correlation between the impurities. It is found that there exists a critical minimum value of the antiferromagnetic correlation between the impurity spins which is necessary for entanglement of the two impurity spins. The critical value is discussed in relation with the unstable fixed point in the two impurity Kondo problem. Specifically, at the fixed point there is no entanglement between the impurity spins. Entanglement will only be created (and quantum information processing (QIP) be possible) if the RKKY interaction exchange energy, $I$, is at least several times larger than the Kondo temperature, $T_K$. Quantitative criteria for QIP are given in terms of the impurity spin-spin correlation.
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