论文标题
长期相互作用的费米昂模型中的纠缠分布
Entanglement distribution in fermion model with long-range interaction
论文作者
论文摘要
如何在多体系统中分布两方纠缠（TPE）？这是一个基本问题，因为一方与其他各方之间的总TPE，$ \ Mathcal {c}^n $，是由科夫曼，昆杜和wootter和wootters（ckw）单智能不平等的上限，从中，$ \ mathcal {c}^n \ le \ le \ sqrt可以证明$ \ sqrt {n-1-1} $ coveential geection fy geection。 Here we explore the total entanglement $\mathcal{C}^\infty$ and the associated total tangle $τ^\infty$ in a $p$-wave free fermion model with long-range interaction, showing that $\mathcal{C}^\infty \sim \mathcal{O}(1)$ and $τ^\infty$ may become vanishing small with the increasing of远程相互作用。但是，我们总是找到$ \ Mathcal {C}^\ infty \ sim2ξτ^\ infty $，其中$ξ$是纠缠的截断长度，除此之外，tpe很快就消失了，因此$τ^\ infty \ sim 1/ξ$。 这种关系是由远程相互作用引起的TPE的指数衰减的直接结果。这些结果统一了Lipkin-Meshkov-Glick（LMG）模型和DICKE模型中的结果，并概括了Koashi，Buzek和Imono绑定到量子多体模型，具有更广泛的适用性。
How two-party entanglement (TPE) is distributed in the many-body systems? This is a fundamental issue because the total TPE between one party with all the other parties, $\mathcal{C}^N$, is upper bounded by the Coffman, Kundu and Wootters (CKW) monogamy inequality, from which $\mathcal{C}^N \le \sqrt{N-1}$ can be proved by the geometric inequality. Here we explore the total entanglement $\mathcal{C}^\infty$ and the associated total tangle $τ^\infty$ in a $p$-wave free fermion model with long-range interaction, showing that $\mathcal{C}^\infty \sim \mathcal{O}(1)$ and $τ^\infty$ may become vanishing small with the increasing of long-range interaction. However, we always find $\mathcal{C}^\infty \sim 2ξτ^\infty$, where $ξ$ is the truncation length of entanglement, beyond which the TPE is quickly vanished, hence $τ^\infty \sim 1/ξ$. This relation is a direct consequence of the exponential decay of the TPE induced by the long-range interaction. These results unify the results in the Lipkin-Meshkov-Glick (LMG) model and Dicke model and generalize the Koashi, Buzek and Imono bound to the quantum many-body models, with much broader applicability.
