arXiv 1404.44472014-04quant-phcond-mat.str-elphysics.atom-ph

N谐振子中的纠缠：玻色子和费米子

Entanglement in N-harmonium: bosons and fermions

C. L. Benavides-Riveros, I. V. Toranzo, J. S. Dehesa

备注：: 27 pages, 9 figures, minor changes, 4 improved figures, references added, some typos corrected
发表信息：: J. Phys. B: At. Mol. Opt. Phys. 47 (2014) 19550
DOI：: 10.1088/0953-4075/47/19/195503

摘要：

N-harmonium系统的单个粒子的基态纠缠（即，一个完全可积的模型$N$粒子的约束和两个粒子的相互作用是谐波）被证明是分析确定的$N$和相对的相互作用强度。对于玻色子，我们利用相应的自然占据数计算了其单体约化密度矩阵的冯诺伊曼熵。存在一个临界粒子数$N_c$，在此值以下，当耦合常数为正值时，纠缠随粒子数的增加而增加;而对于$N > N_c$，情况正好相反。对于费米子，我们计算了闭壳自旋情况下的单体约化密度矩阵。在强耦合区，系统的线性熵随着$N$的增长而减小。对于固定的$N$，发现纠缠（a）随着耦合常数的负（正）增加而减小（增加），（b）随着能量的增加而增加。此外，总纠缠的空间和自旋的贡献被发现是可比的大小。

英文摘要：

The ground-state entanglement of a single particle of the N-harmonium system (i.e., a completely-integrable model of $N$ particles where both the confinement and the two-particle interaction are harmonic) is shown to be analytically determined in terms of $N$ and the relative interaction strength. For bosons, we compute the von Neumann entropy of the one-body reduced density matrix by using the corresponding natural occupation numbers. There exists a critical number $N_c$ of particles so that below it, for positive values of the coupling constant, the entanglement grows when the number of particles is increasing; the opposite occurs for $N > N_c$. For fermions, we compute the one-body reduced density matrix for the closed-shell spinned case. In the strong coupling regime, the linear entropy of the system decreases when $N$ is growing. For fixed $N$, the entanglement is found (a) to decrease (increase) for negatively (positively) increasing values of the coupling constant, and (b) to grow when the energy is increasing. Moreover, the spatial and spin contributions to the total entanglement are found to be of comparable size.

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英文摘要：

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