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arXiv 1507.07384quant-ph
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自旋为1/2的XX链中的磁纠缠

Magnetic Entanglement in Spin-1/2 XX Chains

Fatemeh Khastehdel Fumani, Somayyeh Nemati, Saeed Mahdavifar, Amirhosein Darooneh

摘要:

在研究自旋链中的纠缠时,人们经常考虑最近邻自旋。其动机是短程相互作用在第一近邻(1 N)自旋之间产生量子关联中的主导作用。在这里,我们解决了更远的邻居自旋之间的相同问题。我们考虑了磁场中一维自旋1/2 XY模型。利用费米子化方法,我们对角化系统的哈密顿量。然后,我们提供了第二,第三和第四邻居(分别表示为2N,3 N和4 N)自旋之间的纠缠的分析结果。我们发现了一个磁纠缠,从一个临界纠缠场($h_c^{E}$)在零温度。临界纠缠场取决于自旋之间的距离。除了分析结果,所提到的现象证实了数值Lanczos计算。通过将温度添加到模型中,磁纠缠在达到临界温度$T_c$之前保持稳定。我们的结果表明,纠缠通过降低温度逐步扩展到自旋链中更远的邻居。首先,1 N个自旋纠缠,然后进一步的邻居将分别纠缠。$T_c$取决于磁场的值,并且将在量子临界场处最大化。

英文摘要:

In the study of entanglement in a spin chain, people often consider the nearest-neighbor spins. The motivation is the prevailing role of the short range interactions in creating quantum correlation between the 1st neighbor (1N) spins. Here, we address the same question between farther neighbor spins. We consider the one-dimensional (1D) spin-1/2 XY model in a magnetic field. Using the fermionization approach, we diagonalize the Hamiltonian of the system. Then, we provide the analytical results for entanglement between the 2nd, 3rd and 4th neighbor (denoted as 2N, 3N, and 4N respectively) spins. We find a magnetic entanglement that starts from a critical entangled-field ($h_c^{E}$) at zero temperature. The critical entangled-field depends on the distance between the spins. In addition to the analytical results, the mentioned phenomenon is confirmed by the numerical Lanczos calculations. By adding the temperature to the model, the magnetic entanglement remains stable up to a critical temperature, $T_c$. Our results show that entanglement spreads step by step to farther neighbors in the spin chain by reducing temperature. At first, the 1N spins are entangled and then further neighbors will be entangled respectively. $T_c$ depends on the value of the magnetic field and will be maximized at the quantum critical field.

机构、总结、中文摘要均由AI分析而来,可能存在错误,请以论文正文为准。

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