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arXiv · 1203.4774

Thermal entanglement between non-nearest-neighbor spins on fractal lattices

Yu-Liang Xu·Lu-Shun Wang·Xiang-Mu Kong
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Abstract

We investigate thermal entanglement between two non-nearest-neighbor sites in ferromagnetic Heisenberg chain and on fractal lattices by means of the decimation renormalization-group (RG) method. It is found that the entanglement decreases with increasing temperature and it disappears beyond a critical value T_{c}. Thermal entanglement at a certain temperature first increases with the increase of the anisotropy parameter {\Delta} and then decreases sharply to zero when {\Delta} is close to the isotropic point. We also show how the entanglement evolves as the size of the system L becomes large via the RG method. As L increases, for the spin chain and Koch curve the entanglement between two terminal spins is fragile and vanishes when L\geq17, but for two kinds of diamond-type hierarchical (DH) lattices the entanglement is rather robust and can exist even when L becomes very large. Our result indicates that the special fractal structure can affect the change of entanglement with system size.

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Yu-Liang Xu, Lu-Shun Wang, Xiang-Mu Kong. 2012-03-21. Thermal entanglement between non-nearest-neighbor spins on fractal lattices. https://doi.org/10.1103/physreva.87.012312

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