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

Yu-Liang Xu, Lu-Shun Wang, Xiang-Mu Kong
2013 Physical Review A. Atomic, Molecular, and Optical Physics  
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 Δ and then decreases sharply to zero when Δ is close to the isotropic point.
more » ... e 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≥17, 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.
doi:10.1103/physreva.87.012312 fatcat:midgrnb5w5cxfjhvotc2utodny