1301.0122 (Gehad Sadiek et al.)

Persistence of entanglement in thermal states of spin systems    [PDF]

Gehad Sadiek, Sabre Kais

We study and compare the persistence of bipartite and multipartite entanglement in one and two-dimensional spin XY model in an external transverse magnetic field under the effect of thermal excitations. We compare the threshold temperature at which the entanglement vanishes in both cases. We use the concurrence as a measure of the bipartite entanglement and the geometric measure to evaluate the multipartite entanglement of the system. We have found that for the anisotropic and partially anisotropic systems the nearest neighbor bipartite entanglement vanishes asymptotically at much higher magnetic field compared to both the next to nearest neighbor bipartite entanglement and the multipartite entanglement which asymptotically coincide. Also the same behavior was observed for the threshold temperatures where the nearest neighbor bipartite one is much higher than both of the next to nearest neighbor bipartite and multipartite where the latter two coincide asymptotically and the three of them increase monotonically with the magnetic field strength. Thus as the temperature increases to certain value, the threshold, the multipartite entanglement and the bipartite entanglement of the far parts of the system may vanish while the nearest neighbor bipartite entanglement may sustain up to much higher temperature. For the isotropic system, all types of entanglement and threshold temperatures vanish at the same exact small value of the magnetic field. We emphasis the major role played by both the properties of the ground state of the system and the energy gap as well. Furthermore, we found that the quantum effects in the system can be maintained at high temperatures, where we have observed that the different types of entanglements in the lattice sustain at high temperatures if we apply sufficiently high magnetic fields.

View original: http://arxiv.org/abs/1301.0122