Study On Thermal Entanglement Of Spin Systems On The Koch Curves

As a foundation of quantum communication and quantum computation, quantumentanglement plays an important role on the study of Condensed Matter Physics. Because ofadvantages of abundant entanglement features and convenient integration, quantumentanglement has received widely attention. In this article, we take use of real-spacerenormalization-group (RG) method and combine the concept of Negativity to study theentanglement in one-dimensional ferromagnetic spin chains and Koch curves that have fractalstructure. Our main results are as follows:We studied the end entanglement in spin-1/2ferromagnetic anisotropic Heisenberg chainsversus temperature, anisotropic parameter and system scale. Results indicate that theentanglement decreases monotonously as temperature increases, and the entanglement vanishescompletely when temperature beyond critical temperature. In some certain region, entanglementcan be enhanced by adjusting anisotropic parameter, but it jumps down to zero fast when theanisotropic parameter close to the isotropic point (Δ=0), system undergoes quantum transition.As system scale increases, entanglement in two non-neighbor end sites decreases to zero quickly.According to our results, end site entanglement becomes zero when number of sites exceedsnine.Entanglement in two kinds of Koch curves whose fractal dimension are1.26and1.46respectively is also investigated. It is found that end sites entanglement in both systems decreasesas temperature increases and vanishes when temperature exceeds the critical temperature. Theentanglement can be also effected by system scale, for non-branched Koch curves case,entanglement vanishes when number of sites exceeds17, while for branched Koch curves case,entanglement vanishes only when number of sites exceeds20. Entanglement in these twosystems has two differences: firstly, the critical temperature in branched Koch curves is higherthan the critical temperature in non-branched Koch curves. Secondly, end-to-end entanglement innon-branched Koch curves is not existed even though anisotropic interaction is weak, while theentanglement in branched Koch curves strongly against anisotropic interaction. But at theisotropic point (Δ=0), quantum phase transition occurs in both systems, the entanglement jumpdown to zero at the isotropic point.