Entanglement of spin pairs in alternating open spin-1/2 chains with the XY Hamiltonian

We investigate entanglement of spin pairs in alternating open spin chains (s = 1/2) with spin-spin interactions (SSI) in the thermodynamic equilibrium state in an external magnetic field. The reduced density matrix of an arbitrarily chosen spin pair was calculated. The entanglement of a spin pair was evaluated with the Wootters criterion. The temperature at which the entangled state arises in the chosen pair was determined. Entanglement (concurrence) is shown to oscillate as a function of the position of a spin pair in the chain. The results demonstrate the dependence of the entanglement in arbitrarily chosen pairs of neighboring spins on the temperature, the position of the spin pair in the chain, chain length, and the ratio between the SSI constants. Qualitative explanation of these dependences is offered. The role of the terminal spins in the generation of entanglement is explained.