Effects of impurity on the entanglement of the three-qubit Heisenberg XXX spin chain

We investigate the entanglement of the three-qubit Heisenberg XXX chain in the presence of impurity and obtain the analytical expressions of the concurrence C. It is found that for impurity entanglement, C appears only when J1 > J for J > 0, and J1 > 0 for J < 0, and in these two regions C increases with the increase of J1, so is the critical temperature Tc. When J1 ≫ | J |, C reaches its maximum value 0.5 and Tc reaches the asymptotic value Tc = 3.41448J1. For entanglement between the normal lattices, C appears only when J > 0 and −2J < J1 < J, and initially increases with the increase of J1 and arrives at the maximum value Cmax = (e4J/T −3)/(e4J/T + 3) before it decays to zero gradually, so is the critical temperature Tc with, however, the maximum value Tcmax = 4J/In3.