inserted in the plot.](next_fig2.eps){width="45.00000%"}

![Negativity versus the exchange interaction $J_2$ at the temperature $T=0.02$ in eight-spin system, The ground and the first three excited energy levels versus the $J_2$ are inserted.](next_fig3.eps){width="45.00000%"}

In Fig. 9, we plot the negativity versus $J_2$ for the case of six spins at a lower temperature. The negativity ${\cal
N}_{1/2,1}$ behaves as a decreasing function of $J_2$. It decreases to zero at about $J_2=0.27$, which is the special point corresponding to the energy level crossing. On the contrary, around the point $J_2=0.27$, ${\cal N}_{1,1}$ jumps up to a nonzero value, and then increases gradually until approaching the limit about ${\cal N}_{1,1}=0.33$. This behavior is quite different from that in the four-spin model.

We also see that ${\cal N}_{1/2,1/2}$ is zero all the time. It can be understood as follows. In the six-site system there are three spin halves with the NNN interaction. Even for a pure homogeneous three-qubit system, there is no entanglement between two spins, irrespective of the strength of the exchange interactions [@M_Three]. Now, in addition to the interaction among three spin halves, there are also interaction between spin halves and spin ones. So, it is reasonable that the entanglement between two spin halves 