is zero.

The negativity versus $J_2$ in the eight-site case is shown in Fig. 10. After the first sharp jump to a value (not zero) at about $J_2=0.25$, ${\cal N}_{1/2,1}$ goes down to zero gradually. At approximately $J_2=0.55$, the negativity is zero. On the contrary, the negativity ${\cal N}_{1,1}$ jumps up at about $J_2=0.25$, and then goes up gradually and almost linearly until $J_2$ reaches about $0.55$. Then there happens a sharp decrease to nearly zero, and after that it begins to increase gradually. The negativity ${\cal N}_{1/2,1/2}$ keeps zero until $J_2$ reaches about $0.67$, and then it goes up until reaches a steady value.

In Fig. 10, we find that the three kinds of negativity exhibit different properties. From figure inserted, i.e., the energy levels of the eight-spin system, we can see that in the region from about $J_2=0.55$ to $J_2=0.67$ the first excited energy is quite close to the ground energy. It is known that the energy level crossing can greatly affect the entanglement. Here, the two close energy levels also play an important role in the behavior of entanglement. The approximate degenerate energy levels may remarkably change the probability distribution even at a very low temperature, thereby 