visualizations/zs2.md

8 FIG. 6: Negativity N1/2,1/2 versus both the exchange interac- tion coefficient J2 and the temperature in the four-spin sys- tem. temperature T0 versus different J2 from the curve in the J2 = T plane. When J2 increases, T10 decreases, and when J2 crosses about 0.3758, N1/2,1/2 will disappear at any temperature. Next, we consider the entanglement between NNN spins. In Fig. 7, we plot the negativity N1/2,1/2 as a func- tion of the temperature and J2. We can see that, before J2 reaches the value about J2 = 0.5, N1/2,1/2 keeps being zero at any temperature. And in the region J2 > 0.5, the N1/2,1/2 can be enhanced by the increasing NNN interac- tion. This is a result from the competition of two kinds of exchange interactions. The thermal fluctuation all along suppresses the entanglement. So, from the curve lying on the J2 = T plane which corresponds to the boundary of the nonzero and zero values of N1/2,1/2, we may find that the higher the temperature is, the larger the thresh- old J20 will be. From another point of view, the T10 increases as J2 increases. In Fig. 8, we plot the negativity N1 versus T and J2. In the region of J2 < 0.25, the increasing NNN exchange interaction J2 enhances the negativity and exhibits two particular flat roofs. With the temperature rises, N1 is suppressed to zero. Also we can consider the threshold T0 and J02 from the critical curve on the J2 = T