Damping-like effects in Heisenberg spin chain caused by the site-dependent bilinear interaction

Yu-Juan Zhang,Dun Zhao,Zai-Dong Li

Figure 1. Damping and oscillation of the spin caused by the parameter β(t). Both in (a) and (b), the black, red and blue curves on the Bloch sphere describe the spin state of the spin chain at t = 0.5, t = 1 and t = 2, respectively. In (a), β(t) = 1, it is shown that with the time increasing, the trajectory curves shrink gradually; in (b), $\beta (t)=2\sin (t)$, it is shown that with the time increasing, the trajectory curves oscillate around the direction of S1. The other parameters used are ω1 = 1, ω2 = 0, α(t) = 1, γ(t) = 0.