Defect generation in a spin-\frac{1}{2}\ transverse XY chain under repeated quenching of the transverse field

We study the quenching dynamics of a one-dimensional spin-1/2 XY model in a transverse field when the transverse field $h (= t/ \tau)$ is quenched repeatedly between $-\infty$ and $+ \infty$. A single passage from $h \rightarrow -\infty$ to $h \rightarrow +\infty$ or the other way around is referred to as a half period of quenching. For an even number of half periods, the transverse field is brought back to the initial value of $- \infty$; in the case of an odd number of half periods, the dynamics is stopped at $h \rightarrow +\infty$. The density of defects produced due to the nonadiabatic transitions is calculated by mapping the many-particle system to an equivalent Landau-Zener problem and is generally found to vary as $1/ \sqrt{\tau}$ for large \tau ; however, the magnitude is found to depend on the number of half periods of quenching. For two successive half periods, the defect density is found to decrease in comparison to a single half period, suggesting the existence of a corrective mechanism in the reverse path. A similar behavior of the density of defects and the local entropy is observed for repeated quenching. The defect density decays as $1/ \sqrt{\tau}$ for large \tau for any number of half periods, and shows an increase in kink density for small \tau for an even number; the entropy shows qualitatively the same behavior for any number of half periods. The probability of nonadiabatic transitions and the local entropy saturate to 1/2 and ln 2, respectively, for a large number of repeated quenching