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We study the quenching dynamics of a one-dimensional spin-1/2 $XY$ model in atransverse field when the transverse field $h(=t/\tau)$ is quenched repeatedlybetween $-\infty$ and $+\infty$. A single passage from $h \to - \infty$ to $h\to +\infty$ or the other way around is referred to as a half-period ofquenching. For an even number of half-periods, the transverse field is broughtback to the initial value of $-\infty$; in the case of an odd number ofhalf-periods, the dynamics is stopped at $h \to +\infty$. The density ofdefects produced due to the non-adiabatic transitions is calculated by mappingthe many-particle system to an equivalent Landau-Zener problem and is generallyfound to vary as $1/\sqrt{\tau}$ for large $\tau$; however, the magnitude isfound to depend on the number of half-periods of quenching. For two successivehalf-periods, the defect density is found to decrease in comparison to a singlehalf-period, suggesting the existence of a corrective mechanism in the reversepath. A similar behavior of the density of defects and the local entropy isobserved for repeated quenching. The defect density decays as $1/{\sqrt\tau}$for large $\tau$ for any number of half-periods, and shows a increase in kinkdensity for small $\tau$ for an even number; the entropy shows qualitativelythe same behavior for any number of half-periods. The probability ofnon-adiabatic transitions and the local entropy saturate to 1/2 and $\ln 2$,respectively, for a large number of repeated quenching.

Defect generation in a spin-1/2 transverse XY chain under repeated quenching of the transverse field