Defect generation in a spin-12transverseXYchain under repeated quenching of the transverse field

Abstract

We study the quenching dynamics of a one-dimensional spin-1/2 XY model in a transverse field when the transverse field h(=t/τ) is quenched repeatedly between −∞ and +∞. A single passage from h→−∞ to h→+∞ 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 −∞; in the case of an odd number of half-periods, the dynamics is stopped at h→+∞. The density of defects produced due to the non-adiabatic transitions is calculated by mapping the many-particle system to an equivalent Landau-Zener problem and is generally found to vary as 1/τ−−√ for large τ; 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/τ−−√ for large τ for any number of half-periods, and shows a increase in kink density for small τ for an even number; the entropy shows qualitatively the same behavior for any number of half-periods. The probability of non-adiabatic transitions and the local entropy saturate to 1/2 and ln2, respectively, for a large number of repeated quenching.