Defect generation in a spin-½ transverse XY chain under repeated quenching of the transverse field

Abstract

We study the quenching dynamics of a one-dimensional spin-½ 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 nonadiabatic 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 an 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 nonadiabatic transitions and the local entropy saturate to ½ and ln 2, respectively, for a large number of repeated quenching.