Quenching dynamics of a quantum XY spin-1/2 chain in the presence of transverse field by the application of a generalized Landau-Zener formula

In this paper we review the quenching dynamics of a quantum XY spin-1/2 chain in the presence of a transverse field, when the transverse field or the anisotropic interaction is quenched at a slow but uniform rate. We also extend the results to the cases in which the system starts with any arbitrary initial condition as opposed to the initial fully magnetically aligned state which has been extensively studied earlier. The evolution is non-adiabatic in the time interval when the parameters are close to their critical values, and is adiabatic otherwise. The density of defects produced due to nonadiabatic transitions is calculated by mapping the many-particle system to an equivalent Landau-Zener problem. We show that in one dimension the density of defects in the final state scales as 1/√τ irrespective of the initial condition, where τ is the quenching time-scale. However, the magnitude of density of defects is found to depend on the initial condition.