Effects of interference in the dynamics of a spin-1/2 transverse XY chain driven periodically through quantum critical points

We study the effects of interference on the quenching dynamics of a one-dimensional spin 1/2XY model in the presence of a transverse field (h(t)) which varies sinusoidally with time as h = h(0) cos omega t, with vertical bar t vertical bar <= t(f) = pi/omega. We have explicitly shown that the finite values of t(f) make the dynamics inherently dependent on the phases of probability amplitudes, which had been hitherto unseen in all cases of linear quenching with large initial and final times. In contrast, we also consider the situation where the magnetic field consists of an oscillatory as well as a linearly varying component, i.e., h(t) = h(0) cos omega t + t/tau, where the interference effects lose importance in the limit of large tau. Our purpose is to estimate the defect density and the local entropy density in the final state if the system is initially prepared in its ground state. For a single crossing through the quantum critical point with h = h(0) cos omega t, the density of defects in the final state is calculated by mapping the dynamics to an equivalent Landau-Zener problem by linearizing near the crossing point, and is found to vary as root omega in the limit of small omega. On the other hand, the local entropy density is found to attain a maximum as a function of omega near a characteristic scale omega(0). Extending to the situation of multiple crossings, we show that the role of finite initial and final times of quenching are manifested non-trivially in the interference effects of certain resonance modes which solely contribute to the production of defects. Kink density as well as the diagonal entropy density show oscillatory dependence on the number of full cycles of oscillation. Finally, the inclusion of a linear term in the transverse field on top of the oscillatory component results in a kink density which decreases continuously with tau while it increases monotonically with omega. The entropy density also shows monotonic change with the parameters, increasing with tau and decreasing with omega, in sharp contrast to the situations studied earlier. We also propose appropriate scaling relations for the defect density in the above situations and compare the results with the numerical results obtained by integrating the Schrodinger equations.