Quench dynamics and defects formation in the Ising chain in a transverse magnetic field

We study quench dynamics and defects formation in the one-dimensional quantum Ising chain in a time-dependent transverse magnetic field, given by a semi-infinite pulse and as the pulse of the finite width. The system’s final state depends on the quench time and pulse amplitude, resulting in the emergence of topological defects, and consists of a mixture of ground and excited states. We obtain a new analytical expression, generalizing the Landau–Zener (LZ) and adiabatic-impulse (AI) approximation formulas for the asymptotic probability of remaining in the ground state. We show that our theoretical predictions are in good agreement with the results of the numerical simulations, even when the LZ and AI approximations fail