An Extension of the Adiabatic Theorem

We examine the validity of a potential extension of the adiabatic theorem to quantum quenches, i.e., non-adiabatic changes. In particular, the Transverse Field Ising Model (TFIM) and the Axial Next Nearest Neighbour Ising (ANNNI) model are studied. The proposed extension of the adiabatic theorem is stated as follows: Consider the overlap between the initial ground state and the post-quench Hamiltonian eigenstates for quenches within the same phase. This overlap is largest for the post-quench ground state. In the case of the TFIM, this conjecture is confirmed for both the paramagnetic and ferromagnetic phases numerically and analytically. In the ANNNI model, the conjecture could be analytically proven for a special case. Numerical methods were employed to investigate the conjecture's validity beyond this special case.