Extension of the Adiabatic Theorem

TL;DR

This paper investigates whether the adiabatic theorem can be extended to quantum quenches in specific spin models, confirming the conjecture numerically and analytically for certain cases.

Contribution

It provides a theoretical and numerical analysis supporting a proposed extension of the adiabatic theorem to nonadiabatic quantum quenches in the TFIM and ANNNI models.

Findings

The conjecture holds for the TFIM in both phases.

Analytical proof of the conjecture for a special case in the ANNNI model.

Numerical evidence supports the conjecture beyond the special case.

Abstract

We examine the validity of a potential extension of the adiabatic theorem to quantum quenches, i.e., nonadiabatic changes. In particular, the transverse field Ising model (TFIM) and the axial next nearest neighbor 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 postquench Hamiltonian eigenstates for quenches within the same phase. This overlap is largest for the postquench 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.