Excited-state fidelity as a signal for the many-body localization transition in a disordered Ising chain

In this work, we use exact matrix diagonalization to explore the many-body localization (MBL) transitions in quantum Ising chains with disordered nearest-neighbour couplings, disordered next-nearest-neighbour couplings and disordered external fields. It is demonstrated that the fidelity can be used to characterize the interaction-driven MBL transition in this closed spin system in a manner that is consistent with previous analytical and numerical results. We compute the fidelity for high-energy many-body eigenstates, namely, the excited-state fidelity. It is demonstrated that disordered nearest-neighbour couplings, disordered next-nearest-neighbour couplings and disordered external fields each have different effects on the MBL transition. Furthermore, we investigate the MBL transition of a quantum Ising chain with both disordered nearest-neighbour couplings and disordered next-nearest-neighbour couplings to see how these two types of disordered couplings drive the occurrence of the MBL transition.