The level dynamics across the many-body localization transition is examined for XXZ spin model with a random magnetic field. We compare different scenarios of parameter-dependent motion in the system and consider measures such as level velocities, curvatures, as well as their fidelity susceptibilities. Studying the ergodic phase of the model we find that the level dynamics does not reveal the commonly believed universal behavior after rescaling the curvatures by the level velocity variance. At the same time, distributions of level curvatures and fidelity susceptibilities coincide with properly rescaled distributions for Gaussian orthogonal ensemble of random matrices. Profound differences exist depending on way the level dynamics is imposed in the many-body localized phase of the model in which the level dynamics can be understood with the help of local integrals of motion.

• Received 14 April 2019
• Revised 26 May 2019

DOI:https://doi.org/10.1103/PhysRevB.99.224202