Energy level dynamics across the many-body localization transition

Abstract

The level dynamics across the many body localization transition is examined for XXZ-spin model with a random magnetic field. We compare different scenaria 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 exists 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.

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References in corpus (14)

• Localization of interacting fermions at high temperature
• Many-body localization edge in the random-field Heisenberg chain
• The distribution of the ratio of consecutive level spacings in random matrix ensembles
• Phenomenology of fully many-body-localized systems
• Fidelity, dynamic structure factor, and susceptibility in critical phenomena
• Quantum critical scaling of the geometric tensors
• Ergodicity breaking in a model showing many-body localization
• Mixed-state fidelity and quantum criticality at finite temperature
• Optimal quantum estimation in spin systems at criticality
• Quantum Monte Carlo simulations of fidelity at magnetic quantum phase transitions
• Extended nonergodic states in disordered many-body quantum systems
• Fidelity approach to quantum phase transitions: finite size scaling for quantum Ising model in a transverse field
• Finite temperature fidelity susceptibility for one-dimensional quantum systems
• Many-Body-Localization Transition : sensitivity to twisted boundary conditions

Cited by in corpus (2)

• Exact many-body scars and their stability in constrained quantum chains
• Robustness and Independence of the Eigenstates with respect to the Boundary Conditions across a Delocalization-Localization Phase Transition