Symmetry restoration and quantum Mpemba effect in many-body localization systems

Non-equilibrium dynamics of quantum many-body systems has attracted increasing attention owing to a variety of intriguing phenomena absent in equilibrium physics. A prominent example is the quantum Mpemba effect, where subsystem symmetry is restored more rapidly under a symmetric quench from a more asymmetric initial state. In this work, we investigate symmetry restoration and the quantum Mpemba effect in many-body localized systems for a range of initial states. We show that symmetry can still be restored in the many-body localization regime without approaching thermal equilibrium. Moreover, we demonstrate that the quantum Mpemba effect emerges universally for any tilted product state, in contrast to chaotic systems where its occurrence depends sensitively on the choice of the initial state. We further provide a theoretical analysis of symmetry restoration and the quantum Mpemba effect using an effective model for many-body localization. Overall, this paper fills an important gap in establishing a unified understanding of symmetry restoration and the quantum Mpemba effect in generic many-body systems, and it advances our understanding of many-body localization.