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

The nonequilibrium dynamics of quantum many-body systems have attracted growing attention due to various intriguing phenomena absent in equilibrium physics. One famous example is the quantum Mpemba effect, where the subsystem symmetry is restored faster under a symmetric quench from a more asymmetric initial state. In this work, we investigate symmetry restoration and quantum Mpemba effect in many-body localized systems with various initial states. We reveal that the symmetry can still be fully restored in many-body localization phases without approaching thermal equilibrium. Furthermore, we demonstrate that the presence of the quantum Mpemba effect is universal for any initial tilted product state, contrasting to the cases in the chaotic systems where the presence of the quantum Mpemba effect relies on the choice of initial states. We also provide a theoretical analysis of symmetry restoration and quantum Mpemba effects with the help of the effective model for many-body localization. This work not only fills the missing gap of the unified understanding of symmetry restoration and quantum Mpemba effect in generic many-body systems but also contributes to a deeper understanding of the many-body localization.