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

TL;DR

This work establishes symmetry restoration and the quantum Mpemba effect within many-body localization by combining numerical simulations of disordered and quasiperiodic models with an analytically tractable effective MBL Hamiltonian. It demonstrates that symmetry can be restored on exponentially long timescales in the MBL regime without thermalizing, and that the QME occurs universally for any tilted product initial state in MBL, in contrast to chaotic or integrable settings where state dependence arises. The analysis connects entanglement asymmetry to operator spreading and derives closed-form expressions for initial and steady-state values, revealing robust, initial-state-insensitive behavior in MBL and distinctive finite-size scaling. These results provide a unified framework for understanding symmetry-restoration dynamics in generic many-body systems and suggest measurable signatures for experiments probing MBL and non-equilibrium symmetry dynamics.

Abstract

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.

Figures (13)

• Figure 1: EA dynamics averaged over different random phases $\phi$ with $N=14$ and $N_{A}=3$, i.e., subsystem $A=[1,2,3]$. The initial states of (a)(b) and (c)(d) are TFS and TNS respectively. For TFS, QME consistently appears for all values of $W$. For TNS, QME emerges exclusively in the MBL regime. The insets of panels (b) and (d) show the EA dynamics with fixed $N_{A}=3$ and varying $N$. The QME remains robust with a nearly constant timescale as the total system sizes increase.
• Figure 2: EA dynamics in the Anderson localization phase with $V=0$ and $W=2.0$ with initial (a) TFS and (b) TNS. Here, $N=80$ and $N_{A}=10$.
• Figure 3: The Rényi-2 EA $\Delta S_A^{(2)}$ of the initial state (red) and in the long time limit (blue). System sizes $N=[32,64,128,256]$ are represented with darker colors for larger $N$, and the subsystem sizes are set to $N_{A}=N/8$ and $N/4$ for panels (a) and (b), respectively. A finite peak appears whose height remains unchanged as $N$ increases (see the Supplementary material for more discussions) indicating a finite size crossover to persistently symmetry broken phase for small $\theta\sim \frac{1}{\sqrt{N}}$.
• Figure 4: Rényi-2 EA dynamics $\Delta S_A^{(2)}(t)$ of the effective model in Eq. \ref{['eq:effective']} with $h=10.0$, $J=0.5$ and $\xi=1.0$. The system size is set to $N=14$ with subsystem size $N_{A}=3$. The initial states of (a) and (b) are TFS and TNS respectively. Solid lines denote numerical results, while dashed lines indicate the theoretical late-time predictions.
• Figure S1: Entanglement asymmetry dynamics with random potential averaged over different disorder realizations. We set $N=14$ and $N_{A}=3$. The initial state of (a) and (b) is TFS and the initial state of (c) and (d) is TNS. For TFS, the QME always occurs regardless of the choice of $W$, whereas for TNS, it appears only in the MBL regime. The insets of (b) and (d) show the EA dynamics with fixed $N_{A}=3$ and varying $N$.