Symmetry restoration in a fast scrambling system

Abstract: Entanglement asymmetry -- used here as a direct probe of symmetry restoration -- provides a sharp diagnostic of post-quench dynamics. We test this idea in the complex Sachdev--Ye--Kitaev (cSYK) model with a conserved U(1) charge. Using exact diagonalization, we track the joint evolution of entanglement entropy and entanglement asymmetry after quenches from charge-asymmetric product states. We find rapid volume-law entanglement growth consistent with the subsystem eigenstate thermalization hypothesis, accompanied by a concurrent decay of entanglement asymmetry to a late-time plateau set by finite-size effects: small subsystems display near-complete restoration, while residual cross-sector weight yields a finite plateau. Notably, we uncover a quantum Mpemba effect: states prepared further from symmetry relax faster and approach lower residual asymmetry; disorder in the couplings renders this behavior more robust and monotonic across parameters. We further derive a Pinsker-type lower bound that ties the decay of asymmetry to differences in subsystem purity, identifying dephasing between U(1) charge sectors as the operative mechanism. These results establish entanglement asymmetry as a sensitive probe of symmetry restoration and thermalization, clarifying finite-size limits in fast-scrambling, closed quantum systems.