Magic Barrier before Thermalization

We investigate the time dependence of antiflatness in the entanglement spectrum, a measure for nonstabilizerness and lower bound for nonlocal quantum magic resource, on a subsystem of a linear SU(2) plaquette chain during thermalization. Tracing the time evolution of a large number of initial states, we find that the antiflatness exhibits a barrierlike maximum during the time period when the entanglement entropy of the subsystem grows rapidly from the initial value to the microcanonical entropy. The location of the peak is strongly correlated with the time when the entanglement exhibits the strongest growth. This behavior is found for generic highly excited initial computational basis states and persists for coupling constants across the ergodic regime, revealing a universal structure of the entanglement spectrum during thermalization. We conclude that quantitative simulations of thermalization for non-Abelian gauge theories require quantum computing. We speculate that this property generalizes to other quantum chaotic systems, a conjecture supported by analogous behavior observed in real-time simulations of the mixed-field Ising model.