Quantum State Randomization in the Presence of Non-Abelian Symmetries

Initially unentangled states evolving under generic quantum chaotic dynamics typically evolve into featureless states at late times. In a recent work, we showed that even in the presence of conservation laws—so that states do not explore the entire Hilbert space—quantum states at late times can nevertheless exhibit the same statistical behavior as Haar-random states at the level of finite statistical moments. This holds as long as the initial state spreads uniformly over the eigenbasis of the symmetry operator and the conserved quantities commute. In this talk, I will extend our previous results to systems with non-Abelian symmetries, showing that these symmetries strongly constrain the exploration of Hilbert space and thereby limit the amount of entanglement that can be generated.