The delocalization or scrambling of quantum information has emerged as a central ingredient in the understanding of thermalization in isolated quantum many-body systems. Recently, significant progress has been made analytically by modeling non-integrable systems as periodically driven or stochastic systems, while honest Hamiltonian dynamics are frequently limited to small system sizes due to computational constraints. In this talk, we address this by investigating the role of conservation laws (including energy conservation) in thermalization from an information-theoretic perspective. For general non-integrable models, we use the “equilibrium approximation” to show that the maximal amount of information is scrambled (as measured by the tripartite mutual information of the time-evolution operator) at late times even when a system conserves energy. In contrast, when a system has additional symmetries that lead to degeneracies in the spectrum, the amount of information scrambled must decrease. This general theory is exemplified in case studies of the Sachdev-Ye-Kitaev (SYK) model and the holographic conformal field theories (CFTs). In particular, contrary to common belief, the holographic CFTs — which are dual to black holes in higher dimensions — exhibit sub-maximal chaos seen by the non-saturation of the second Renyi tripartite mutual information, which we argue is due to the large Virasoro symmetry in 1+1D.
