Slow quantum thermalization and many-body revivals from mixed phase space

Describing the way strongly interacting quantum systems approach thermal equilibrium remains an important open problem. Recent works discovered systems in which thermalization rates may depend very sensitively on the initial conditions, via a mechanism reminiscent of quantum scars in chaotic billiards. While strongly interacting systems do not always have an obvious quasiclassical limit, time-dependent variational principle (TDVP) allows one to project the unitary dynamics onto the matrix-product state manifold, resulting in a classical nonlinear dynamical system. We show that such dynamical systems exhibit a mixed phase space which includes both regular and chaotic regions. Provided TDVP errors are small, the mixed phase space leaves a footprint on the exact dynamics of the quantum model: when the system is initialized in a state situated on the stable periodic orbit, it exhibits robust many-body revivals. Intriguingly, the initial state giving rise to strongest revivals may be entangled. Surprisingly, even when TDVP errors are large, as in the thermalizing Ising model with transverse and longitudinal fields, initializing the system in the regular region of phase space leads to a slowdown of thermalization. Our work establishes TDVP as a method for identifying interacting quantum systems with anomalous dynamics. Mixed-phase space classical variational equations allow one to find slowly-thermalizing initial conditions in interacting models. These results provide an intriguing connection between classical and quantum chaos, pointing towards possible extensions of classical KAM theorem to quantum systems.