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Relaxation of few-body quantum systems can strongly depend on the initialstate when the system's semiclassical phase space is mixed, i.e., regions ofchaotic motion coexist with regular islands. In recent years, there has beenmuch effort to understand the process of thermalization in strongly interactingquantum systems that often lack an obvious semiclassical limit. Time-dependentvariational principle (TDVP) allows to systematically derive an effectiveclassical (nonlinear) dynamical system by projecting unitary many-body dynamicsonto a manifold of weakly-entangled variational states. We demonstrate thatsuch dynamical systems generally possess mixed phase space. When TDVP errorsare small, the mixed phase space leaves a footprint on the exact dynamics ofthe quantum model. For example, when the system is initialized in a statebelonging to a stable periodic orbit or the surrounding regular region, itexhibits persistent many-body quantum revivals. As a proof of principle, weidentify new types of "quantum many-body scars", i.e., initial states that leadto long-time oscillations in a model of interacting Rydberg atoms in one andtwo dimensions. Intriguingly, the initial states that give rise to most robustrevivals are typically entangled states. On the other hand, even when TDVPerrors are large, as in the thermalizing tilted-field Ising model, initializingthe system in a regular region of phase space leads to slowdown ofthermalization. Our work establishes TDVP as a method for identifyinginteracting quantum systems with anomalous dynamics in arbitrary dimensions.Moreover, the mixed-phase space classical variational equations allow to findslowly-thermalizing initial conditions in interacting models. Our results shedlight on a link between classical and quantum chaos, pointing towards possibleextensions of classical Kolmogorov-Arnold-Moser theorem to quantum systems.

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