Abstract
Relaxation of few-body quantum systems can strongly depend on the initial state when the system's semiclassical phase space is mixed, i.e., regions of chaotic motion coexist with regular islands. In recent years, there has been much effort to understand the process of thermalization in strongly interacting quantum systems that often lack an obvious semiclassical limit. Time-dependent variational principle (TDVP) allows to systematically derive an effective classical (nonlinear) dynamical system by projecting unitary many-body dynamics onto a manifold of weakly-entangled variational states. We demonstrate that such dynamical systems generally possess mixed phase space. When TDVP errors are small, the mixed phase space leaves a footprint on the exact dynamics of the quantum model. For example, when the system is initialized in a state belonging to a stable periodic orbit or the surrounding regular region, it exhibits persistent many-body quantum revivals. As a proof of principle, we identify new types of "quantum many-body scars", i.e., initial states that lead to long-time oscillations in a model of interacting Rydberg atoms in one and two dimensions. Intriguingly, the initial states that give rise to most robust revivals are typically entangled states. On the other hand, even when TDVP errors are large, as in the thermalizing tilted-field Ising model, initializing the system in a regular region of phase space leads to slowdown of thermalization. Our work establishes TDVP as a method for identifying interacting quantum systems with anomalous dynamics in arbitrary dimensions. Moreover, the mixed-phase space classical variational equations allow to find slowly-thermalizing initial conditions in interacting models. Our results shed light on a link between classical and quantum chaos, pointing towards possible extensions of classical Kolmogorov-Arnold-Moser theorem to quantum systems.
Highlights
Technological advances in synthetic quantum systems [1,2] have started an era where nonequilibrium dynamics of isolated quantum matter can be experimentally probed
This approach is different from the time-dependent mean field and semiclassical treatments used in few-body quantum chaos in that it incorporates short-range entanglement
We demonstrate the relevance of mixed phase space, identified in the time-dependent variational principle (TDVP) dynamics, for the exact dynamics of quantum manybody systems
Summary
Technological advances in synthetic quantum systems [1,2] have started an era where nonequilibrium dynamics of isolated quantum matter can be experimentally probed. A mixed classical phase space leaves an imprint on quantum dynamics in interacting many-body systems, giving rise to slow, atypical thermalization for certain initial conditions. Our approach provides a potential direction to generalize the results on few-body chaos to many-body systems and for approaching the KAM theorem in quantum systems by utilizing the classical KAM for the TDVP equations of motion This approach is distinct from other approaches that rely on broken Bethe-ansatz integrability [38] or the absence of quantum resonances in the MBL phase [39,40,41]. V, we study the transverse-field Ising model (TFIM) in a longitudinal field, which is a typical example of a thermalizing system In this case, we show that mixed phase space does not give rise to many-body revivals but leads to a state-dependent thermalization rate.
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