Quantum Complexity in Rule-Based Constrained Many-Body Models: Scars, Fragmentation, and Chaos

Kinetic constraints in quantum many-body systems strongly restrict the accessible Hilbert space, giving rise to highly nontrivial dynamical behavior. In recent years, such systems have attracted growing interest as they provide insight into mechanisms of thermalization and into regimes where thermalization fails. In this work, we study a family of rule-based kinetically constrained models, including the celebrated Quantum Game of Life, from the perspective of quantum complexity, with a focus on entanglement, nonstabilizerness, and quantum chaos. Using spectral diagnostics such as level statistics and spectral form factors, we show that these models exhibit robust chaotic behavior while simultaneously supporting both strong and weak Hilbert-space fragmentation and quantum many-body scar states. To further elucidate the structure of these fragmented subspaces, we characterize them through their ability to generate quantum resources. In particular, we show that resource-generation capacity does not necessarily correlate with the dimensionality of a fragmented sector, and that entanglement structure and the ability to generate nonstabilizerness provide effective diagnostics for distinguishing dynamically disconnected sectors. Our work therefore explores kinetically constrained models in a general framework that is not restricted to Rydberg blockade-based constraints alone.