Graph-theoretical proof of nonintegrability in quantum many-body systems: Application to the PXP model

The Yang-Baxter method is a powerful tool for studying integrable systems, but proving whether a system possesses local conserved quantities remains challenging. Shiraishi's proof of the XYZ model's nonintegrability with a magnetic field inspired the authors' demonstration of the PXP model's nonintegrability, previously only conjectured via level statistics. As the PXP model is a key example of quantum many-body scars exhibiting exotic long-time behavior, the present work highlights that such behavior is unrelated to local conserved quantities and introduces a graph-theoretical approach, suggesting universality in nonintegrability proofs.