Proof of absence of local conserved quantities in two- and higher-dimensional quantum Ising models

Local conserved quantities are key to understanding macroscopic phenomena, and their absence indicates quantum nonintegrability. Here, the author rigorously proves that quantum Ising models on two- and higher-dimensional lattices possess no local conserved quantities. The proof holds for arbitrary parameter values, thereby theoretically confirming that there are no integrable systems other than the trivial case. Their result establishes this widely studied model as a definitive example of a nonintegrable quantum many-body system.