The S=1/2 XY and XYZ models on d≥2 hypercubic lattices possess no nontrivial local conserved quantities.
Remarks on the notion of quantum integrability
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abstract
We discuss the notion of integrability in quantum mechanics. Starting from a review of some definitions commonly used in the literature, we propose a different set of criteria, leading to a classification of models in terms of different integrability classes. We end by highlighting some of the expected physical properties associated to models fulfilling the proposed criteria.
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Absence of simple slow operators implies that typical low-complexity states thermalize in quantum systems.
The quantum compass model on the square lattice possesses no nontrivial local conserved quantities besides the Hamiltonian.