Exact strong zero modes arise generically in integrable anisotropic spin models from quasi-periodicity of R-matrices and tracelessness of K-matrices, unifying known cases and predicting new ones.
Remarks on the notion of quantum integrability
5 Pith papers cite this work. Polarity classification is still indexing.
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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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Long-range deformations of homogeneous Yang-Baxter integrable spin chains are generated by a twist of the quantum group that produces a non-associative algebra whose Drinfeld associator encodes the long-range terms up to first order.
The S=1/2 XY and XYZ models on d≥2 hypercubic lattices possess no nontrivial local conserved quantities.
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.
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The $S=\frac{1}{2}$ XY and XYZ models on the two or higher dimensional hypercubic lattice do not possess nontrivial local conserved quantities
The S=1/2 XY and XYZ models on d≥2 hypercubic lattices possess no nontrivial local conserved quantities.
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Absence of nontrivial local conserved quantities in the quantum compass model on the square lattice
The quantum compass model on the square lattice possesses no nontrivial local conserved quantities besides the Hamiltonian.