The one-dimensional Holstein model and Holstein-Hubbard model have no nontrivial local conserved quantities other than the Hamiltonian and total fermion number.
Hokkyo, Rigorous Test for Quantum Integrability and Nonintegrabili ty, (preprint, 2025)
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In XX spin chains with open boundaries, a local quench via a single-spin impurity prevents thermalization and produces a strong violation of the eigenstate thermalization hypothesis, including its weak version.
Non-Hermitian bosonic chains with symmetric hopping can host k-local charges for selected k only, providing counterexamples to all-or-nothing integrability and showing the Grabowski-Mathieu 3-local test is not universal.
The S=1/2 XY and XYZ models on d≥2 hypercubic lattices possess no nontrivial local conserved quantities.
The quantum compass model on the square lattice possesses no nontrivial local conserved quantities besides the Hamiltonian.
citing papers explorer
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Proof of the absence of local conserved quantities in the Holstein model
The one-dimensional Holstein model and Holstein-Hubbard model have no nontrivial local conserved quantities other than the Hamiltonian and total fermion number.
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Absence of thermalization after a local quench and strong violation of the eigenstate thermalization hypothesis
In XX spin chains with open boundaries, a local quench via a single-spin impurity prevents thermalization and produces a strong violation of the eigenstate thermalization hypothesis, including its weak version.
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Violating the All-or-Nothing Picture of Local Charges in Non-Hermitian Bosonic Chains
Non-Hermitian bosonic chains with symmetric hopping can host k-local charges for selected k only, providing counterexamples to all-or-nothing integrability and showing the Grabowski-Mathieu 3-local test is not universal.
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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.