The one-dimensional Holstein model and Holstein-Hubbard model have no nontrivial local conserved quantities other than the Hamiltonian and total fermion number.
Futami, Absence of nontrivial local conserved quan- tities in the hubbard model on the two or higher di- mensional hypercubic lattice (2025), arXiv:2507.20106 [cond-mat.stat-mech]
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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.
Asymptotic quantum many-body scars in SU(N) Hubbard chains are realized explicitly as gapless magnons of an embedded SU(N) ferromagnetic Heisenberg parent 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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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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Construction of asymptotic quantum many-body scar states in the SU($N$) Hubbard model
Asymptotic quantum many-body scars in SU(N) Hubbard chains are realized explicitly as gapless magnons of an embedded SU(N) ferromagnetic Heisenberg parent Hamiltonian.