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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Hybrid Lanczos and MPS methods with classical Ehrenfest phonons provide numerical evidence that electron-phonon coupling delocalizes strongly disordered systems and destabilizes finite-size many-body localization.
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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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Hybrid quantum-classical matrix-product state and Lanczos methods for electron-phonon systems with strong electronic correlations: Application to disordered systems coupled to Einstein phonons
Hybrid Lanczos and MPS methods with classical Ehrenfest phonons provide numerical evidence that electron-phonon coupling delocalizes strongly disordered systems and destabilizes finite-size many-body localization.