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PreprintarXiv licencearXiv

Proof of the absence of local conserved quantities in the Holstein model

  • Fuga Ishii
  • Mizuki Sanatani
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Abstract

Absence of local conserved quantities, or nonintegrability, is often assumed when discussing various phenomena in quantum many-body systems, such as thermalization and transport. However, no concrete proof of this property is known in electron--phonon coupled systems, a typical setting for condensed matter physics. In this paper, we show that the one-dimensional Holstein model has no nontrivial local conserved quantities other than the Hamiltonian itself and the total fermion number operator. We further show that the absence of nontrivial local conserved quantities also holds for the more general Holstein--Hubbard model. We also establish the absence of nontrivial local conserved quantities in these models on higher-dimensional hypercubic lattices. Our result has accomplished an advance in nonintegrability proofs by expanding their scope to systems in which particles with different statistical properties are mixed.

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Cite

BibTeXRIS
BibTeX
@misc{ishii2026proof,
  title = {{Proof of the absence of local conserved quantities in the Holstein model}},
  author = {Fuga Ishii and Mizuki Sanatani},
  howpublished = {arXiv},
  year = {2026},
  month = oct,
  doi = {10.48550/arxiv.2605.19606},
  eprint = {2605.19606},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2605.19606},
}
RIS
TY  - UNPB
TI  - Proof of the absence of local conserved quantities in the Holstein model
AU  - Fuga Ishii
AU  - Mizuki Sanatani
PY  - 2026
DA  - 2026/10/07
PB  - arXiv
DO  - 10.48550/arxiv.2605.19606
UR  - https://arxiv.org/abs/2605.19606
AB  - Absence of local conserved quantities, or nonintegrability, is often assumed when discussing various phenomena in quantum many-body systems, such as thermalization and transport. However, no concrete proof of this property is known in electron--phonon coupled systems, a typical setting for condensed matter physics. In this paper, we show that the one-dimensional Holstein model has no nontrivial local conserved quantities other than the Hamiltonian itself and the total fermion number operator. We further show that the absence of nontrivial local conserved quantities also holds for the more general Holstein--Hubbard model. We also establish the absence of nontrivial local conserved quantities in these models on higher-dimensional hypercubic lattices. Our result has accomplished an advance in nonintegrability proofs by expanding their scope to systems in which particles with different statistical properties are mixed.
ER  -