English

Asymptotic Localization in the Bose-Hubbard Model

Mathematical Physics 2016-12-15 v1 Statistical Mechanics math.MP

Abstract

We consider the Bose-Hubbard model. Our focus is on many-body localization, which was described by many authors in such models, even in the absence of disorder. Since our work is rigorous, and since we believe that the localization in this type of models is not strictly valid in the infinite-time limit, we necessarily restrict our study to 'asymptotic localization': We prove that transport and thermalization are small beyond perturbation theory in the limit of large particle density. Our theorem takes the form of a many-body Nekhoroshev estimate. An interesting and new aspect of this model is the following: even though our analysis proceeds by perturbation in the hopping, the localization can not be inferred from a lack of hybridization between zero-hopping eigenstates.

Keywords

Cite

@article{arxiv.1612.04731,
  title  = {Asymptotic Localization in the Bose-Hubbard Model},
  author = {Alex Bols and Wojciech De Roeck},
  journal= {arXiv preprint arXiv:1612.04731},
  year   = {2016}
}

Comments

27 pages, 1 figure. The proofs in section 5.3 are almost identical to the analogous proofs in arXiv:1305.5127

R2 v1 2026-06-22T17:23:48.563Z