Ground state energy of the dilute Bose-Hubbard gas on Bravais lattices
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arXiv
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| Autori principali: | , , |
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| Natura: | Preprint |
| Pubblicazione: |
2026
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| _version_ | 1866914339085090816 |
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| author | Mokrzański, Norbert Napiórkowski, Marcin Wojtkiewicz, Jacek |
| author_facet | Mokrzański, Norbert Napiórkowski, Marcin Wojtkiewicz, Jacek |
| contents | We study interacting bosons on a three-dimensional Bravais lattice with positive hopping amplitudes and on-site repulsive interactions. We prove that, in the dilute limit $ρ\to 0$, the ground state energy density satisfies $$e_0(ρ) = 4πa ρ^2 \big(1+O(ρ^{1/6})\big),$$ where $a$ is the lattice scattering length defined through the corresponding two-body problem. This establishes the analogue of the Dyson and Lieb-Yngvason theorems for the Bose-Hubbard gas. Our result shows that the leading-order energy is universal: although the lattice geometry affects the microscopic dispersion relation, it enters the leading order asymptotics only through the scattering length. In particular, it is independent of other features of the underlying Bravais lattice. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2602_16566 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Ground state energy of the dilute Bose-Hubbard gas on Bravais lattices Mokrzański, Norbert Napiórkowski, Marcin Wojtkiewicz, Jacek Mathematical Physics We study interacting bosons on a three-dimensional Bravais lattice with positive hopping amplitudes and on-site repulsive interactions. We prove that, in the dilute limit $ρ\to 0$, the ground state energy density satisfies $$e_0(ρ) = 4πa ρ^2 \big(1+O(ρ^{1/6})\big),$$ where $a$ is the lattice scattering length defined through the corresponding two-body problem. This establishes the analogue of the Dyson and Lieb-Yngvason theorems for the Bose-Hubbard gas. Our result shows that the leading-order energy is universal: although the lattice geometry affects the microscopic dispersion relation, it enters the leading order asymptotics only through the scattering length. In particular, it is independent of other features of the underlying Bravais lattice. |
| title | Ground state energy of the dilute Bose-Hubbard gas on Bravais lattices |
| topic | Mathematical Physics |
| url | https://arxiv.org/abs/2602.16566 |