Ground state energy of the Bose--Hubbard model with large coordination number with a polaron-type quantum de Finetti theorem
Fuente:
arXiv
Saved in:
| Main Authors: | , , |
|---|---|
| Format: | Preprint |
| Published: |
2026
|
| Subjects: | |
| Online Access: | |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| _version_ | 1866917373235167232 |
|---|---|
| author | Farhat, Shahnaz Périce, Denis Petrat, Sören |
| author_facet | Farhat, Shahnaz Périce, Denis Petrat, Sören |
| contents | We consider the ground state energy of the Bose--Hubbard model on a graph with large and homogeneous coordination number. In the limit of infinite coordination number, we prove convergence of the ground state energy to the minimizer of a mean-field energy functional. This functional is obtained by averaging the hopping term over the large number of connected sites, while the interaction energy is not averaged. Hence, the resulting mean-field description is in the strong coupling regime, and is expected to provide a qualitatively correct picture of the phase diagram of the Bose--Hubbard model for large enough coordination number. For our proof, we develop a new version of a de Finetti-type theorem, which we call the polaron-type quantum de Finetti theorem, and which we expect to be a more broadly useful extension of existing quantum de Finetti results. Our theorem covers the case where the Hilbert space is a tensor product of some Hilbert space with a bosonic Fock space. This theorem is applied to the convergence of the ground state energy of the Bose--Hubbard model after reducing it to a polaron-type model. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2603_29562 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Ground state energy of the Bose--Hubbard model with large coordination number with a polaron-type quantum de Finetti theorem Farhat, Shahnaz Périce, Denis Petrat, Sören Mathematical Physics Quantum Gases We consider the ground state energy of the Bose--Hubbard model on a graph with large and homogeneous coordination number. In the limit of infinite coordination number, we prove convergence of the ground state energy to the minimizer of a mean-field energy functional. This functional is obtained by averaging the hopping term over the large number of connected sites, while the interaction energy is not averaged. Hence, the resulting mean-field description is in the strong coupling regime, and is expected to provide a qualitatively correct picture of the phase diagram of the Bose--Hubbard model for large enough coordination number. For our proof, we develop a new version of a de Finetti-type theorem, which we call the polaron-type quantum de Finetti theorem, and which we expect to be a more broadly useful extension of existing quantum de Finetti results. Our theorem covers the case where the Hilbert space is a tensor product of some Hilbert space with a bosonic Fock space. This theorem is applied to the convergence of the ground state energy of the Bose--Hubbard model after reducing it to a polaron-type model. |
| title | Ground state energy of the Bose--Hubbard model with large coordination number with a polaron-type quantum de Finetti theorem |
| topic | Mathematical Physics Quantum Gases |
| url | https://arxiv.org/abs/2603.29562 |