Saved in:
| Main Authors: | , |
|---|---|
| Format: | Preprint |
| Published: |
2026
|
| Subjects: | |
| Online Access: | https://arxiv.org/abs/2604.19703 |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| _version_ | 1866914496397705216 |
|---|---|
| author | Haag-Fank, Leon Mielke, Andreas |
| author_facet | Haag-Fank, Leon Mielke, Andreas |
| contents | The lowest eigenstates of the hopping matrix on the line graph of a cubic lattice with periodic boundary conditions are highly degenerate, they form a lowest flat band. Further, these states are localized. If one considers a repulsive bosonic Hubbard model on this lattice it is possible to construct exact multi-particle ground states simply by putting particles in the localized single particle ground states such that they avoid each other. This can be done up to a certain critical particle number $N_c$. We prove that at this particle number the ground state entropy is subextensive $\propto N_c^{2/3}$. For lower densities the entropy is extensive. We further show that the problem is related to the number of 4-cycle decompositions of the cubic lattice with periodic boundary conditions. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2604_19703 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | The bosonic Hubbard model on a three dimensional flat band lattice Haag-Fank, Leon Mielke, Andreas Mathematical Physics Statistical Mechanics Combinatorics 81V73 (Primary), 81-10, 81Q80, 05C30, 05C38 (Secondary) The lowest eigenstates of the hopping matrix on the line graph of a cubic lattice with periodic boundary conditions are highly degenerate, they form a lowest flat band. Further, these states are localized. If one considers a repulsive bosonic Hubbard model on this lattice it is possible to construct exact multi-particle ground states simply by putting particles in the localized single particle ground states such that they avoid each other. This can be done up to a certain critical particle number $N_c$. We prove that at this particle number the ground state entropy is subextensive $\propto N_c^{2/3}$. For lower densities the entropy is extensive. We further show that the problem is related to the number of 4-cycle decompositions of the cubic lattice with periodic boundary conditions. |
| title | The bosonic Hubbard model on a three dimensional flat band lattice |
| topic | Mathematical Physics Statistical Mechanics Combinatorics 81V73 (Primary), 81-10, 81Q80, 05C30, 05C38 (Secondary) |
| url | https://arxiv.org/abs/2604.19703 |