Variational approach for the two-body problem in a multiband extended-Hubbard model
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arXiv
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| Format: | Preprint |
| Published: |
2024
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| _version_ | 1866916351942066176 |
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| author | Iskin, M. |
| author_facet | Iskin, M. |
| contents | Considering a spin-up and a spin-down fermion in a generic tight-binding lattice with a multi-site basis, we investigate the two-body problem using a multiband extended-Hubbard model with finite-ranged hopping and interaction parameters. We derive a linear eigenvalue problem for the entire two-body spectrum, alongside a nonlinear eigenvalue problem for the bound states in the form of a self-consistency equation. Our results, based on an exact variational approach, suggest potential applications across various lattice geometries. As an illustration, we apply them to the linear-chain model and show that the resultant spin singlet and triplet bound states align well with the existing literature. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2404_01117 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Variational approach for the two-body problem in a multiband extended-Hubbard model Iskin, M. Superconductivity Quantum Gases Strongly Correlated Electrons Considering a spin-up and a spin-down fermion in a generic tight-binding lattice with a multi-site basis, we investigate the two-body problem using a multiband extended-Hubbard model with finite-ranged hopping and interaction parameters. We derive a linear eigenvalue problem for the entire two-body spectrum, alongside a nonlinear eigenvalue problem for the bound states in the form of a self-consistency equation. Our results, based on an exact variational approach, suggest potential applications across various lattice geometries. As an illustration, we apply them to the linear-chain model and show that the resultant spin singlet and triplet bound states align well with the existing literature. |
| title | Variational approach for the two-body problem in a multiband extended-Hubbard model |
| topic | Superconductivity Quantum Gases Strongly Correlated Electrons |
| url | https://arxiv.org/abs/2404.01117 |