Nonstandard Hubbard model and electron pairing
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arXiv
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| Autores principales: | , , , |
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| Formato: | Preprint |
| Publicado: |
2023
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| _version_ | 1866914792163246080 |
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| author | Zendra, M. Borgonovi, F. Celardo, G. L. Gurvitz, S. |
| author_facet | Zendra, M. Borgonovi, F. Celardo, G. L. Gurvitz, S. |
| contents | We present a non-standard Hubbard model applicable to arbitrary single-particle potential profiles and inter-particle interactions. Our approach involves a novel treatment of Wannier functions, free from the ambiguities of conventional methods and applicable to finite systems without periodicity constraints. To ensure the consistent evaluation of Wannier functions, we develop a perturbative approach, utilizing the barrier penetration coefficient as a perturbation parameter. With the newly defined Wannier functions as a basis, we derive the Hubbard Hamiltonian, revealing the emergence of density-induced and pair tunneling terms alongside standard contributions. Our investigation demonstrates that long-range inter-particle interactions can induce a novel mechanism for repulsive particle pairing. This mechanism relies on the effective suppression of single-particle tunneling due to density-induced tunneling. Contrary to expectations based on the standard Hubbard model, an increase in inter-particle interaction does not lead to an insulating state. Instead, our proposed mechanism implies the coherent motion of correlated electron pairs, similar to bound states within a multi-well system, resistant to decay from single-electron tunneling transitions. These findings carry significant implications for various phenomena, including the formation of flat bands, the emergence of superconductivity in twisted bilayer graphene, and the possibility of a novel metal-insulator transition. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2307_16737 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Nonstandard Hubbard model and electron pairing Zendra, M. Borgonovi, F. Celardo, G. L. Gurvitz, S. Strongly Correlated Electrons Quantum Physics We present a non-standard Hubbard model applicable to arbitrary single-particle potential profiles and inter-particle interactions. Our approach involves a novel treatment of Wannier functions, free from the ambiguities of conventional methods and applicable to finite systems without periodicity constraints. To ensure the consistent evaluation of Wannier functions, we develop a perturbative approach, utilizing the barrier penetration coefficient as a perturbation parameter. With the newly defined Wannier functions as a basis, we derive the Hubbard Hamiltonian, revealing the emergence of density-induced and pair tunneling terms alongside standard contributions. Our investigation demonstrates that long-range inter-particle interactions can induce a novel mechanism for repulsive particle pairing. This mechanism relies on the effective suppression of single-particle tunneling due to density-induced tunneling. Contrary to expectations based on the standard Hubbard model, an increase in inter-particle interaction does not lead to an insulating state. Instead, our proposed mechanism implies the coherent motion of correlated electron pairs, similar to bound states within a multi-well system, resistant to decay from single-electron tunneling transitions. These findings carry significant implications for various phenomena, including the formation of flat bands, the emergence of superconductivity in twisted bilayer graphene, and the possibility of a novel metal-insulator transition. |
| title | Nonstandard Hubbard model and electron pairing |
| topic | Strongly Correlated Electrons Quantum Physics |
| url | https://arxiv.org/abs/2307.16737 |