Pair size and quantum geometry in a multiband Hubbard model
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arXiv
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| Format: | Preprint |
| Publié: |
2024
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| _version_ | 1866913633752055808 |
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| author | Iskin, M. |
| author_facet | Iskin, M. |
| contents | We study the size of two-body bound states and Cooper pairs within a multiband Hubbard model that features time-reversal symmetry and uniform pairing on a generic lattice. Our analysis involves (i) an exact calculation of the localization tensor to determine the size of lowest-lying two-body bound state in vacuum, and (ii) an evaluation of the analogous tensor to estimate the average size of Cooper pairs within the mean-field BCS-BEC crossover theory at zero temperature. Beyond the conventional intraband contribution that depends on Bloch bands, we show that pair size also has a geometric contribution governed by the quantum-metric tensor of the Bloch states and their band-resolved quantum-metric tensors. As a concrete example, we investigate the pyrochlore-Hubbard model numerically and demonstrate that, while the pair size diverges in the weakly interacting BCS regime of dispersive bands, it remains finite and relatively small in the flat-band regime, even for infinitesimal interaction, perfectly matching the exact two-body result in the dilute limit. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2409_14921 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Pair size and quantum geometry in a multiband Hubbard model Iskin, M. Superconductivity Quantum Gases Strongly Correlated Electrons We study the size of two-body bound states and Cooper pairs within a multiband Hubbard model that features time-reversal symmetry and uniform pairing on a generic lattice. Our analysis involves (i) an exact calculation of the localization tensor to determine the size of lowest-lying two-body bound state in vacuum, and (ii) an evaluation of the analogous tensor to estimate the average size of Cooper pairs within the mean-field BCS-BEC crossover theory at zero temperature. Beyond the conventional intraband contribution that depends on Bloch bands, we show that pair size also has a geometric contribution governed by the quantum-metric tensor of the Bloch states and their band-resolved quantum-metric tensors. As a concrete example, we investigate the pyrochlore-Hubbard model numerically and demonstrate that, while the pair size diverges in the weakly interacting BCS regime of dispersive bands, it remains finite and relatively small in the flat-band regime, even for infinitesimal interaction, perfectly matching the exact two-body result in the dilute limit. |
| title | Pair size and quantum geometry in a multiband Hubbard model |
| topic | Superconductivity Quantum Gases Strongly Correlated Electrons |
| url | https://arxiv.org/abs/2409.14921 |