Mean Field Study of Superconductivity in the Square Lattice $t$-$J$ Model with Three-Site Hopping
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arXiv
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| Format: | Preprint |
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2024
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| _version_ | 1866916412229943296 |
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| author | Yang, Ke Chen, Qianqian Qiao, Lei Zhu, Zheng |
| author_facet | Yang, Ke Chen, Qianqian Qiao, Lei Zhu, Zheng |
| contents | It remains an open question whether the two-dimensional single-band pure Hubbard model and its related pure $t$-$J$ model truly capture the superconducting order in cuprates. Recent numerical studies on this issue have raised a notable disparity in superconducting order between the pure Hubbard model and the pure $t$-$J$ model. Inspired by these, we investigate the role of the three-site hopping term in $d$-wave superconductivity, such a term is usually neglected in the effective Hamiltonian of the Hubbard model, though its amplitude is of the same order as the superexchange coupling $J$ in the $t$-$J$ model. Our slave-boson mean-field solution demonstrates the suppression of $d$-wave superconducting order by incorporating the three-site hopping term, consistent with numerical observations by the density matrix renormalization group. This suppression could be understood as a result of competition between superexchange interaction and three-site hopping, the former favors $d$-wave pairing while the latter favors $s$-wave pairing. We also discussed its role in quasiparticle dispersion and boson-condensation temperature. Our findings may offer an alternative understanding of the recent numerical contrasting findings in the strong coupling regime: the absent or weak superconductivity in the pure Hubbard model, while the robust superconductivity in the $t$-$J$ model without including the three-site hopping term. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2406_08780 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Mean Field Study of Superconductivity in the Square Lattice $t$-$J$ Model with Three-Site Hopping Yang, Ke Chen, Qianqian Qiao, Lei Zhu, Zheng Strongly Correlated Electrons Superconductivity It remains an open question whether the two-dimensional single-band pure Hubbard model and its related pure $t$-$J$ model truly capture the superconducting order in cuprates. Recent numerical studies on this issue have raised a notable disparity in superconducting order between the pure Hubbard model and the pure $t$-$J$ model. Inspired by these, we investigate the role of the three-site hopping term in $d$-wave superconductivity, such a term is usually neglected in the effective Hamiltonian of the Hubbard model, though its amplitude is of the same order as the superexchange coupling $J$ in the $t$-$J$ model. Our slave-boson mean-field solution demonstrates the suppression of $d$-wave superconducting order by incorporating the three-site hopping term, consistent with numerical observations by the density matrix renormalization group. This suppression could be understood as a result of competition between superexchange interaction and three-site hopping, the former favors $d$-wave pairing while the latter favors $s$-wave pairing. We also discussed its role in quasiparticle dispersion and boson-condensation temperature. Our findings may offer an alternative understanding of the recent numerical contrasting findings in the strong coupling regime: the absent or weak superconductivity in the pure Hubbard model, while the robust superconductivity in the $t$-$J$ model without including the three-site hopping term. |
| title | Mean Field Study of Superconductivity in the Square Lattice $t$-$J$ Model with Three-Site Hopping |
| topic | Strongly Correlated Electrons Superconductivity |
| url | https://arxiv.org/abs/2406.08780 |