Pairing susceptibility in the weakly interacting multilayer Hubbard model evaluated by direct perturbative expansion
Fuente:
arXiv
Gespeichert in:
| Hauptverfasser: | , |
|---|---|
| Format: | Preprint |
| Veröffentlicht: |
2024
|
| Schlagworte: | |
| Online-Zugang: | |
| Tags: |
Tag hinzufügen
Keine Tags, Fügen Sie den ersten Tag hinzu!
|
| _version_ | 1866914970312114176 |
|---|---|
| author | Farid, Rayan LeBlanc, J. P. F. |
| author_facet | Farid, Rayan LeBlanc, J. P. F. |
| contents | We present a systematic study of the interaction, doping, and layer dependence of the $d_{x^2-y^2}$-wave pairing susceptibility of the Hubbard model for a stacked 2D square lattice. We perform a multi-index perturbative expansion up to fourth-order to obtain coefficients in powers of the Hubbard $U$, the inter-layer $V$, and the pair-hopping $J$ interactions. We evaluate the vertex diagrams that contribute to the pairing susceptibility for $\ell= 2,3, 4$ layered models in the $U$-$V$-$J$ interaction space. This provides unprecedented access to the pairing amplitudes, allowing us to identify the processes that enhance or reduce pairing. We distinguish pairing within the diagonal channel, $P^{\parallel}_{d}$, and off-diagonal channel, $P^{\perp}_{d}$, and find that, in the absence of $J$, the qualitative behavior of the layered system is equivalent to the single-layer model. In the presence of $J$, we show that pairing is enhanced sublinearly with increasing $\ell$ and is primarily mediated by the $P^{\perp}_{d}$ component and find which coefficients and diagram sets are responsible. Finally, we construct a generalized $\ell$-dependent equation for $ P^{\perp}_{d}$ to speculate pairing beyond $\ell=4$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2406_02656 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Pairing susceptibility in the weakly interacting multilayer Hubbard model evaluated by direct perturbative expansion Farid, Rayan LeBlanc, J. P. F. Superconductivity Strongly Correlated Electrons We present a systematic study of the interaction, doping, and layer dependence of the $d_{x^2-y^2}$-wave pairing susceptibility of the Hubbard model for a stacked 2D square lattice. We perform a multi-index perturbative expansion up to fourth-order to obtain coefficients in powers of the Hubbard $U$, the inter-layer $V$, and the pair-hopping $J$ interactions. We evaluate the vertex diagrams that contribute to the pairing susceptibility for $\ell= 2,3, 4$ layered models in the $U$-$V$-$J$ interaction space. This provides unprecedented access to the pairing amplitudes, allowing us to identify the processes that enhance or reduce pairing. We distinguish pairing within the diagonal channel, $P^{\parallel}_{d}$, and off-diagonal channel, $P^{\perp}_{d}$, and find that, in the absence of $J$, the qualitative behavior of the layered system is equivalent to the single-layer model. In the presence of $J$, we show that pairing is enhanced sublinearly with increasing $\ell$ and is primarily mediated by the $P^{\perp}_{d}$ component and find which coefficients and diagram sets are responsible. Finally, we construct a generalized $\ell$-dependent equation for $ P^{\perp}_{d}$ to speculate pairing beyond $\ell=4$. |
| title | Pairing susceptibility in the weakly interacting multilayer Hubbard model evaluated by direct perturbative expansion |
| topic | Superconductivity Strongly Correlated Electrons |
| url | https://arxiv.org/abs/2406.02656 |