Numerically Exact Study of Flat-Band Superconductivity
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arXiv
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| Autori principali: | , , , , |
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| Natura: | Preprint |
| Pubblicazione: |
2026
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| author | Tupitsyn, I. S. Currie, B. Svistunov, B. V. Kozik, E. Prokof'ev, N. V. |
| author_facet | Tupitsyn, I. S. Currie, B. Svistunov, B. V. Kozik, E. Prokof'ev, N. V. |
| contents | Current theories of high-temperature superconductivity in flat-band systems predict a linear dependence of the transition temperature on the attractive interaction, $T_c(U) = c|U|$. However, neither the value of $c$ nor the full nonlinear $T_c(U)$ curve -- with a maximum at large $|U|$ -- is known beyond mean-field and quantum geometry estimates. Using a controlled diagrammatic Monte Carlo technique, we trace the onset of superfluid response in the Lieb lattice with attractive Hubbard interaction. Focusing on the half-filled flat-band case, where the ordering mechanism differs fundamentally from both BCS and preformed Cooper pair scenarios, we find that the pairing response diverges linearly with decreasing temperature over a broad range of $U$, leading to a sharp crossover to long-range correlations at a characteristic temperature $T_*$, which provides a controlled upper bound on $T_c$. The highest $T_*$ occurs when all three bands touch at a single momentum point, potentially corresponding to high $T_c$ values. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2604_05997 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Numerically Exact Study of Flat-Band Superconductivity Tupitsyn, I. S. Currie, B. Svistunov, B. V. Kozik, E. Prokof'ev, N. V. Superconductivity Computational Physics Current theories of high-temperature superconductivity in flat-band systems predict a linear dependence of the transition temperature on the attractive interaction, $T_c(U) = c|U|$. However, neither the value of $c$ nor the full nonlinear $T_c(U)$ curve -- with a maximum at large $|U|$ -- is known beyond mean-field and quantum geometry estimates. Using a controlled diagrammatic Monte Carlo technique, we trace the onset of superfluid response in the Lieb lattice with attractive Hubbard interaction. Focusing on the half-filled flat-band case, where the ordering mechanism differs fundamentally from both BCS and preformed Cooper pair scenarios, we find that the pairing response diverges linearly with decreasing temperature over a broad range of $U$, leading to a sharp crossover to long-range correlations at a characteristic temperature $T_*$, which provides a controlled upper bound on $T_c$. The highest $T_*$ occurs when all three bands touch at a single momentum point, potentially corresponding to high $T_c$ values. |
| title | Numerically Exact Study of Flat-Band Superconductivity |
| topic | Superconductivity Computational Physics |
| url | https://arxiv.org/abs/2604.05997 |