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arXiv · 2604.05997

Numerically Exact Study of Flat-Band Superconductivity

I. S. Tupitsyn·B. Currie·B. V. Svistunov·E. Kozik·N. V. Prokof'ev
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Abstract

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, the value of $c$ and the full nonlinear $T_c(U)$ curve---with a maximum at large $|U|$---are known beyond mean-field and quantum geometry estimates only for systems with isolated flat bands. 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 BEC (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.

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I. S. Tupitsyn, B. Currie, B. V. Svistunov, E. Kozik, N. V. Prokof'ev. 2026-08-08. Numerically Exact Study of Flat-Band Superconductivity. https://arxiv.org/abs/2604.05997

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