AI 中文总结
研究采用含432个格点的神经量子态，揭示三角晶格Hofstadter-Hubbard模型中超导性与量子临界性的相互作用，发现掺杂后相变两侧均存在拓扑超导体，超导体能量尺度由相变邻近性决定。
AI 中文摘要
理解母体绝缘态如何调控掺杂后出现的超导电性，是自安德森提出共振价键理论以来的长期问题。具有每个格点π/2磁通的三角晶格Hofstadter-Hubbard模型为该问题提供了理想场景：半填充时它存在两种不同的母体态——弱耦合下的整数量子霍尔绝缘体和中间耦合下的手性自旋液体，二者被拓扑相变分隔。我们使用最多含432个格点的环面上的神经量子态，提供了该相变是连续相变的有力证据，其2e电荷间隙消失，且存在临界电荷涨落。掺杂后，我们发现在相变两侧均存在符合d+id配对的具有非对角长程序的拓扑超导体。超导电性的两个要素——配对形成和相位相干性，对母体态的响应方式截然不同：配对序参量在相变两侧几乎不变，而超流刚度在临界点附近显著增强。因此，超导体的能量尺度并非由掺杂的母体态决定，而是由二者之间的相变邻近性决定。我们的结果确立了神经量子态是理解长程电子关联与超导电性之间微妙相互作用的强大工具。
英文摘要
Understanding how a parent insulating state shapes the superconductivity that emerges upon doping is a long-standing problem dating back to Anderson's resonating-valence-bond proposal. The triangular-lattice Hofstadter-Hubbard model with $π/2$ flux per plaquette offers an ideal setting: at half filling it hosts two distinct parent states---an integer quantum Hall insulator and a chiral spin liquid---separated by a topological phase transition. Using neural quantum states on tori of up to $432$ sites, we present strong evidence that the transition is continuous, with a vanishing $2e$ charge gap and critical charge fluctuations. Upon doping, we find a topological superconductor on either side of the transition. While the pairing order parameter remains nearly unchanged across the transition, the superfluid stiffness is strongly enhanced near the critical point. The energy scale of the superconductor is therefore set not by which parent state is doped, but by proximity to the transition between them. Our results establish neural quantum states as a powerful tool for understanding the interplay between unconventional electronic correlations and superconductivity.
Comments14 pages, 11 figures
