标题： 自旋子单态：部分填充条纹中$d$波配对的微观机制 显示英文标题

标题： Spinon Singlet: Microscopic Mechanism of $d$-Wave Pairing in a Partially-Filled Stripe

摘要： 显著的研究进展已经导致一种共识，即费米-哈伯德模型及其扩展变体是阐明空穴掺杂的高-$T_c$材料中条纹序与超导性之间相互关系的典型框架。 值得注意的是，哈伯德量子模拟器最近取得了几项显著突破，例如成功冷却到低温区域并实现了稳定波动条纹的观察。 然而，由于强关联效应和不可忽略的热涨落之间的复杂相互作用，在低温下条纹存在的情况下电子的$d$波配对的微观机制仍然了解甚少。 在此，我们通过数值和解析方法对代表性$t$-$J$和费米-哈伯德模型中的部分填充条纹进行了深入研究。 类似于量子气体显微镜，完美的采样技术使我们能够获得基态波函数中出现的福克基态状态的高置信度统计结果。 在一个令人耳目一新的物理范式中，这些数据表明具有相反手性的两个自旋子倾向于自发地配对成一个单态，这自然导致了$d$波配对模式。 然后，利用量子彩色弦的有效理论，我们重建了波函数并确定了自旋子配对的性质及其与$d$波配对模式的联系。 此外，自旋子单态对使得双条纹之间的长程对-对相关性得以建立。 我们的工作为条纹序在介导$d$波超导性中的作用提供了新的见解，并为在费米-哈伯德模型中进一步探索多条纹介导的配对机制铺平了道路。 显示英文摘要

摘要： Significant research advances have led to a consensus that the Fermi-Hubbard model and its extended variants are archetypal frameworks for elucidating the intertwined relationship between stripe orders and superconductivity in hole-doped high-$T_c$ materials. Notably, the Hubbard quantum simulator has recently achieved several remarkable breakthroughs, e.g., being successfully cooled down to the cryogenic regime and enabling the observation of stable fluctuating stripes. However, the microscopic mechanism behind $d$-wave pairing of electrons in the presence of stripes at low temperatures remains poorly understood due to the intricate interplay among the strongly correlated effects and non-negligible thermal fluctuations. Here, we conduct a close investigation of a partially-filled stripe in the representative $t$-$J$ and Fermi-Hubbard models with both numerical and analytical methods. Analogous to quantum gas microscopy, the perfect sampling technique allows us to obtain the high-confidence statistics of the Fock basis states appearing in the ground-state wavefunction. In a refreshing physical paradigm, these data demonstrate that two spinons with opposite chiralities tend to spontaneously pair into a singlet state, which naturally gives rise to the $d$-wave pairing pattern. Then, using the effective theory of quantum colored string, we reconstruct the wavefunction and determine the nature of spinon pairing and its connection to the $d$-wave pairing pattern. Furthermore, spinon singlet pairs enable the establishment of a long-range pair-pair correlation between double stripes. Our work offers new insights into the role of stripe orders in mediating $d$-wave superconductivity and paves the way for further exploration of multi-stripe-mediated pairing mechanisms in the Fermi-Hubbard model.