发表机构
Kavli Institute for Theoretical Sciences and School of Quantum, University of Chinese Academy of Sciences（中国科学院大学量子学院和理论物理研究所）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
该研究用变分均匀矩阵乘积态方法在无限圆柱上求解纯 $t$-$J$ 模型，发现 $1/8$ 掺杂下均匀电荷密度 $d$-波超导基态，无条纹序，为长期争论提供新证据。
AI 中文摘要
方格 $t$-$J$ 模型在 $1/8$ 空穴掺杂下的基态一直是长期争议的主题，关于条纹序与超导性的数值报告相互矛盾。在此，我们使用变分均匀矩阵乘积态（VUMPS）方法来解决这一争论，该方法直接在热力学极限下沿圆柱轴优化波函数，并消除了有限圆柱计算中可能出现的边界钉扎效应。在周长 $L_y = 8$ 的无限圆柱上，我们发现了一个具有准长程配对关联的均匀电荷密度 $d$-波超导基态。主导配对发生在零质心动量处，而未检测到显著的有限动量配对分量。扭曲边界条件计算揭示了有限的超导相位刚度，序参量相位平滑缠绕以跟随施加的磁通量，提供了超导稳健性的独立探针。此外，电荷和自旋关联均快速衰减，没有长程条纹或磁序的迹象，这与 $L_y=6$ 圆柱在 $1/6$ 掺杂下同一方法容易识别条纹序的情况形成对比。我们的结果为纯 $t$-$J$ 模型中长期存在的条纹-超导性争论提供了方法论上独特的证据，并在掺杂莫特绝缘体的最小模型中揭示了均匀 $d$-波超导性。
英文摘要
The ground state of the square-lattice $t$-$J$ model at $1/8$ hole doping has been the subject of a long-standing controversy, with conflicting numerical reports of stripe order versus superconductivity. Here, we address this debate using the variational uniform matrix product state (VUMPS) method, which optimizes the wave function directly in the thermodynamic limit along the cylinder axis and eliminates the boundary pinning effects that can arise in finite-cylinder calculations. On an infinite cylinder of circumference $L_y = 8$, we find a uniform-charge-density $d$-wave superconducting ground state with quasi-long-range pairing correlations. The dominant pairing occurs at zero center-of-mass momentum, while no sizable finite-momentum pairing component is detected. Twisted-boundary-condition calculations reveal a finite superconducting phase stiffness, with the order-parameter phase winding smoothly to follow the applied flux, providing an independent probe of the robustness of the superconductivity. Moreover, both charge and spin correlations decay rapidly, with no signatures of long-range stripe or magnetic order, in contrast to an $L_y=6$ cylinder at $1/6$ doping where the same method readily identifies stripe order. Our results provide methodologically distinct evidence in the long-standing stripe--superconductivity debate in the pure $t$-$J$ model and reveal uniform $d$-wave superconductivity in a minimal model of doped Mott insulators.
Comments7 pages (incl. references) + 3 pages Supplemental Material; 7 figures
