Understanding physics of high-$T_c$ cuprate superconductors remains one of the important problems in materials science. Though a number of diverse theories argue about the superconductivity and competing orders, ab initio and quantitative understanding is lacking. Here, we reproduce the experimental phase diagram of ${\mathrm{HgBa}}_2{\mathrm{CuO}}_{4+y}$ by solving its ab initio low-energy effective Hamiltonian without adjustable parameters. It shows a superconducting phase in a wide range of hole density $\delta$, and its competition with charge period-4 plus spin period-8 stripe order near $\delta \sim 0.1$, in agreement with experimental results including recent x-ray scattering. Then a crucial role of off-site interactions in stabilizing the superconductivity is elucidated with emphasis on charge fluctuations. It also clarifies the condensation energy mainly contributed from the on-site Coulomb interaction. The present achievement will enable deeper, predictable understanding on open issues of the high-$T_c$ superconducting mechanism and promote ab initio studies on strongly correlated electrons beyond parametrized model studies.

中文翻译：

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基于汞的铜酸盐超导体的超导性和不均匀性的从头开始

了解高物理${Ť}_C$铜酸盐超导体仍然是材料科学中的重要问题之一。尽管许多不同的理论争论超导性和竞争秩序，但缺乏从头开始和定量的理解。在这里，我们再现了${\mathrm{汞钡}}_2{\mathrm{氧化铜}}_{4+ÿ}$通过从头算起没有可调参数的从头算起的低能量有效哈密顿量。它在宽范围的孔密度中显示了超导相$\delta$，并且其与充电周期4加上自旋周期8的条纹顺序的竞争接近 $\delta 〜0.1$与实验结果一致，包括最近的X射线散射。然后阐明了场外相互作用在稳定超导性中的关键作用，重点是电荷波动。它还阐明了凝结能主要来自现场库仑相互作用。目前的成就将使人们对高${Ť}_C$超越超参数化模型研究，并促进对强相关电子的从头算研究。