Understanding physics of high-Tc 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 HgBa2CuO4+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 δ, and its competition with charge period-4 plus spin period-8 stripe order near δ∼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-Tc superconducting mechanism and promote ab initio studies on strongly correlated electrons beyond parametrized model studies.
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