Emergent Superconductivity and Competing Charge Orders in Hole-Doped Square-Lattice t−J Model

The square-lattice Hubbard and closely related $t\text{\ensuremath{-}}J$ models are considered as basic paradigms for understanding strong correlation effects and unconventional superconductivity (SC). Recent large-scale density matrix renormalization group simulations on the extended $t\text{\ensuremath{-}}J$ model have identified $d$-wave SC on the electron-doped side (with the next-nearest-neighbor hopping ${t}_{2}>0$) but a dominant charge density wave (CDW) order on the hole-doped side (${t}_{2}<0$), which is inconsistent with the SC of hole-doped cuprate compounds. We re-examine the ground-state phase diagram of the extended $t\text{\ensuremath{-}}J$ model by employing the state-of-the-art density matrix renormalization group calculations with much enhanced bond dimensions, allowing more accurate determination of the ground state. On six-leg cylinders, while different CDW phases are identified on the hole-doped side for the doping range $\ensuremath{\delta}=1/16\ensuremath{-}1/8$, a SC phase emerges at a lower doping regime, with algebraically decaying pairing correlations and $d$-wave symmetry. On the wider eight-leg systems, the $d$-wave SC also emerges on the hole-doped side at the optimal $1/8$ doping, demonstrating the winning of SC over CDW by increasing the system width. Our results not only suggest a new path to SC in general $t\text{\ensuremath{-}}J$ model through weakening the competing charge orders, but also provide a unified understanding on the SC of both hole- and electron-doped cuprate superconductors.