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The square-lattice Hubbard and closely related $t$-$J$ models are consideredas basic paradigms for understanding strong correlation effects andunconventional superconductivity (SC). Recent large-scale density matrixrenormalization group (DMRG) simulations on the extended $t$-$J$ model haveidentified $d$-wave SC on the electron-doped side (with thenext-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 ofhole-doped cuprate compounds. We re-examine the ground-state phase diagram ofthe extended $t$-$J$ model by employing the state-of-the-art DMRG calculationswith much enhanced bond dimensions, allowing more accurate determination of theground state. On 6-leg cylinders, while different CDW phases are identified onthe hole-doped side for the doping range $\delta= 1/16-1/8$, a SC phase emergesat a lower doping regime, with algebraically decaying pairing correlations and$d$-wave symmetry. On the wider 8-leg systems, the $d$-wave SC also emerges onthe hole-doped side at the optimal $1/8$ doping, demonstrating the winning ofSC over CDW by increasing the system width. Our results not only suggest a newpath to SC in general $t$-$J$ models through weakening the competing chargeorders, but also provide a unified understanding on the SC of both hole- andelectron-doped cuprate superconductors.

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