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

Understand

The square-lattice Hubbard and closely related $t$-$J$ models are considered as basic paradigms for understanding strong correlation effects and unconventional superconductivity (SC).

• Recent large-scale density matrix renormalization group (DMRG) simulations on the extended $t$-$J$ 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 $t$-$J$ model by employing the state-of-the-art DMRG calculations with much enhanced bond dimensions, allowing more accurate determination of the ground state.
• On 6-leg cylinders, while different CDW phases are identified on the hole-doped side for the doping range $\delta= 1/16-1/8$, a SC phase emerges at a lower doping regime, with algebraically decaying pairing correlations and $d$-wave symmetry.