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Understanding the doped Mott insulator is a central challenge in condensedmatter physics. This study identifies an intrinsic Berry-phase-like signstructure for the square-lattice $t$-$t'$-$J$ model with the nearest-neighbor($t$) and next-nearest-neighbor hopping ($t'$), which could help explain theorigin of the quasi-long-range superconducting and stripe phases observedthrough density matrix renormalization group (DMRG) calculation. We firstdemonstrate that the hole binding underlies both the superconducting and stripeorders, and then show that the hole pairing generically disappears once thephase-string or mutual statistics component of the sign structure is switchedoff in DMRG calculation. In the latter case, the superexchange interaction nolonger plays a crucial role in shaping the charge dynamics, where aFermi-liquid-like phase with small hole Fermi pockets is found. It is in sharpcontrast to the large Fermi surfaces in either the stripe phase found at$t'/t<0$ or the superconducting phase at $t'/t>0$ in the original $t$-$t'$-$J$model on the 6-leg ladder.

Sign structure in the square-lattice $t$-$t^\prime$-$J$ model and numerical consequences