In this work, we propose a one-dimensional $t\text{−}J\text{−}K\text{−}U$ model, where itinerant spin-1/2 fermions are coupled to a spin-1/2 Heisenberg chain via a Kondo interaction $J_k$. Depending on the sign of $J_k$, the system realizes either a high-spin or low-spin ground state. Using the density matrix renormalization group (DMRG) calculations, we demonstrate the emergence of a pairing density wave (PDW) with wave vector $Q=\pi$ in this model. In the low-spin state, the ground state of the system is identified as a Luther-Emery liquid. In the high-spin state, superconducting pairing correlations are suppressed, and a quasi-long-range (QLR) spin density wave (SDW) emerges. In addition to the Kondo coupling $J_K$, strong correlations among the itinerant electrons also play a significant role in stabilizing these density wave orders. We suggest that this model may be realized in a ${\mathrm{Ni}}^{2+}$ chain with Ni in the $d^8$ configurations. Although superconductivity has not yet been observed in these materials, charge and spin ordering phenomena have been widely reported. Our results provide a potential pairing mechanism, indicating the possible existence of these intertwined orders in nickelates.

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• Density matrix renormalization group
• Pair density wave
• Mott insulators
• Strongly correlated systems
• t-J model