Intertwined Orders, Pair-Density-Wave, and D-Wave Superconductivity in the Square-Lattice t-J Model

The pure t-J model has long been considered as the simplest model for doped Mott insulators, yet after

more than three decades of intense theoretical investigations, it remains illusive whether its ground state hosts

unconventional superconductivity (SC). Through state-of-the-art density matrix renormalization group calcula-

tions using the grand canonical ensemble and extremely large bond dimensions, we establish the ground-state

phase diagram of the square lattice t-J model. On 8-leg cylinders approximating two-dimensional systems,

we demonstrate that the pure t-J model, for a wide range of hole doping (δ = 0.1 − 0.2), hosts an exotic

SC state where the unidirectional pair density wave and d-wave SC intertwine with the spin bond order and a

weak charge density wave. We reveal a simple mechanism for SC in the family of t-J models, in which the

nearest-neighbor hopping plays an essential role in driving the formation of Cooper pairs with real-space sign

oscillations balancing the competition between the kinetic and exchange energies. Furthermore, a small

next-nearest-neighbor hopping t2 suppresses the spin bond order and pair density wave, leading to a d-wave

SC phase in both electron- and hole-doped systems. Our work supports the t-J model as a proper platform for

describing fundamental physics of cuprate superconductors.