Stripes, pair density wave, and holon Wigner crystal in single-band Hubbard model on diagonal square lattice

We employ large-scale density-matrix renormalization group (DMRG) simulations to investigate the quantum phase diagram of the hole-doped Hubbard model on a square lattice. By implementing a diagonally oriented square lattice (rotated by π/4) and GPU-accelerated DMRG with up to 48000 states, we identify three distinct quantum phases across a doping range of δ = 5% to 15%: (i) A diagonal stripe phase (δ ≲ 9%) with short-range uniform superconductivity (SC); (ii) An interme- diate holon Wigner crystal phase exhibiting bidirectional charge-density order and short-range SC with spatial oscillating correlation; (iii) An unprecedented infinite-length stripe (i-stripe) phase at δ ≳ 12% hosting long charge/spin stripes spanning the whole lattice. Crucially, the short range SC in the crystallized phase fully develops into 2D-like pair density wave (PDW) order with divergent susceptibility in the i-stripe phase, constituting probably the first controlled numerical evidence of dominant PDW in the single-band square-lattice Hubbard model. The observed modulation of PDW along the i-stripes and the evolution from short-range SC to robust PDW provide new perspectives on dynamical layer decoupling phenomena and the multifaceted relationships between charge, spin and SC orders in cuprates and related quantum materials.