Pair density wave, infinite-length stripes, 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 square lattices. By implementing a diagonally oriented square lattice and GPU-accelerated DMRG with up to $48000$ states, we identify three distinct quantum phases across $\delta =5\mathrm{\%}$ to $15\mathrm{\%}$ doping: (i) A diagonal stripe phase with short-range uniform superconductivity (SC) at lower doping $\delta \lesssim 9\mathrm{\%}$; (ii) An intermediate holon Wigner crystal (WC*) phase exhibiting bidirectional charge-density order and short-range SC with spatial oscillating correlations; (iii) An unprecedented infinite-length stripe (i-stripe) phase at $\delta \gtrsim 12\mathrm{\%}$ hosting long stripes spanning the whole lattice. Remarkably, as doping increases, the short-range SC in WC* phase evolves into a 2D-like pair density wave (PDW) 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 established 2D-like PDW and its interplay with charge orders provide new perspectives on dynamical layer decoupling phenomena in cuprates and multifaceted relationships between charge, spin and SC orders in quantum materials.