Superconductivity in the lightly doped Hubbard model on the cylindrical honeycomb lattice

We have performed large-scale density-matrix renormalization group studies of the lightly doped Hubbard model on the honeycomb lattice using three- and four-leg cylinders. At our largest accessible MPS bond dimension, together with extrapolation analysis, we find a variational ground state with coexisting quasi-long-range superconducting and charge density wave orders upon light doping. Both the superconducting and charge density wave correlations decay as power laws at long distances, with corresponding exponents Ksc<2 and Kc<2. In contrast, the spin-spin and single-particle correlations decay exponentially, although with relatively long correlation lengths.