  We study the ground state properties of the doped Hubbard model with strong
interactions on honeycomb lattice by the Density Matrix Renormalization Group
(DMRG) method. At half-filling, due to the absence of minus sign problem, it is
now well established by large-scale Quantum Monte Carlo calculations that a
Dirac semi-metal to anti-ferromagnetic Mott insulator transition occurs with
the increase of the interaction strength $U$ for the Hubbard model on honeycomb
lattice. However, an understanding of the fate of the anti-ferromagnetic Mott
insulator when holes are doped into the system is still lacking. In this work,
by calculating the local spin and charge density for width-4 cylinders with
DMRG, we discover a half-filled stripe order in the doped Hubbard model on
honeycomb lattice. We also perform complementary large-scale mean-field
calculations with renormalized interaction strength. We observe half-filled
stripe order and find stripe states with filling close to one half are nearly
degenerate in energy.

Strongly Correlated Electrons;Superconductivity