  We study the ground state of the doped Hubbard model on the honeycomb lattice
in the small doping and strongly interacting region. The nature of the ground
state by doping holes into the anti-ferromagnetic Mott insulating states on the
honeycomb lattice remains a long-standing unsolved issue, even though
tremendous efforts have been spent to investigate this challenging problem. An
accurate determination of the ground state in this system is crucial to
understand the interplay between the topology of Fermi surface and strong
correlation effect. In this work, we employ two complementary,
state-of-the-art, many-body computational methods -- constrained path (CP)
auxiliary-field quantum Monte Carlo (AFQMC) with self-consistent constraint and
density matrix renormalization group (DMRG) methods. Systematic and detailed
cross-validations are performed between these two methods for narrow systems
where DMRG can produce reliable results. AFQMC are then utilized to study wider
systems to investigate the thermodynamic limit properties. The ground state is
found to be a half-filled stripe state in the small doping and strongly
interacting region. The pairing correlation shows $d$-wave symmetry locally,
but decays exponentially with the distance between two pairs.
