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Stripe versus superconductivity in the doped Hubbard model on the honeycomb lattice

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.