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Recently two interesting candidate quantum phases --- the chiral spin densitywave state featuring anomalous quantum Hall effect and the d+id superconductor--- were proposed for the Hubbard model on the honeycomb lattice at 1/4 doping.Using a combination of exact diagonalization, density matrix renormalizationgroup, the variational Monte Carlo method and quantum field theories, we studythe quantum phase diagrams of both the Hubbard model and t-J model on thehoneycomb lattice at 1/4-doping. The main advantage of our approach is the useof symmetry quantum numbers of ground state wavefunctions on finite sizesystems (up to 32 sites) to sharply distinguish different quantum phases. Ourresults show that for $1\lesssim U/t< 40$ in the Hubbard model and for $0.1<J/t<0.80(2)$ in the t-J model, the quantum ground state is either a chiral spindensity wave state or a spin-charge-Chern liquid, but not a d+idsuperconductor. However, in the t-J model, upon increasing $J$ the system goesthrough a first-order phase transition at $J/t=0.80(2)$ into the d+idsuperconductor. Here the spin-charge-Chern liquid state is a new type oftopologically ordered quantum phase with Abelian anyons and fractionalizedexcitations. Experimental signatures of these quantum phases, such as tunnelingconductance, are calculated. These results are discussed in the context of1/4-doped graphene systems and other correlated electronic materials on thehoneycomb lattice.

Chiral spin density wave, spin-charge-Chern liquid and d+id superconductivity in 1/4-doped correlated electronic systems on the honeycomb lattice