At sufficiently low temperatures, condensed-matter systems tend to develop order. An exception are quantum spin-liquids, where fluctuations prevent transition to an ordered state down to the lowest temperatures. Using large-scale quantum Monte Carlo simulations, we found a quantum spin-liquid phase of correlated electrons on the honeycomb lattice, this spin-liquid emerges between the state described by massless Dirac fermions and an antiferromagnetically ordered Mott insulator, and is found to be a short-range resonating valence bond liquid, akin to the one proposed for high temperature superconductors. We also extend the quantum Monte Carlo study of correlated electrons to honeycomb ribbons, where we are investigating the possibility of having edge magnetism on zigzag edges.