  At sufficiently low temperatures, condensed-matter systems tend to develop
order. An exception are quantum spin-liquids, where fluctuations prevent a
transition to an ordered state down to the lowest temperatures. While such
states are possibly realized in two-dimensional organic compounds, they have
remained elusive in experimentally relevant microscopic two-dimensional models.
Here, we show by means of large-scale quantum Monte Carlo simulations of
correlated fermions on the honeycomb lattice, a structure realized in graphene,
that a quantum spin-liquid emerges between the state described by massless
Dirac fermions and an antiferromagnetically ordered Mott insulator. This
unexpected quantum-disordered state is found to be a short-range resonating
valence bond liquid, akin to the one proposed for high temperature
superconductors. Therefore, the possibility of unconventional superconductivity
through doping arises. We foresee its realization with ultra-cold atoms or with
honeycomb lattices made with group IV elements.
