Molecular building blocks provide a versatile platform for exploring the exotic quantum phases and complex many-body physics. Here we demonstrate a showcase system based on pure-carbon, defect-free, charge-neutral fullerene networks, which can be constructed from a molecular synthon with quantised spins due to symmetry. We report a rich variety of condensed matter models that are challenging to realise, including antiferromagnetic spin-1/2 chain in Janus fullerene nanoribbons, ferromagnetic Haldane fullerene monolayers, and altermagnetic Shastry-Sutherland fullerene networks that can be continuously tuned into a quantum spin liquid phase. Our findings open new a frontier for exploring quantum phenomena based on scalable, chemically-stable, molecular building units can potentially operate at room temperature.
