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In crystalline solids the interactions of charge and spin can result in avariety of emergent quantum ground states, especially in partially filled,topological flat bands such as Landau levels or in 'magic-angle' bilayergraphene. Much less explored is rhombohedral graphite (RG), perhaps thesimplest and structurally most perfect condensed matter system to host a flatband protected by symmetry. By scanning tunneling microscopy we map the flatband charge density of 8, 10 and 17 layers and identify a domain structureemerging from a competition between a sublattice antiferromagnetic insulatorand a gapless correlated paramagnet. Our density-matrix renormalization groupcalculations explain the observed features and demonstrate that thecorrelations are fundamentally different from graphene based magnetismidentified until now, forming the ground state of a quantum magnet. Our workestablishes RG as a new platform to study many-body interactions beyond themean-field approach, where quantum fluctuations and entanglement dominate.

Observation of competing, correlated ground states in the flat band of rhombohedral graphite