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

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