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" graphene layers. 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, 14, 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 platform to study many-body interactions beyond the mean-field approach, where quantum fluctuations and entanglement dominate.