  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.
