We thoroughly examine the ground state of the triangular lattice of Pb on Si(111) using scanning tunneling microscopy. We detect charge-order, accompanied by a subtle structural reconstruction. Applying the extended variational cluster approach we map out the phase diagram as a function of local and non-local Coulomb interactions. Comparing the experimental data with the theoretical modeling leads us to conclude that electron correlations are the driving force of the charge-ordered state in Pb/Si(111), rather than Fermi surface nesting. These results resolve the discussion about the origin of the well known $3times 3$ reconstruction forming below $86,$K. By exploiting the tunability of correlation strength, hopping parameters and bandfilling, this material class represents a promising platform to search for exotic states of matter, in particular, for chiral topological superconductivity.
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