Systems of adatoms on semiconductor surfaces display competing ground states and exotic spectral properties typical of two-dimensional correlated electron materials which are dominated by a complex interplay of spin and charge degrees of freedom. We report a fully ab initio derivation of low-energy Hamiltonians for the adatom systems $\mathrm{Si}(111):X$, with $X=\mathrm{Sn}$, Si, C, Pb, that we solve within self-consistently combined $GW$ and dynamical mean-field theory. Calculated photoemission spectra are in agreement with available experimental data. We rationalize experimentally observed trends from Mott physics toward charge ordering along the series as resulting from substantial long-range interactions.

• Received 17 January 2013

DOI:https://doi.org/10.1103/PhysRevLett.110.166401