Triangular-lattice systems attract a lot of attention due to various frustration-induced and strongly correlated effects. Here, we focus on the charge-ordering phenomenon by means of investigation of the extended Hubbard model with dynamical mean-field theory (DMFT). By considering the intersite nearest-neighbor interaction we have found a very rich phase diagram that contains a large number of features, phases, and phase transitions. Among them are site-selective Mott transitions; pinball-liquid (PL) phases where we distinguish charge-transfer-driven and Mott-localization-driven PLs; phase transitions that change their order as model parameters evolve (from discontinuous to continuous); very strong particle-hole asymmetry. Various features of the phase diagram are found to be better understood by means of the simple mean-field approximation (MFA). Moreover, besides helping with interpretation of the phase diagram, the MFA results together with results for the atomic-limit model are found to be able to set rather good expectations on how the DMFT phase diagram should look. Nevertheless, a few features were not expected and are found within the DMFT, such as a small-region intermediate metallic phase on an electron-doped side of the phase diagram.

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• Charge order
• Phase transitions
• Quantum phase transitions
• Lattice models in statistical physics
• Mott insulators
• Strongly correlated systems
• Triangular lattice
• Two-dimensional electron gas
• Two-dimensional electron system
• Dynamical mean field theory
• Extended Hubbard model
• Lattice models in condensed matter