Abstract
Correlated systems with hexagonal layered structures have come to thefore with renewed interest in cobaltates, transition metal dichalcogenides andGdI2. While superconductivity, unusual metal and possible exotic states (prevented fromlong-range order by strong local fluctuations) appear to come from frustration andcorrelation working in tandem in such systems, they freeze at a lower temperature tocrystalline states. The underlying effective Hamiltonian in some of these systems is believedto be the Falicov–Kimball model and therefore, a thorough study of the ground state ofthis model and its extended version on a non-bipartite lattice is important. Using a MonteCarlo search algorithm, we identify a large number of different possible ground states withcharge order as well as valence and metal–insulator transitions. Such competing states,close in energy, give rise to complex charge order and other broken symmetry structures aswell as the phase segregations observed in the ground state of these systems.
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