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Based on the ladder dual-fermion approach, we present a comprehensive studyof the phases of the isotropic Hubbard model on the triangular lattice. We finda rich phase diagram containing most of the phases that have already beenexperimentally observed in systems where the interplay between geometricfrustration and electronic correlations is important: paramagnetic metal,paramagnetic insulator, Mott-insulator with $120^{\circ}$ antiferromagnetic anda non-magnetic insulating state, i.e. possibly a spin liquid state. Thisestablishes that the Hubbard model on frustrated lattices can serve as aminimal model to address the intricate interplay of frustration andcorrelation. We also show that entropic considerations can be successfully usedfor understanding many striking features of the triangular systems, such as thelarge thermopower found in Na$_{x}$CoO$_{2}\cdot$$y$H$_{2}$O.

Competing phases of the Hubbard model on a triangular lattice -- insights from the entropy