Competing phases of the Hubbard model on a triangular lattice: Insights from the entropy

In this Rapid Communication, we present a comprehensive study of the Hubbard model on the isotropic triangular lattice by using the recently developed ladder dual-fermion approach. This method is a nonlocal extension of the dynamical mean-field theory and is free of finite-size effect. In addition to confirming the much-discussed phase diagram at half-filling, our work provides insights into both hole- and electron-doped regimes and, in particular, the finite-temperature phase diagrams. We find the triangular system to be short-range correlated with an associated magnetic phase diagram, which is asymmetric with respect to hole and electron doping. In contrast to the unfrustrated lattice, it can adiabatically be cooled by increasing the interactions. Strikingly, at the electron-doped side, the entropy displays a maximum. This latter example, as well as other results of our work, may provide insights for a variety of correlated triangular materials, such as the water-intercalated sodium-doped cobaltates