Geometrical frustration of an extended Hubbard diamond chain in the quasiatomic limit

We study the geometrical frustration of an extended Hubbard model on a diamond chain, where vertical lines correspond to the hopping and repulsive Coulomb interaction terms between sites while the remaining lines represent only the Coulomb repulsion term. The phase diagrams at zero temperature show quite curious phases: five types of frustrated states and four types of nonfrustrated states, ordered antiferromagnetically. Although a decoration transformation was derived for spin-coupling systems, this approach can be applied to electron-coupling systems. Thus the extended Hubbard model can be mapped onto another effective extended Hubbard model in the atomic limit with additional three- and four-body couplings. This effective model is solved exactly using the transfer-matrix method. In addition, using the exact solution of this model, we discuss several thermodynamic properties away from the half-filled band, such as chemical potential behavior, electronic density, and entropy, for which we study geometrical frustration. Consequently, we investigate the specific heat as well.