Zero and Finite Temperature Phase Diagram of the Spinless Fermion Model in Infinite Dimensions

The phase diagram of the model of spinless fermions with repulsive nearest neighbour interaction is calculated analytically on a hypercubic lattice in infinite dimensions $(d\to \infty)$. In spite of its simplicity the model displays a rich phase diagram depending on the doping $\delta$, the interaction $U$ and the temperature $T$. The system can be in the homogeneous phase (HOM), the nonsegregated AB charge density wave (AB-CDW), the AB phase separation region (PS-AB/HOM; coexistence of AB-CDW and HOM), the incommensurate phase (IP) or the IP phase separation region (PS-AB/IP; coexistence of AB-CDW and IP). We identify three important values of the interaction $U_{IPL}=0.572< U_{IPH}=1.914<U_{IP/PS}=4.212$ which distinguish four intervals of $U$. These imply four different types of phase diagrams. In all the three phase diagrams with $U$ below $U_{IP/PS}$ the IP appears. We propose a {\em new} general ansatz for the order parameter of this phase. A competition between the IP, the PS-AB/IP and the PS-AB/HOM is found. The relevance of our findings for the phase scenario of the Hubbard model is shown.