Stability of the coexistent superconducting-nematic phase under the presence of intersite interactions

We analyze the effect of intersite-interaction terms on the stability of the coexisting superconucting-nematic phase (SC+N) within the extended Hubbard and $t$-$J$-$U$ models on the square lattice. In order to take into account the correlation effects with a proper precision, we use the approach based on the \textit{diagrammatic expansion of the Gutzwiller wave function} (DE-GWF), which goes beyond the renormalized mean field theory (RMFT) in a systematic manner. As a starting point of our analysis we discuss the stability region of the SC+N phase on the intrasite Coulomb repulsion-hole doping plane for the case of the Hubbard model. Next, we show that the exchange interaction term enhances superconductivity while suppresses the nematicity, whereas the intersite Coulomb repulsion term acts in the opposite manner. The competing character of the SC and N phases interplay is clearly visible throughout the analysis. A universal conclusion is that the nematic phase does not survive within the $t$-$J$-$U$ model with the value of $J$ integral typical for the high-T$_C$ cuprates ($J\approx 0.1$eV). For the sake of completeness, the effect of the correlated hopping term is also analyzed. Thus the present discussion contains all relevant two-site interaction terms which appear in the parametrized one-band model within the second quantization scheme. At the end, the influence of the higher-order terms of the diagrammatic expansion on the rotational symmetry breaking is also shown by comparing the DE-GWF results with those corresponding to the RMFT.