Superconducting order parameter symmetry for the extended Hubbard model below $T_c$

The extended Hubbard model is known to host $s$-wave, $d$-wave and $p$-wave superconducting phases depending on the values of the on-site and nearest-neighbour interactions. By examining the free energy functional of the gap in this model, we find that these symmetries are often dependent on temperature. The critical points of this functional are highly constrained by symmetry and allow us to formulate stringent conditions on the temperature profile of the gap function, applicable to other models as well. We discuss the finite temperature phase diagram of the extended Hubbard model, and point out the existence of first and second order symmetry transitions below $T_c$. Understanding the nature of these transitions may be important for assessing the symmetry of some unconventional superconductors such as UPt$_3$.