Nematic phase in a two-dimensional Hubbard model at weak coupling and finite temperature

We apply the self-consistent renormalized perturbation theory to the Hubbard model on the square lattice at finite temperatures to study the evolution of the Fermi surface (FS) as a function of temperature and doping. Previously, a nematic phase for the same model has been reported to appear at weak coupling near a Lifshitz transition from closed to open FS at zero temperature where the self-consistent renormalized perturbation theory was shown to be sensitive to small deformations of the FS. We find that the competition with the superconducting order leads to a maximal nematic order appearing at nonzero temperature. We explicitly observe the two competing phases near the onset of nematic instability, and by comparing the grand canonical potentials, we find that the transitions are first order. We explain the origin of the interaction-driven spontaneous symmetry breaking to a nematic phase in a system with several symmetry-related Van Hove points and discuss the required conditions.