FERMIONIC LATTICE MODELS WITH INTERNALLY COMPETING SYMMETRIES - NONTRIVIAL ALGEBRAIC CORRECTIONS IN THE HARTREE-FOCK GROUND-STATE ENERGY

We show that even for homogeneous ground states the Hartree-Fock (HF) energy of fermionic lattice models may contain nontrivial algebraic corrections in the interaction. Hence the standard HF result for the energy, i.e., the linear dependence on the interaction, is found to be nongeneric. Algebraic corrections will appear in the HF energy whenever the k-space symmetry of the interaction is different from that of the kinetic energy, this being the generic case. The ensuing symmetry conflict leads to a distortion of the noninteracting Fermi surface. The energy corrections are explicitly evaluated for a generalized, two-dimensional Hubbard model with nearest-neighbor hopping and interaction along the diagonal. Algebraic corrections in the HF ground-state energy due to spontaneously broken symmetries may only occur if epsilon(k), the dispersion of free particles, has a special form.