  Nematicity is a well known property of liquid crystals and has been recently
discussed in the context of strongly interacting electrons. An electronic
nematic phase has been seen by many experiments in certain strongly correlated
materials, in particular, in the pseudogap phase generic to many hole-doped
cuprate superconductors. Recent measurements in high $T_c$ superconductors has
shown even if the lattice is perfectly rotationally symmetric, the ground state
can still have strongly nematic local properties. Our study of the
two-dimensional Hubbard model provides strong support of the recent
experimental results on local rotational $C_4$ symmetry breaking. The
variational cluster approach is used here to show the possibility of an
electronic nematic state and the proximity of the underlying symmetry-breaking
ground state within the Hubbard model. We identify this nematic phase in the
overdoped region and show that the local nematicity decreases with increasing
electron filling. Our results also indicate that strong Coulomb interaction may
drive the nematic phase into a phase similar to the stripe structure. The
calculated spin (magnetic) correlation function in momentum space shows the
effects resulting from real-space nematicity.
