Charge density wave solutions of the Hubbard model in the composite operator formalism

We investigate the charge density wave phase in the strongly correlated Hubbard model without any other broken symmetry phase. Starting from the atomic Hamiltonian with no hopping, we generate quasiparticle operators corresponding to holons and doublons in the strongly correlated limit of the repulsive Hubbard model. We develop a real-space composite operator formalism using the equation of motion technique to include the intersite hopping perturbatively. Our fully self-consistent calculation stabilizes multiple unidirectional translation symmetry broken states within the doping range $\ensuremath{\delta}=0.07\ensuremath{-}0.2$. The charge-ordered states become increasingly unfavorable with hole doping. The unidirectional density waves manifest as periodic modulations of half-filled Mott regions separated by hole-rich regions. Notably, density wave solutions with periods of 3--8 lattice spacing remain energetically higher than those with larger periods. Quenched disorder on the charge-ordered states induces the merging of the Mott regions and, consequently, forms short-ranged charge modulations. The density of states shows signatures of strongly correlated Mott regions, potentially relevant to the physics of underdoped cuprates.