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Charge- and pair-density-wave orders in the one-band Hubbard model with dynamical mean field theory

We study the charge-density-wave order and its competition with superconductivity in the one-band Hubbard model for high-$T_c$ superconducting cuprates. We use cluster dynamical mean field theory (CDMFT) at $T=0$. The one-band Hubbard model only contains copper atoms, and a physical charge-density-wave with charge excesses located on the oxygen atoms manifests itself as a bond-density-wave (BDW) within this context. It arises purely out of local correlation effects and also leads to a $s'$-wave pair-density-wave in the presence of $d$-wave superconductivity. The $d$-wave BDW is suppressed on increasing $U$ and is favored on increasing the magnitude of the second-neighbor hopping $t'$. Further, the $d$-wave BDW order is weakened when in competition with superconductivity, as seen in experiments. Additionally it behaves quite differently on varying $U$ in the superconducting state compared to the normal state.