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

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