  The Su-Schrieffer-Heeger (SSH) model, with bond phonons modulating electron
tunneling, is a paradigmatic electron-phonon model that hosts an
antiferromagnetic order to bond order transition at half-filling. In the
presence of repulsive Hubbard interaction, the antiferromagnetic phase is
enhanced, but the phase transition remains first-order. Here we explore the
physics of the SSH model with attractive Hubbard interaction, which hosts an
interesting interplay among charge order, s-wave pairing, and bond order. Using
the numerically exact determinant quantum Monte Carlo method, we show that both
charge order, present at weak electron-phonon coupling, and bond order, at
large coupling, give way to s-wave pairing when the system is doped.
Furthermore, we demonstrate that the SSH electron-phonon interaction competes
with the attractive Hubbard interaction and reduces the s-wave pairing
correlation.
