Renormalization of spectra by phase competition in the half-filled Hubbard-Holstein model

We present electron and phonon spectral functions calculated from determinant quantum Monte Carlo simulations of the half-filled two-dimensional Hubbard-Holstein model on a square lattice. By tuning the relative electron-electron (e-e) and electron-phonon (e-ph) interaction strengths, we show the electron spectral function evolving between antiferromagnetic insulating, metallic, and charge-density-wave (CDW) insulating phases. The phonon spectra concurrently gain a strong momentum dependence and soften in energy upon approaching the CDW phase. In particular, we study how the e-e and e-ph interactions renormalize the spectra and find that the presence of both interactions suppresses the amount of renormalization at low energy, thus allowing the emergence of a metallic phase at intermediate coupling strengths. In addition, we find a modest enhancement of the d-wave pairing susceptibility in the metallic regime, although spin and charge correlations are still dominant at the temperatures considered in our study. These findings demonstrate the importance of considering the influence of multiple interactions in spectroscopically determining any one interaction strength in strongly correlated materials.