Phase diagram of the two-dimensional Hubbard-Holstein model

Electron-phonon correlations are integral to understand the properties of conventional superconductors but it is also thought they may be important for unconventional high-Tc superconductivity. Here, the authors investigate the interplay between antiferromagnetic ordering and charge density wave formation in 2D square lattice Hubbard-Holstein model at half-filling using unbiased quantum Monte Carlo simulations, and demonstrate an intermediate phase with enhancement of s-wave pairing correlations. The electron-electron and electron-phonon interactions play an important role in correlated materials, being key features for spin, charge and pair correlations. Thus, here we investigate their effects in strongly correlated systems by performing unbiased quantum Monte Carlo simulations in the square lattice Hubbard-Holstein model at half-filling. We study the competition and interplay between antiferromagnetism (AFM) and charge-density wave (CDW), establishing its very rich phase diagram. In the region between AFM and CDW phases, we have found an enhancement of superconducting pairing correlations, favouring (nonlocal) s-wave pairs. Our study sheds light over past inconsistencies in the literature, in particular the emergence of CDW in the pure Holstein model case.