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.

电子-电子和电子-声子相互作用在相关材料中起重要作用，是自旋，电荷和对相关的关键特征。因此，在这里我们通过在半填充时在方格Hubbard-Holstein模型中执行无偏量子蒙特卡洛模拟来研究它们在强相关系统中的作用。我们研究了反铁磁（AFM）与电荷密度波（CDW）之间的竞争和相互作用，建立了非常丰富的相图。在AFM和CDW相之间的区域中，我们发现超导配对相关性得到了增强，有利于（非局部）s波对。我们的研究揭示了过去文献中的矛盾，特别是在纯Holstein模型案例中CDW的出现。