Static stripe order in the two-dimensional Hubbard-Holstein model

The competition of coupled spin and charge orders (i.e. stripes) with unconventional superconductivity has been experimentally observed in high temperature (high-T_c) cuprate superconductors. Several state-of-the-art numerical methods have also observed these orders in single- and three-band Hubbard models. While strong electron-phonon (e-ph) coupling has been seen in the cuprates, it is unclear how they might influence stripe correlations. We study the static stripe order in the doped two-dimensional Hubbard-Holstein model using zero temperature variational Monte Carlo. We observe that the lattice degrees of freedom can enhance the charge component of the stripes while suppressing the spin component for some values of the next-nearest-neighbor hopping t′. However, we also find that VMC predicts an increased tendency towards phase separation in many instances. Our results show that e-ph interactions can be an important factor in establishing stripe or superconducting correlations in the Hubbard-Holstein model, with implications for the high-T_c cuprates.