Stripe correlations in the two-dimensional Hubbard-Holstein model

TL;DR

This study investigates how electron-phonon interactions influence stripe correlations in the doped two-dimensional Hubbard-Holstein model, revealing that lattice coupling can enhance or suppress stripe order depending on parameters, thus affecting the balance with superconductivity.

Contribution

It provides the first detailed analysis of the impact of electron-phonon coupling on stripe correlations in the Hubbard-Holstein model using advanced numerical methods.

Findings

Lattice coupling affects charge component of stripes more strongly.

Electron-phonon interaction can enhance or suppress stripe correlations.

Results suggest e-ph interaction influences the competition between stripe and superconducting phases.

Abstract

Several state-of-the-art numerical methods have observed static or fluctuating spin and charge stripes in doped two-dimensional Hubbard models, suggesting that these orders play a significant role in shaping the cuprate phase diagram. Many experiments, however, also indicate that the cuprates have strong electron-phonon ($e$-ph) coupling, and it is unclear how this interaction influences stripe correlations. We study static and fluctuating stripe orders in the doped singleband Hubbard-Holstein model using zero temperature variational Monte Carlo and finite temperature determinant quantum Monte Carlo. We find that the lattice couples more strongly with the charge component of the stripes, leading to an enhancement or suppression of stripe correlations, depending on model parameters like the next-nearest-neighbor hopping $t^\prime$ or phonon energy $\Omega$. Our results help elucidate how the $e$-ph interaction can tip the delicate balance between stripe and superconducting correlations in the Hubbard-Holstein model with implications for our understanding of the high-$T_\mathrm{c}$ cuprates.