Charge stripe and superconductivity tuned by interlayer interaction in a sign-problem-free bilayer extended Hubbard model

Competing orders represent a central challenge in understanding strongly correlated systems. In this work, we employ projector quantum Monte Carlo simulations to study a sign-problem-free bilayer extended Hubbard model. In this model, a charge stripe phase, characterized by a peak at momentum $k_x=2\pi \delta$ is induced by highly anisotropic interlayer spin-exchange coupling $J_z$, and strongly suppressed upon introducing the spin-flip term $J_{\mathrm{\perp }}$; in contrast, $J_{\perp }$ favors the emergence of interlayer pairing superconductivity. We further demonstrate that the anisotropy of the interlayer spin-exchange directly governs the competition between these two phases, while the on-site interaction $U$ plays a complex role in tuning both the charge stripe and superconductivity. Our work identifies the key factors driving charge stripe formation, highlights the sensitivity of both the charge stripe and superconducting phases to interaction parameters, and thereby provides valuable insights into competing orders in strongly correlated systems.