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

TL;DR

The paper addresses how charge stripe order and interlayer superconductivity compete in a sign-problem-free bilayer extended Hubbard model. It employs projector quantum Monte Carlo within a time-reversal-invariant formulation to map out how interlayer spin-exchange anisotropy ($J_z$ and $J_ot$) and on-site interaction $U$ control these orders. The main findings show that a stripe phase arises under highly anisotropic interlayer coupling and is suppressed by the spin-flip term, which in turn enhances interlayer pairing superconductivity; the role of $U$ is doping-dependent and can either suppress or enhance superconductivity depending on stripe presence. These results shed light on competing orders in strongly correlated systems and connect to stripe phenomena observed in cuprate-like models, offering a pathway to tune superconductivity via interlayer interactions.

Abstract

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 $k_x=2πδ$ is induced by highly anisotropic interlayer spin-exchange coupling $J_z$, and strongly suppressed upon introducing the spin-flip term $J_\bot$; 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.

Figures (6)

• Figure 1: The charge correlation function $S_{ch}(\mathbf{k})$ from momentum $k=(-\pi, 0)$ to $k=(\pi, 0)$ for different hole doping densities $\delta$ at on-site interaction $U=2.0$ with pure z-component interlayer spin-exchange $J_{z}=4U$. The peak indicates charge stripe order. We fix $L_y=8$ and $L_x = 2/\delta$ in our simulations.
• Figure 2: The charge correlation function $S_{ch}(k_{x},0)$ at $U=2.0$ for different $J_{\bot}$ and $J_{z}$ in the system of (a) $L_{x}=16$, $L_{y}=8$ at $1/8$ doping and (b) $L_{x}=12$, $L_{y}=8$ at $1/6$ doping.
• Figure 3: The charge correlation function $S_{ch}(k_{x},0)$ for different values of $U$ with doping $\delta = 1/8$ (dashed line) and $\delta = 1/6$ (solid line) at (a) $J_{z} = 7.2$ and $J_{\bot}=0.4$ and (b) $J_{z} = 11.0$ and $J_{\bot}=0.5$.
• Figure 4: The pairing correlation function $S_{sc}$ as a function of electron filling $\langle n\rangle$ for different values of $J_{z}$ and $J_{\bot}$ at (a) $U=2.0$ and (b) $U=3.0$. The system size is $L_{x}=8$ and $L_{y}=8$.
• Figure 5: The pairing correlation function $S_{sc}$ as a function of electron interaction $U$ for fixed values of $J_{z}$ and $J_{\bot}$ at (a) $\langle n \rangle = 0.5$ and (b) $\langle n \rangle = 0.875$. The system size is $L_{x}=L_{y}=8$.