Strong ferromagnetic fluctuations in a doped checkerboard lattice

Using the determinant quantum Monte Carlo method, we study the magnetic susceptibility in the parameter space of the on-site interaction $U$, temperature $T$, electron filling $\text{avg}n$, and the frustration control parameter $t^{\mathrm{\prime }}$ within the Hubbard model on a two-dimensional checkerboard lattice. It is shown that the system exhibits stable and strong ferromagnetic fluctuations about the electron filling $\text{avg}n\ge 1.2$ for different $t^{\mathrm{\prime }}$, and the ferromagnetic susceptibility is strongly enhanced by the increasing interaction and decreasing tempeture. We also discuss the sign problem to clarify which parameter region is accessible and reliable. Our findings not only demonstrate important implications for modulating magnetism in the checkerboard lattice, but will also provide a theoretical platform for a flat-band model that demonstrates a variety of physical properties.