Capturing spin fluctuations in CaCuO$_2$: $\textit{Ab initio}$ QMC calculations with multi-determinant wave functions

We present an advanced $\textit{ab initio}$ quantum Monte Carlo (QMC) calculation of the ground state of undoped CaCuO$_2$. We extend the traditional single-determinant Slater-Jastrow approach to include multi-determinant wave functions, inhomogeneous Jastrow factors, and orbital optimization. Our results demonstrate not only an improvement in the variational bound of the ground state energy -- 2.3 eV per formula unit lower than previous state of the art techniques -- but also confirm the presence of spin fluctuations in multi-determinant wave functions in a strongly correlated cuprate system, which is integral to understanding high-$T_c$ superconductivity. This is the first demonstration of capturing spin fluctuations in QMC wave functions on a cuprate, establishing the groundwork for new studies on doped cuprates in the superconducting state, where spin fluctuations require more accurate characterization.