  Quantum embedding (QE) methods such as the Ghost Gutzwiller Approximation
(gGA) offer a powerful approach to simulating strongly-correlated systems, but
come with the computational bottleneck of computing the ground state of an
auxiliary embedding Hamiltonian (EH) iteratively. In this work, we introduce an
active learning (AL) framework integrated within the gGA to address this
challenge. The methodology is applied to the single-band Hubbard model and
results in a significant reduction in the number of instances where the EH must
be solved. Through a principal component analysis (PCA), we find that the EH
parameters form a low-dimensional structure that is largely independent of the
geometric specifics of the systems, especially in the strongly-correlated
regime. Our AL strategy enables us to discover this low-dimensionality
structure on the fly, while leveraging it for reducing the computational cost
of gGA, laying the groundwork for more efficient simulations of complex
strongly-correlated materials.
