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Quantum embedding theories provide a feasible route for obtainingquantitative descriptions of correlated materials. However, a criticalchallenge is solving an effective impurity model of correlated orbitalsembedded in an electron bath. Many advanced impurity solvers require theapproximation of a bath continuum using a finite number of bath levels,producing a highly nonconvex, ill-conditioned inverse problem. To address thisdrawback, this study proposes an efficient fitting algorithm for matrix-valuedhybridization functions based on a data-science approach, sparse modeling, anda compact representation of Matsubara Green's functions. The efficiency of theproposed method is demonstrated by fitting random hybridization functions withlarge off-diagonal elements as well as those of a 20-orbital impurity model fora high-Tc compound, LaAsFeO, at low temperatures (T). The results setquantitative goals for the future development of impurity solvers towardquantum embedding simulations of complex correlated materials.

Sparse modeling of large-scale quantum impurity models with low symmetries