  Quantum embedding theories provide a feasible route for obtaining
quantitative descriptions of correlated materials. However, a critical
challenge is solving an effective impurity model of correlated orbitals
embedded in an electron bath. Many advanced impurity solvers require the
approximation of a bath continuum using a finite number of bath levels,
producing a highly nonconvex, ill-conditioned inverse problem. To address this
drawback, this study proposes an efficient fitting algorithm for matrix-valued
hybridization functions based on a data-science approach, sparse modeling, and
a compact representation of Matsubara Green's functions. The efficiency of the
proposed method is demonstrated by fitting random hybridization functions with
large off-diagonal elements as well as those of a 20-orbital impurity model for
a high-Tc compound, LaAsFeO, at low temperatures (T). The results set
quantitative goals for the future development of impurity solvers toward
quantum embedding simulations of complex correlated materials.
