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

Quantum embedding theories can be used 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 and those of a 20-orbital impurity model for a high-T-c 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.

Automated summary

Quantum embedding theories can be used to describe correlated materials, but an effective impurity model of correlated orbitals embedded in an electron bath poses a challenge. This study proposes an efficient fitting algorithm for matrix-valued hybridization functions to address this issue, demonstrating its effectiveness in fitting hybridization functions and impurity models for high-Tc compounds.