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arXiv · 2007.03955

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

Hiroshi Shinaoka·Yuki Nagai
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Abstract

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.

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Hiroshi Shinaoka, Yuki Nagai. 2020-08-03. Sparse modeling of large-scale quantum impurity models with low symmetries. https://doi.org/10.1103/physrevb.103.045120

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