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

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.

Minor updates from v1, 9 pages including Supplemental Material

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• Unconventional pairing originating from disconnected Fermi surfaces in superconducting LaFeAsO${}_{1-x}$F${}_x$}
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• Sum-rules and bath-parametrization for quantum cluster theories
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Cited by in corpus (8)

• Discrete Lehmann representation of imaginary time Green's functions
• Efficient ab initio many-body calculations based on sparse modeling of Matsubara Green's function
• Hybrid quantum-classical algorithm for computing imaginary-time correlation functions
• Decomposing imaginary time Feynman diagrams using separable basis functions: Anderson impurity model strong coupling expansion
• Stabilizing the calculation of the self-energy in dynamical mean-field theory using constrained residual minimization
• Compressing the two-particle Green's function using wavelets: Theory and application to the Hubbard atom
• Sparse modeling approach for quasiclassical theory of superconductivity
• Comparative study on compact quantum circuits of hybrid quantum-classical algorithms for quantum impurity models