Self-Consistent Spectral Quadrature Approach to Many-Body Green Functions
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arXiv
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| Format: | Preprint |
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2026
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| author | Kruchinin, Stanislav Yu. |
| author_facet | Kruchinin, Stanislav Yu. |
| contents | We develop a self-consistent spectral quadrature (sc-SQ) framework for the calculation of many-body Green functions. The method approximates the Källén--Lehmann spectral measure by Gauss--Christoffel (GC) quadrature, yielding a rational Green function representation with guaranteed spectral positivity that exactly reproduces the first $2N$ spectral moments at pole order $N$. A key component is an SVD-based rank-selection criterion on the Hankel matrix, which identifies the numerically resolvable pole rank $N^*$ from the singular-value gap and acts as a precision-guided diagnostic of correlation complexity. The scheme is made self-consistent by requiring that the spectral function used to evaluate expectation values coincides with the spectral function generated by the quadrature reconstruction. This defines a fixed-point hierarchy that connects systematically to established approximations, including Hartree--Fock and Hubbard-I, and incorporates non-perturbative features such as multi-peak spectral structure. We benchmark the approach for the Anderson impurity model against numerical renormalization group (NRG) results and apply it within dynamical mean-field theory for the Hubbard model on the Bethe lattice. The method captures the three-peak Anderson impurity spectrum and the suppression of quasiparticle weight in the half-filled Hubbard model on the Bethe lattice, including Mott-gap formation on the insulating branch for $N\geqslant 5$, in qualitative agreement with NRG references. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2605_26887 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Self-Consistent Spectral Quadrature Approach to Many-Body Green Functions Kruchinin, Stanislav Yu. Strongly Correlated Electrons Mesoscale and Nanoscale Physics We develop a self-consistent spectral quadrature (sc-SQ) framework for the calculation of many-body Green functions. The method approximates the Källén--Lehmann spectral measure by Gauss--Christoffel (GC) quadrature, yielding a rational Green function representation with guaranteed spectral positivity that exactly reproduces the first $2N$ spectral moments at pole order $N$. A key component is an SVD-based rank-selection criterion on the Hankel matrix, which identifies the numerically resolvable pole rank $N^*$ from the singular-value gap and acts as a precision-guided diagnostic of correlation complexity. The scheme is made self-consistent by requiring that the spectral function used to evaluate expectation values coincides with the spectral function generated by the quadrature reconstruction. This defines a fixed-point hierarchy that connects systematically to established approximations, including Hartree--Fock and Hubbard-I, and incorporates non-perturbative features such as multi-peak spectral structure. We benchmark the approach for the Anderson impurity model against numerical renormalization group (NRG) results and apply it within dynamical mean-field theory for the Hubbard model on the Bethe lattice. The method captures the three-peak Anderson impurity spectrum and the suppression of quasiparticle weight in the half-filled Hubbard model on the Bethe lattice, including Mott-gap formation on the insulating branch for $N\geqslant 5$, in qualitative agreement with NRG references. |
| title | Self-Consistent Spectral Quadrature Approach to Many-Body Green Functions |
| topic | Strongly Correlated Electrons Mesoscale and Nanoscale Physics |
| url | https://arxiv.org/abs/2605.26887 |