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| Format: | Preprint |
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2026
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| Online Access: | https://arxiv.org/abs/2604.00606 |
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| _version_ | 1866914538834624512 |
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| author | Huang, Zhi-qiang Cai, Qing-yu |
| author_facet | Huang, Zhi-qiang Cai, Qing-yu |
| contents | We develop a resolvent-based self-consistent framework for strongly correlated many-body systems by reorganizing many-body expansions at the level of the resolvent rather than through perturbative expansions in a small parameter. Starting from the spectral representation of the diagonal Green's function, we derive an exact recursive hierarchy for the self-energy in terms of correlated multi-resolvent propagation processes. The resulting hierarchy remains formally closed in terms of diagonal resolvents and provides a systematically improvable description of fluctuations beyond mean-field theory.
The framework contains two complementary nonperturbative structures. The Lanczos continued-fraction representation governs recursive single-resolvent renormalization and generates non-Lorentzian spectral broadening beyond conventional self-consistent Born approximations (SCBA). By contrast, the multi-resolvent hierarchy introduces correlated frequency mixing through products of resolvents and Hilbert-transform couplings, providing a microscopic mechanism for spectral asymmetry and skewness absent in parity-preserving single-resolvent closures.
To solve the hierarchy, we introduce Lorentzian, Gaussian, and hybrid Voigt-type closure schemes together with an effective Faddeeva self-energy representation preserving analyticity and causality. Spectral broadening, tail structures, and higher-order fluctuation effects then emerge naturally from the interplay between recursive renormalization and multi-resolvent correlations. Unlike conventional diagrammatic resummations, the present approach does not rely on finite-order truncations or small expansion parameters. Instead, correlations are organized through an exact resolvent hierarchy combined with ETH-type statistical assumptions, making the framework particularly suitable for nonintegrable many-body systems with dense spectra. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2604_00606 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Resolvent-Based Self-Consistent Framework with Hierarchical Correlation Expansion for Strongly Correlated Many-Body Systems Huang, Zhi-qiang Cai, Qing-yu Quantum Physics We develop a resolvent-based self-consistent framework for strongly correlated many-body systems by reorganizing many-body expansions at the level of the resolvent rather than through perturbative expansions in a small parameter. Starting from the spectral representation of the diagonal Green's function, we derive an exact recursive hierarchy for the self-energy in terms of correlated multi-resolvent propagation processes. The resulting hierarchy remains formally closed in terms of diagonal resolvents and provides a systematically improvable description of fluctuations beyond mean-field theory. The framework contains two complementary nonperturbative structures. The Lanczos continued-fraction representation governs recursive single-resolvent renormalization and generates non-Lorentzian spectral broadening beyond conventional self-consistent Born approximations (SCBA). By contrast, the multi-resolvent hierarchy introduces correlated frequency mixing through products of resolvents and Hilbert-transform couplings, providing a microscopic mechanism for spectral asymmetry and skewness absent in parity-preserving single-resolvent closures. To solve the hierarchy, we introduce Lorentzian, Gaussian, and hybrid Voigt-type closure schemes together with an effective Faddeeva self-energy representation preserving analyticity and causality. Spectral broadening, tail structures, and higher-order fluctuation effects then emerge naturally from the interplay between recursive renormalization and multi-resolvent correlations. Unlike conventional diagrammatic resummations, the present approach does not rely on finite-order truncations or small expansion parameters. Instead, correlations are organized through an exact resolvent hierarchy combined with ETH-type statistical assumptions, making the framework particularly suitable for nonintegrable many-body systems with dense spectra. |
| title | Resolvent-Based Self-Consistent Framework with Hierarchical Correlation Expansion for Strongly Correlated Many-Body Systems |
| topic | Quantum Physics |
| url | https://arxiv.org/abs/2604.00606 |