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| Main Authors: | , , |
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| Format: | Preprint |
| Published: |
2025
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2511.02292 |
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| _version_ | 1866917058059436032 |
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| author | Li, Hui Li, Ziyu Yu, Chen-run |
| author_facet | Li, Hui Li, Ziyu Yu, Chen-run |
| contents | The accurate simulation of strongly correlated electron systems remains a central challenge in condensed matter physics, motivating the development of various non-perturbative many-body methods. Such methods are typically benchmarked against the numerical exact determinant quantum Monte Carlo (DQMC) in the Hubbard model; however, DQMC is limited by the fermionic sign problem and the uncertainties of numerical analytic continuation. To address these issues, we use the exactly solvable Hatsugai-Kohmoto (HK) model as a benchmarking platform to evaluate three many-body approximations: $GW$, $HGW$, and $SGW$. We compare the Green's functions, spectral functions, and response functions obtained from these approximations with the exact solutions. Our analysis shows that the $GW$ approximation, often considered insufficient for describing strong correlation, exhibits a previously unreported solution branch that accurately reproduces Mott physics in the HK model. In addition, using a covariant formalism, we find that $HGW$ provides an accurate description of charge response, while $SGW$ performs well for spin correlations. Overall, our work demonstrates that the HK model can effectively benchmark many-body approximations and helps refine the understanding of $GW$ methods in strongly correlated regimes. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2511_02292 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Benchmarking Non-perturbative Many-Body Approaches in the Exactly Solvable Hatsugai-Kohmoto Model Li, Hui Li, Ziyu Yu, Chen-run Strongly Correlated Electrons The accurate simulation of strongly correlated electron systems remains a central challenge in condensed matter physics, motivating the development of various non-perturbative many-body methods. Such methods are typically benchmarked against the numerical exact determinant quantum Monte Carlo (DQMC) in the Hubbard model; however, DQMC is limited by the fermionic sign problem and the uncertainties of numerical analytic continuation. To address these issues, we use the exactly solvable Hatsugai-Kohmoto (HK) model as a benchmarking platform to evaluate three many-body approximations: $GW$, $HGW$, and $SGW$. We compare the Green's functions, spectral functions, and response functions obtained from these approximations with the exact solutions. Our analysis shows that the $GW$ approximation, often considered insufficient for describing strong correlation, exhibits a previously unreported solution branch that accurately reproduces Mott physics in the HK model. In addition, using a covariant formalism, we find that $HGW$ provides an accurate description of charge response, while $SGW$ performs well for spin correlations. Overall, our work demonstrates that the HK model can effectively benchmark many-body approximations and helps refine the understanding of $GW$ methods in strongly correlated regimes. |
| title | Benchmarking Non-perturbative Many-Body Approaches in the Exactly Solvable Hatsugai-Kohmoto Model |
| topic | Strongly Correlated Electrons |
| url | https://arxiv.org/abs/2511.02292 |