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| Auteurs principaux: | , , , , , , |
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| Format: | Preprint |
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2026
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| Sujets: | |
| Accès en ligne: | https://arxiv.org/abs/2605.02228 |
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| _version_ | 1866915976862236672 |
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| author | Goldberger, Dolev Zemach, Ido Zhang, Lei Yu, Yang Gull, Emanuel Cohen, Guy Erpenbeck, André |
| author_facet | Goldberger, Dolev Zemach, Ido Zhang, Lei Yu, Yang Gull, Emanuel Cohen, Guy Erpenbeck, André |
| contents | Low-order hybridization expansion methods such as the non-crossing approximation (NCA) and the one-crossing approximation (OCA) are widely used impurity solvers in the study of strongly correlated systems, yet their accuracy in genuine multi-orbital settings remains poorly understood. Using the decoupled orbital limit as a controlled reference point, we derive analytic results connecting multi-orbital restricted propagators and Green's functions to their single-orbital counterparts, identify the diagrammatic mechanisms responsible for the breakdown of low-order methods in multi-orbital settings, and determine their regimes of applicability. Our central finding is that the accuracy of these methods is governed by the least correlated orbital: i.e., the orbital with the most rapidly decaying retarded Green's function. That orbital's properties are transferred to all other orbitals through a spurious coupling generated by the truncated expansion, thereby suppressing correlation-induced features such as the Kondo resonance. This occurs even in orbitals that are themselves strongly correlated within single-orbital calculations using the same approximation scheme. We confirm this numerically across representative two-orbital model systems in the steady-state, systematically identifying the parameter regimes in which low-order methods succeed or fail. Our results provide a practical guide for assessing when insights from single-orbital calculations carry over to multi-orbital settings, and serve as a benchmark for the development and validation of higher-order multi-orbital impurity solvers. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2605_02228 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Validity and Limits of Low Order Hybridization Expansion Approaches for Multi-Orbital Systems Goldberger, Dolev Zemach, Ido Zhang, Lei Yu, Yang Gull, Emanuel Cohen, Guy Erpenbeck, André Strongly Correlated Electrons Mesoscale and Nanoscale Physics Quantum Physics Low-order hybridization expansion methods such as the non-crossing approximation (NCA) and the one-crossing approximation (OCA) are widely used impurity solvers in the study of strongly correlated systems, yet their accuracy in genuine multi-orbital settings remains poorly understood. Using the decoupled orbital limit as a controlled reference point, we derive analytic results connecting multi-orbital restricted propagators and Green's functions to their single-orbital counterparts, identify the diagrammatic mechanisms responsible for the breakdown of low-order methods in multi-orbital settings, and determine their regimes of applicability. Our central finding is that the accuracy of these methods is governed by the least correlated orbital: i.e., the orbital with the most rapidly decaying retarded Green's function. That orbital's properties are transferred to all other orbitals through a spurious coupling generated by the truncated expansion, thereby suppressing correlation-induced features such as the Kondo resonance. This occurs even in orbitals that are themselves strongly correlated within single-orbital calculations using the same approximation scheme. We confirm this numerically across representative two-orbital model systems in the steady-state, systematically identifying the parameter regimes in which low-order methods succeed or fail. Our results provide a practical guide for assessing when insights from single-orbital calculations carry over to multi-orbital settings, and serve as a benchmark for the development and validation of higher-order multi-orbital impurity solvers. |
| title | Validity and Limits of Low Order Hybridization Expansion Approaches for Multi-Orbital Systems |
| topic | Strongly Correlated Electrons Mesoscale and Nanoscale Physics Quantum Physics |
| url | https://arxiv.org/abs/2605.02228 |