{"paper":{"title":"Low-scaling \\textit{GW} calculations of quasi-particle energies for extended systems within the numerical atomic orbital framework","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"Space-time algorithm in numerical atomic orbitals reduces GW scaling to O(N^2) for quasi-particle energies.","cross_cats":[],"primary_cat":"cond-mat.mtrl-sci","authors_text":"Min-Ye Zhang, Peize Lin, Rong Shi, Xinguo Ren","submitted_at":"2026-03-28T14:48:16Z","abstract_excerpt":"The many-body perturbation theory within the $GW$ approximation is a widely used method for describing the electronic band structures in real materials. Its application to large-scale systems is, however, impeded by its high computational cost. The rate-limiting steps in a typical $GW$ implementation are the evaluation of the polarization function under the random phase approximation (RPA) and the evaluation of the $GW$ self-energy, both of which have a canonical $O(N^4)$ scaling with $N$ being the system size. The conventional space-time algorithm within the plane-wave basis sets reduces the "},"claims":{"count":4,"items":[{"kind":"strongest_claim","text":"the low-scaling implementation yields quasi-particle energies in close agreement with the conventional O(N^4) k-space formalism previously implemented in FHI-aims... the low-scaling implementation becomes advantageous already for systems containing fewer than 100 atoms.","source":"verdict.strongest_claim","status":"machine_extracted","claim_id":"C1","attestation":"unclaimed"},{"kind":"weakest_assumption","text":"The localized resolution of identity (LRI) technique preserves sufficient accuracy for the polarization function and self-energy when applied to extended periodic systems in the NAO basis.","source":"verdict.weakest_assumption","status":"machine_extracted","claim_id":"C2","attestation":"unclaimed"},{"kind":"one_line_summary","text":"A NAO-based LRI-enhanced space-time GW method reduces scaling to O(N^2) while matching conventional results for quasi-particle energies in solids with fewer than 100 atoms.","source":"verdict.one_line_summary","status":"machine_extracted","claim_id":"C3","attestation":"unclaimed"},{"kind":"headline","text":"Space-time algorithm in numerical atomic orbitals reduces GW scaling to O(N^2) for quasi-particle energies.","source":"verdict.pith_extraction.headline","status":"machine_extracted","claim_id":"C4","attestation":"unclaimed"}],"snapshot_sha256":"d30f1b54f2adf8351cbd67cafae467f449003ba398e88f77358f4176c0585b6b"},"source":{"id":"2603.27292","kind":"arxiv","version":2},"verdict":{"id":"8034a355-3443-4763-b031-7dd89e32b433","model_set":{"reader":"grok-4.3"},"created_at":"2026-05-14T21:53:16.416659Z","strongest_claim":"the low-scaling implementation yields quasi-particle energies in close agreement with the conventional O(N^4) k-space formalism previously implemented in FHI-aims... the low-scaling implementation becomes advantageous already for systems containing fewer than 100 atoms.","one_line_summary":"A NAO-based LRI-enhanced space-time GW method reduces scaling to O(N^2) while matching conventional results for quasi-particle energies in solids with fewer than 100 atoms.","pipeline_version":"pith-pipeline@v0.9.0","weakest_assumption":"The localized resolution of identity (LRI) technique preserves sufficient accuracy for the polarization function and self-energy when applied to extended periodic systems in the NAO basis.","pith_extraction_headline":"Space-time algorithm in numerical atomic orbitals reduces GW scaling to O(N^2) for quasi-particle energies."},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2603.27292/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"references":{"count":12,"sample":[{"doi":"","year":1964,"title":"Inhomogeneous Electron Gas.Phys","work_id":"afbf1a4c-0490-4745-b8df-33326ebb9d76","ref_index":1,"cited_arxiv_id":"","is_internal_anchor":false},{"doi":"","year":1965,"title":"New Method for Calculating the One-Particle Green’s Function with Appli- cation to the Electron-Gas Problem.1965,139, A796–A823","work_id":"29941316-3690-4b7b-bcd1-dbb39201f314","ref_index":2,"cited_arxiv_id":"","is_internal_anchor":false},{"doi":"","year":2002,"title":"Electronic Excitations: Density-Functional versus Many-Body Green’s-Function Approaches.Rev","work_id":"2f62374f-ef27-417c-a198-a2f62798133a","ref_index":3,"cited_arxiv_id":"","is_internal_anchor":false},{"doi":"","year":2025,"title":"r.; Kaltak, M.; Kresse, G","work_id":"13140b43-4309-4949-bbb1-c0fe4ee5dc96","ref_index":4,"cited_arxiv_id":"","is_internal_anchor":false},{"doi":"","year":1999,"title":"M.; Steinbeck, L.; White, I","work_id":"ac7d27c1-f3e3-445f-8520-6a52f1014a61","ref_index":5,"cited_arxiv_id":"","is_internal_anchor":false}],"resolved_work":12,"snapshot_sha256":"03c086a5d7931bcd806c584f1c2b9f5a1a251e504dba0cd06edc3f4b6e6a5e9f","internal_anchors":0},"formal_canon":{"evidence_count":2,"snapshot_sha256":"8b46484e46816db96f95de5d615c09d64f92d5ac76df44f91f134f56ed4c1554"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"}