{"paper":{"title":"Resolvent-Based Self-Consistent Framework with Hierarchical Correlation Expansion for Strongly Correlated Many-Body Systems","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"A resolvent hierarchy for the self-energy closes exactly in diagonal resolvents and supplies a systematically improvable description of fluctuations beyond mean-field theory.","cross_cats":[],"primary_cat":"quant-ph","authors_text":"Qing-yu Cai, Zhi-qiang Huang","submitted_at":"2026-04-01T08:11:58Z","abstract_excerpt":"We develop a nonperturbative framework for generic nonintegrable many-body systems that reorganizes the expansion of diagonal Green's functions. Starting from exact projection identities and the spectral representation of the resolvent, we derive a recursive hierarchy for the self-energy in which cross-correlated propagation processes are systematically rewritten in terms of diagonal resolvents. Under a diagonal closure approximation, the hierarchy becomes formally closed yet remains systematically improvable.\n  The framework combines two nonperturbative mechanisms. First, a Lanczos continued-"},"claims":{"count":4,"items":[{"kind":"strongest_claim","text":"The resulting hierarchy remains formally closed in terms of diagonal resolvents and provides a systematically improvable description of fluctuations beyond mean-field theory.","source":"verdict.strongest_claim","status":"machine_extracted","claim_id":"C1","attestation":"unclaimed"},{"kind":"weakest_assumption","text":"ETH-type statistical assumptions are invoked to close the multi-resolvent hierarchy for nonintegrable systems with dense spectra.","source":"verdict.weakest_assumption","status":"machine_extracted","claim_id":"C2","attestation":"unclaimed"},{"kind":"one_line_summary","text":"A resolvent hierarchy with Lanczos and multi-resolvent closures yields systematically improvable spectral broadening and asymmetry for nonintegrable many-body systems.","source":"verdict.one_line_summary","status":"machine_extracted","claim_id":"C3","attestation":"unclaimed"},{"kind":"headline","text":"A resolvent hierarchy for the self-energy closes exactly in diagonal resolvents and supplies a systematically improvable description of fluctuations beyond mean-field theory.","source":"verdict.pith_extraction.headline","status":"machine_extracted","claim_id":"C4","attestation":"unclaimed"}],"snapshot_sha256":"3d37ceccfdea703e69b2e47f898169137b5a6da5367458f47b27316f7d8fbec0"},"source":{"id":"2604.00606","kind":"arxiv","version":4},"verdict":{"id":"21749922-1a57-4791-881f-f1e04801f002","model_set":{"reader":"grok-4.3"},"created_at":"2026-05-13T22:43:25.461352Z","strongest_claim":"The resulting hierarchy remains formally closed in terms of diagonal resolvents and provides a systematically improvable description of fluctuations beyond mean-field theory.","one_line_summary":"A resolvent hierarchy with Lanczos and multi-resolvent closures yields systematically improvable spectral broadening and asymmetry for nonintegrable many-body systems.","pipeline_version":"pith-pipeline@v0.9.0","weakest_assumption":"ETH-type statistical assumptions are invoked to close the multi-resolvent hierarchy for nonintegrable systems with dense spectra.","pith_extraction_headline":"A resolvent hierarchy for the self-energy closes exactly in diagonal resolvents and supplies a systematically improvable description of fluctuations beyond mean-field theory."},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2604.00606/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":2,"snapshot_sha256":"090d293d0945dff89424710da6fb1e5245338402040e851da1305ab435383438"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"}