{"paper":{"title":"Fermionic mean-field dynamics for spin systems beyond free fermions","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"A fermionic mean-field method reproduces qualitative dynamics in interacting spin systems with polynomial classical cost.","cross_cats":["quant-ph"],"primary_cat":"cond-mat.str-el","authors_text":"Karol Kowalski, Marc Illa, Niranjan Govind, Rishab Dutta","submitted_at":"2026-04-02T23:41:06Z","abstract_excerpt":"We introduce the fermionized time-dependent Hartree-Fock (fTDHF), a real-time quantum dynamics method for spin-1/2 Hamiltonians following their mapping to fermions via the Jordan-Wigner transformation. fTDHF is formally equivalent to exact dynamics in the case of free fermions and can efficiently handle non-local string operators arising from long-range interactions via transition matrix elements between non-orthogonal Slater determinants. We show that the fTDHF method can be implemented on a classical computer with a cost that scales polynomially with system size, and linearly with the time s"},"claims":{"count":4,"items":[{"kind":"strongest_claim","text":"fTDHF is formally equivalent to exact dynamics in the case of free fermions and can efficiently handle non-local string operators arising from long-range interactions via transition matrix elements between non-orthogonal Slater determinants. We show that the fTDHF method can be implemented on a classical computer with a cost that scales polynomially with system size, and linearly with the time steps.","source":"verdict.strongest_claim","status":"machine_extracted","claim_id":"C1","attestation":"unclaimed"},{"kind":"weakest_assumption","text":"The mean-field approximation in the fermionic representation remains accurate enough to reproduce qualitative dynamics for interacting spin systems beyond the free-fermion limit, as tested in the three benchmark models.","source":"verdict.weakest_assumption","status":"machine_extracted","claim_id":"C2","attestation":"unclaimed"},{"kind":"one_line_summary","text":"fTDHF is a mean-field dynamics method for spin systems that is formally exact for free fermions and reproduces qualitative features of exact evolution in benchmarks for adiabatic preparation, many-body localization, and the Schwinger model.","source":"verdict.one_line_summary","status":"machine_extracted","claim_id":"C3","attestation":"unclaimed"},{"kind":"headline","text":"A fermionic mean-field method reproduces qualitative dynamics in interacting spin systems with polynomial classical cost.","source":"verdict.pith_extraction.headline","status":"machine_extracted","claim_id":"C4","attestation":"unclaimed"}],"snapshot_sha256":"269976a28f02aa36f1264c6f8fe76348034a6461717841df345b84caa8d9ddc5"},"source":{"id":"2604.02584","kind":"arxiv","version":2},"verdict":{"id":"6cb1ec3c-04d5-4569-88ca-39fd6d898966","model_set":{"reader":"grok-4.3"},"created_at":"2026-05-13T19:54:32.560238Z","strongest_claim":"fTDHF is formally equivalent to exact dynamics in the case of free fermions and can efficiently handle non-local string operators arising from long-range interactions via transition matrix elements between non-orthogonal Slater determinants. We show that the fTDHF method can be implemented on a classical computer with a cost that scales polynomially with system size, and linearly with the time steps.","one_line_summary":"fTDHF is a mean-field dynamics method for spin systems that is formally exact for free fermions and reproduces qualitative features of exact evolution in benchmarks for adiabatic preparation, many-body localization, and the Schwinger model.","pipeline_version":"pith-pipeline@v0.9.0","weakest_assumption":"The mean-field approximation in the fermionic representation remains accurate enough to reproduce qualitative dynamics for interacting spin systems beyond the free-fermion limit, as tested in the three benchmark models.","pith_extraction_headline":"A fermionic mean-field method reproduces qualitative dynamics in interacting spin systems with polynomial classical cost."},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2604.02584/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":"05081ed317b0624caf559841dc743f5c8301600d2f004eaeda802b685dbf7102"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"}