{"paper":{"title":"Exact Criterion for Ground-State Overlap Dominance after Quantum Quenches","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"For free-fermion Hamiltonians that split into independent 2x2 sectors, the final ground state has the largest overlap with the initial ground state after a quench exactly when the initial and final Bloch vectors point into the same half of ","cross_cats":["quant-ph"],"primary_cat":"cond-mat.stat-mech","authors_text":"Taisanul Haque","submitted_at":"2026-04-13T13:03:11Z","abstract_excerpt":"It was recently conjectured and verified for the transverse-field Ising model [Phys. Rev. B 113, 165102 (2026)] that, after a sudden quench within the same equilibrium phase, the initial ground state has its largest overlap with the final ground state. We show that this phase-based criterion is generally false, even in translationally invariant free-fermion systems. For Hamiltonians that factorize into independent $2\\times 2$ momentum sectors, we derive the exact necessary-and-sufficient condition for ground-state overlap dominance: the initial and final sector Bloch vectors must have positive"},"claims":{"count":4,"items":[{"kind":"strongest_claim","text":"For Hamiltonians that factorize into independent 2×2 sectors, the final ground state is uniquely maximal if and only if the initial and final sector Bloch vectors have positive dot product.","source":"verdict.strongest_claim","status":"machine_extracted","claim_id":"C1","attestation":"unclaimed"},{"kind":"weakest_assumption","text":"The Hamiltonians are translationally invariant free-fermion systems that factorize into independent 2×2 sectors (as stated for the class solved exactly).","source":"verdict.weakest_assumption","status":"machine_extracted","claim_id":"C2","attestation":"unclaimed"},{"kind":"one_line_summary","text":"For translationally invariant free-fermion systems with Hamiltonians factorizing into independent 2x2 sectors, the final ground state is the unique maximal-overlap state after a same-phase quench if and only if the initial and final sector Bloch vectors have positive dot product; this fails for some","source":"verdict.one_line_summary","status":"machine_extracted","claim_id":"C3","attestation":"unclaimed"},{"kind":"headline","text":"For free-fermion Hamiltonians that split into independent 2x2 sectors, the final ground state has the largest overlap with the initial ground state after a quench exactly when the initial and final Bloch vectors point into the same half of ","source":"verdict.pith_extraction.headline","status":"machine_extracted","claim_id":"C4","attestation":"unclaimed"}],"snapshot_sha256":"42cb7e644d13e7df74eed853781a307588f166a8f8f9bfc0d39d66ce4c8b49f8"},"source":{"id":"2604.11420","kind":"arxiv","version":2},"verdict":{"id":"37f55716-f137-41aa-8e1d-eb392b116669","model_set":{"reader":"grok-4.3"},"created_at":"2026-05-10T15:36:25.662881Z","strongest_claim":"For Hamiltonians that factorize into independent 2×2 sectors, the final ground state is uniquely maximal if and only if the initial and final sector Bloch vectors have positive dot product.","one_line_summary":"For translationally invariant free-fermion systems with Hamiltonians factorizing into independent 2x2 sectors, the final ground state is the unique maximal-overlap state after a same-phase quench if and only if the initial and final sector Bloch vectors have positive dot product; this fails for some","pipeline_version":"pith-pipeline@v0.9.0","weakest_assumption":"The Hamiltonians are translationally invariant free-fermion systems that factorize into independent 2×2 sectors (as stated for the class solved exactly).","pith_extraction_headline":"For free-fermion Hamiltonians that split into independent 2x2 sectors, the final ground state has the largest overlap with the initial ground state after a quench exactly when the initial and final Bloch vectors point into the same half of "},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2604.11420/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":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"}