{"record":{"author":{"account_ref":null,"orcid":null},"builds_on":[],"content_schema":"pubphys.content.revision/1","content_sha256":"8e68ab45f29a90940c56557654ea8559e02cb2423e40d6ab9b7542a6b541dd10","created":"2026-10-15T23:43:22Z","files":[],"origin":{"assisted_by":[],"kind":"seed"},"parents":["3d0ebde56aa5d069ee4ba5650def899c469f5ceee1a40bbf6315c13df3a063c6","ce59fb6cd812fc05906d0c60a71c75ea22bc686bcf38e7c3ef7010834d98ee7b"],"salt":"6f011e1c754c7b0a4d924b7932a6e87c3da868407b5f97b4ef5833701f0e7ad8","schema":"pubphys.record/2","site":"pubphys.com","target":null,"type":"revision"},"content":{"answer_type":"yes-no","assisted_by":[],"external_id":"cm.mbl.many-body-mobility-edge","kind":"well-posed","literature_status":"contested","n":"2","parents":[],"plain":"Small-system numerics suggest that at moderate disorder, low-energy states stay localized while high-energy states thermalize, separated by an energy threshold called a mobility edge. Theory argues that hot regions would then wander through the system and thermalize all of it.","posed_since":"2015","precise":"For the random-field Heisenberg chain at disorder $W$ where exact diagonalization at $L \\le 22$ shows an energy-dependent localization threshold $\\epsilon_c(W)$ (Luitz, Laflorencie, Alet, PRB 91, 081103, 2015), do eigenstates with energy density below $\\epsilon_c$ remain localized as $L \\to \\infty$? De Roeck, Huveneers, Muller, Schiulaz (PRB 93, 014203, 2016) argued that mobile ergodic bubbles exclude this, so MBL requires localization at all energies. Answer yes or no.","problem_ref":"3d0ebde56aa5d069ee4ba5650def899c469f5ceee1a40bbf6315c13df3a063c6","references":"","settled_by":"Time evolution of low-energy-density initial states at sizes where rare high-energy-density bubbles are typical, or a theory that closes or validates the bubble mechanism.","status_note":"The 2016 bubble argument is unrefuted while finite-size mobility edges persist in numerics; no decisive large-system result is known (moderate confidence).","title":"Can a many-body mobility edge exist in the thermodynamic limit?","topic_ref":null},"attested":{"attestation":{"batch":null,"client_id":null,"id_token_sha256":null,"kind":"platform"},"record_hash":"b1917bf7d006b43689ae6147adc78f9a61c0bb2e1858773f1800d4e2f59639fd","schema":"pubphys.attested/1"},"envelope":{"attested_hash":"25241b563f4f7526bebb493c0d2cf19dacb0a0e87ceb406df14fd9c2564aa0be","platform_signature":{"key_id":"c6afc19b31429869751f06879c75cd64ea92654423d15b44be775bf1310a60da","sig":"ArJFstgXBGjjRHrozwp_XNO-8RLxLz39lzD1deXkeegMKnAnCAr6njoXF_PktFzzspWat9LO5YVVX1LfjDxvAw"},"schema":"pubphys.envelope/1"},"record_hash":"b1917bf7d006b43689ae6147adc78f9a61c0bb2e1858773f1800d4e2f59639fd","leaf_index":2934}