{"record":{"author":{"account_ref":null,"orcid":null},"builds_on":[],"content_schema":"pubphys.content.revision/1","content_sha256":"f863642955876d50432938e2f5f37f393313677bfa2caac25b85d526907cd769","created":"2026-10-03T07:18:00Z","files":[],"origin":{"assisted_by":[],"kind":"seed"},"parents":["5475cf5dc5b1a72283d26dc95dc6e00d7ea4e00096a7c6492e409a1816eeb011"],"salt":"0229db6086936633501528f1cd47ff834263338ef2b9eeff76678dfe1fc61268","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":"1","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":null,"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":"7f4724a8f5124a8d3b0876fec78a4f3f0f7b467672032acb318713bcededaa82"},"attested":{"attestation":{"batch":null,"client_id":null,"id_token_sha256":null,"kind":"platform"},"record_hash":"3d0ebde56aa5d069ee4ba5650def899c469f5ceee1a40bbf6315c13df3a063c6","schema":"pubphys.attested/1"},"envelope":{"attested_hash":"d58f4ff13cd00ba8ce8a0003979813a51c8383a4cfd408513c4d1bc77d650f8f","platform_signature":{"key_id":"c6afc19b31429869751f06879c75cd64ea92654423d15b44be775bf1310a60da","sig":"q9kUDmmUXx43VCulVeZqZt3E_-ToD5Fvq71uhofOpcH4Tu2pE8O9hKhfTaFtU26Q4W4CYcHrnDlCzZUSFz-CDw"},"schema":"pubphys.envelope/1"},"record_hash":"3d0ebde56aa5d069ee4ba5650def899c469f5ceee1a40bbf6315c13df3a063c6","leaf_index":1087}