{"record":{"author":{"account_ref":null,"orcid":null},"builds_on":[],"content_schema":"pubphys.content.revision/1","content_sha256":"18ee789836d8d11a6cb6ab4d1632a595c443e98d937de6cd48c7bf78d0838562","created":"2026-10-03T07:18:00Z","files":[],"origin":{"assisted_by":[],"kind":"seed"},"parents":["5475cf5dc5b1a72283d26dc95dc6e00d7ea4e00096a7c6492e409a1816eeb011"],"salt":"cf529a71e5967a2d389f5fa2e3976efd3490e6dc1a5a88c8c9ad9cf1075e6f0f","schema":"pubphys.record/2","site":"pubphys.com","target":null,"type":"revision"},"content":{"answer_type":"identification","assisted_by":[],"external_id":"cm.lattice-transport.heisenberg-superdiffusion","kind":"well-posed","literature_status":"partially-resolved","n":"1","parents":[],"plain":"In the spin-$1/2$ Heisenberg chain at high temperature, magnetization spreads faster than ordinary diffusion, with distance growing as time to the power $2/3$. The spreading has the scaling of a classical surface-growth model called KPZ (Kardar-Parisi-Zhang), but the full statistics does not match it, and the correct description is unknown.","posed_since":"2019","precise":"For the isotropic spin-$1/2$ Heisenberg chain at infinite temperature and zero net magnetization, spin transport has dynamical exponent $z = 3/2$ and the spin structure factor matches the KPZ scaling function. The full counting statistics of magnetization transferred across a cut is known not to be KPZ (Rosenberg et al. 2024; Gopalakrishnan et al. 2023). Derive the exact asymptotic distribution of transferred magnetization and its scaling with t, and identify the universality class it defines. Answer: the limiting distribution, or its cumulant ratios as $t \\to \\infty$.","problem_ref":null,"references":"","settled_by":"An exact theory (for example nonlinear fluctuating hydrodynamics of the giant quasiparticles) of the transferred-magnetization distribution, matched by numerics or quantum simulation at times long enough for cumulant ratios to converge.","status_note":"Non-KPZ statistics were established by a 2024 superconducting-processor experiment (Rosenberg et al., Science 2024, arXiv:2306.09333) and by theory; the limiting distribution is not derived for the quantum chain.","title":"Full counting statistics of spin superdiffusion in the Heisenberg chain","topic_ref":"4eabb15038d6d57d5e03c97f1f539dd576f4c861190c15bebd3e84acc25a5dc8"},"attested":{"attestation":{"batch":null,"client_id":null,"id_token_sha256":null,"kind":"platform"},"record_hash":"7489205ec37df5a6968d2ebe6ef5436311033651de95a9877409174ef7c19fa3","schema":"pubphys.attested/1"},"envelope":{"attested_hash":"8c8ed598f0a770494d16b1ae4fd358ea69bdf49da08cd11be253728d77890cc7","platform_signature":{"key_id":"c6afc19b31429869751f06879c75cd64ea92654423d15b44be775bf1310a60da","sig":"GW93pZ6UFPCR_aTiElXV0brNAXkUlBi-eMBD8tTGbRQvEGfAnOqPdnIpxvrMuOM6NQt1NimZ5efEh1XVK0wXBA"},"schema":"pubphys.envelope/1"},"record_hash":"7489205ec37df5a6968d2ebe6ef5436311033651de95a9877409174ef7c19fa3","leaf_index":1063}