{"record":{"author":{"account_ref":null,"orcid":null},"builds_on":[],"content_schema":"pubphys.content.revision/1","content_sha256":"46458e3b0904c810bd6c70984c4dbfc7ad2c1608e3736ca6fe389f470518f5bb","created":"2026-10-03T07:18:11Z","files":[],"origin":{"assisted_by":[],"kind":"seed"},"parents":["5475cf5dc5b1a72283d26dc95dc6e00d7ea4e00096a7c6492e409a1816eeb011"],"salt":"cddb62c64b23fe4cecf405559806378ec7fc001c3e54cb9c5d884cdc5575a6ab","schema":"pubphys.record/2","site":"pubphys.com","target":null,"type":"revision"},"content":{"answer_type":"classification","assisted_by":[],"external_id":"stat.mpemba-relaxation.quantum-symmetry-criterion","kind":"well-posed","literature_status":"partially-resolved","n":"1","parents":[],"plain":"In some quantum spin chains, a state that breaks a symmetry more strongly at the start regains that symmetry faster in a small region than a weakly broken one. The task is a general rule, valid beyond special solvable models, for when this happens.","posed_since":"2023","precise":"Chain of $L$ qubits with conserved charge $Q = (1/2) \\sum_i \\sigma^{z}_{i}$, initial tilted ferromagnet with tilt angle $\\theta$ that breaks the $U(1)$ symmetry, unitary $U(1)$-symmetric dynamics (Hamiltonian or random circuit). For a subsystem of length $l << L$, the entanglement asymmetry $A_{l}(t)$ = S(rho_A,Q) - S(rho_A), with rho_A,Q the reduced density matrix projected onto charge sectors and S the von Neumann entropy. Find necessary and sufficient conditions on the initial-state charge statistics and on the dynamics (integrable or chaotic, closed or open) for A_l(t) of a larger-$\\theta$ state to cross below that of a smaller-$\\theta$ state at finite $t$; the analogous question for a non-Abelian group $G$ with charges $Q_{a}$ uses the corresponding $G$-asymmetry.","problem_ref":null,"references":"","settled_by":"A proved criterion for the crossing of $A_l(t)$ in generic chaotic symmetric dynamics, tested against exact numerics and quantum-simulator data.","status_note":"Criteria exist for integrable chains (Rylands et al., PRL 2024) and U(1) random circuits (Liu et al., PRL 133, 140405, 2024; Turkeshi, Calabrese and De Luca 2024), with a trapped-ion observation (Joshi et al., PRL 133, 010402, 2024); thermal (energy) analogues in chaotic chains are treated hydrodynamically (Muller, Pappalardi and Fazio, arXiv:2604.11876, 2026); no general criterion for symmetry restoration in chaotic dynamics is established.","title":"General criterion for the quantum Mpemba effect in symmetry restoration","topic_ref":"b9dc5bd92d3519c9f31327e4098f8e26bf4890131f68cb53d43d3834030d1d0c"},"attested":{"attestation":{"batch":null,"client_id":null,"id_token_sha256":null,"kind":"platform"},"record_hash":"089e407ef0ab07602258bcfde97018cd498e1b544ac5ed40d62ed0b063df2e05","schema":"pubphys.attested/1"},"envelope":{"attested_hash":"97ab8f5eb2c5fd59669da7cc10fa7a0257f64d0ddad501842c06f18478c2a04a","platform_signature":{"key_id":"c6afc19b31429869751f06879c75cd64ea92654423d15b44be775bf1310a60da","sig":"d-da1n8460fF1VK4-M829ZWjRMhZeiN1ZR7RxQMrLZOsi29TNJe6irUentwR0sTNyheOwpjuRaSqZO32HZ1QAw"},"schema":"pubphys.envelope/1"},"record_hash":"089e407ef0ab07602258bcfde97018cd498e1b544ac5ed40d62ed0b063df2e05","leaf_index":2103}