{"id":"d3b9bd71-9057-462c-b8c0-b68d3396c647","arxiv_id":"2606.06653","paper_version":1,"verdict":"UNVERDICTED","confidence":"LOW","novelty_score":7.0,"correctness_risk":"medium","formal_verification":"none","parameter_count":0,"one_line_summary":"In charge- and dipole-conserving fragmented systems, charge and dipole asymmetries exhibit Mpemba-like crossings on parametrically distinct timescales, driven by frozen sectors retaining asymmetry and active sectors relaxing.","lead":"This paper finds that the quantum Mpemba effect persists in systems with strong Hilbert-space fragmentation from simultaneous charge and dipole conservation, but appears as crossings in charge and dipole asymmetries on distinct timescales. A smart generalist might read it to see how conservation laws reshape symmetry restoration in constrained quantum many-body systems.","discovery_kind":"new_application","skeptic_critique":{"model":"grok-4.3","headline":"No significant objection identified","rationale":"Reader's weakest assumption correctly flags the TN accuracy and sector accounting, yet the multi-method validation already addresses the primary risk. No further load-bearing gap is visible in the argument structure.","tokens_in":1745,"tokens_out":264,"duration_ms":15169,"concrete_test":"Compare the long-time charge and dipole asymmetry values extracted from the exactly solvable dissipative model against the TN data at the largest accessible L; if the frozen-sector plateau values agree within 5% and the crossing times remain parametrically separated, the sector-based mechanism is corroborated independently of the TN approximation.","verdict_should_be":"UNCHANGED","load_bearing_attack":"The central claim rests on three independent lines of evidence (replica TN for annealed Rényi-2 asymmetry up to L=128, direct Hamiltonian evolution, and an exactly solvable dissipative model) that all exhibit the reported charge/dipole crossings on distinct timescales. The frozen/active sector decomposition follows directly from the defining charge and dipole conservation laws that generate the fragmentation; no additional dynamical assumption is required for the sectors to remain disconnected. The mechanism (finite retained asymmetry in frozen fragments, relaxation confined to active fragments) is therefore a direct consequence of the Hilbert-space structure rather than an extra postulate.","agreement_with_reader":"agree"},"referee_report":{"model":"grok-4.3","summary":"The manuscript claims that Hilbert-space fragmentation due to simultaneous charge and dipole conservation does not preclude the quantum Mpemba effect but reshapes it into a higher-order symmetric version: charge and dipole asymmetries each exhibit Mpemba-like crossings on parametrically distinct timescales. This is demonstrated via a replica tensor-network method for the annealed Rényi-2 entanglement asymmetry (reaching L=128), direct Hamiltonian evolution, and an exactly solvable dissipative model. The mechanism is identified by decomposing the state into frozen and active Krylov sectors, where frozen fragments retain finite asymmetry while active fragments drive the relaxation.","tokens_in":1873,"tokens_out":398,"duration_ms":16842,"significance":"If the results hold, the work supplies a concrete framework for Mpemba phenomenology under higher-moment conservation laws by showing how fragmentation converts the effect into frozen memory plus active-sector relaxation. The combination of three independent lines of evidence—large-scale replica tensor networks, Hamiltonian simulations, and exact solvability—constitutes a clear methodological strength that directly ties the observed crossings to the defining conservation laws without additional dynamical assumptions.","major_comments":[],"minor_comments":[{"comment":"Abstract: the claim that the replica tensor-network computation reaches L=128 would be strengthened by a brief statement on convergence checks or error estimates, even if these appear in the main text.","section":"Abstract"},{"comment":"The distinction between frozen and active sectors is derived directly from the charge and dipole conservation laws, but a short explicit statement confirming that the sector decomposition is exhaustive (i.e., no additional sectors are needed) would improve clarity in the mechanism section.","section":null},{"comment":"Figure captions for the asymmetry crossings should explicitly label the parametrically distinct timescales for charge versus dipole to make the higher-order character immediately visible.","section":null}],"recommendation":"minor_revision","confidential_remarks":null},"author_rebuttal":{"model":"grok-4.3","summary":"We thank the referee for the positive evaluation of our manuscript, the accurate summary of our results on the higher-order symmetric quantum Mpemba effect, and the recommendation for minor revision. The combination of replica tensor networks, Hamiltonian simulations, and exact solvability is indeed a methodological strength.","responses":[],"tokens_in":1231,"tokens_out":74,"duration_ms":15704,"standing_objections":[]},"desk_editor":{"model":"grok-4.3","letter":"The main result is that charge and dipole asymmetries each exhibit Mpemba-like crossings, but on parametrically different timescales, in charge-dipole conserving circuits and Hamiltonians. The mechanism is that frozen Krylov sectors keep a finite asymmetry while active sectors handle the relaxation. This follows straight from the conservation laws that fragment the space, without needing extra postulates.\n\nThe paper does a solid job combining three independent checks: replica tensor networks for the annealed Rényi-2 asymmetry up to L=128, direct Hamiltonian evolution, and an exactly solvable dissipative model. All three lines show the crossings, and the sector decomposition is reproducible from the defining constraints. That gives the claim real grounding rather than just a numerical observation.\n\nThe soft spots are limited. The tensor-network method is approximate, so finite-size effects or replica artifacts could in principle shift the apparent crossings, though L=128 reduces that risk and the other two methods line up. The abstract gives no explicit error bars or convergence details, which is a minor gap but not load-bearing given the cross-checks.\n\nThis is for people working on non-equilibrium dynamics in fragmented systems or on quantum Mpemba effects. Anyone already following Hilbert-space fragmentation will see a clean connection to an existing anomaly. It is specific enough and evidence-based enough to merit a serious referee, even if revisions are needed on the numerics presentation.","headline":"The paper shows the quantum Mpemba effect survives fragmentation but splits into higher-order form with distinct charge and dipole timescales, driven directly by frozen and active Krylov sectors.","tokens_in":2370,"tokens_out":354,"would_cite":true,"duration_ms":19311,"reading_group":"yes","serious_thinker":"yes","would_accept_peer_review":true},"rs_alignment":null,"lean_confirmation":null,"pith_extraction":{"msc":[],"pacs":[],"model":"grok-4.3","headline":"Charge and dipole asymmetries in fragmented systems each exhibit Mpemba-like crossings on parametrically distinct timescales.","keywords":["quantum Mpemba effect","Hilbert space fragmentation","Krylov sectors","charge conservation","dipole conservation","entanglement asymmetry","symmetry restoration"],"falsifier":"A calculation or simulation in which active sectors are removed or suppressed yet the asymmetry crossings still appear, or one in which the crossings disappear when frozen sectors are eliminated.","tokens_in":2647,"feed_emoji":"❄️","tokens_out":631,"duration_ms":14683,"temperature":0.7,"pith_summary":"The paper shows that the quantum Mpemba effect survives in Hilbert spaces fragmented by simultaneous charge and dipole conservation. Greater initial breaking of either symmetry still leads to faster restoration, but the two asymmetries cross on separate timescales. The mechanism is resolved by splitting states into frozen Krylov sectors that keep a fixed asymmetry and active sectors that relax. This turns the original effect into a higher-order version shaped by the conservation laws rather than erased by them.","feed_headline":"Fragmented systems retain Mpemba crossings for charge and dipole","feed_subtitle":"Asymmetries cross on separate timescales because frozen sectors keep memory while active sectors relax.","key_machinery":"The split into frozen and active Krylov sectors set by charge and dipole conservation, which keeps persistent asymmetry in one subset of sectors while allowing relaxation-driven crossings in the other.","core_discovery":"The authors uncover a higher-order symmetric quantum Mpemba effect: the charge and dipole asymmetries each display Mpemba-like crossings on parametrically distinct timescales. Resolving the state into frozen and active Krylov sectors reveals the mechanism: frozen fragments retain a finite asymmetry that obstructs full restoration, while active fragments host the relaxation responsible for the crossings. Fragmentation thus does not preclude the quantum Mpemba effect but reshapes it into frozen memory and active-fragment relaxation, providing a framework for the Mpemba phenomenology of higher-moment symmetries.","pith_inferences":["Similar higher-order crossings could appear whenever multiple independent conservation laws fragment the space.","The separation of timescales might allow selective control of relaxation for different multipole moments in experiments.","Exact solutions in small fragmented systems could be used to test whether the active-sector relaxation rate matches the observed crossing time."],"forward_implications":["The quantum Mpemba effect persists under strong Hilbert-space fragmentation but appears separately for each conserved moment.","Frozen sectors leave a permanent memory of the initial asymmetry while active sectors produce the Mpemba crossing.","The same phenomenology appears in both unitary circuits, Hamiltonians, and an exactly solvable dissipative model.","Higher-moment symmetries acquire their own Mpemba timescales set by the fragmentation structure."],"fun_headline_variants":["Mpemba crossings retained in fragmented charge-dipole systems","Charge and dipole Mpemba effects on separate timescales","Fragmentation turns Mpemba into frozen and active relaxation","Higher-order Mpemba in systems with charge and dipole conservation"],"cache_read_input_tokens":2112,"weakest_assumption_plain":"The split between frozen and active Krylov sectors fully explains the observed crossings and that the replica tensor-network and Hamiltonian calculations capture the true long-time dynamics without large finite-size artifacts.","fun_headline_variants_meta":{"raw":{"variants":["Mpemba crossings retained in fragmented charge-dipole systems","Charge and dipole Mpemba effects on separate timescales","Fragmentation turns Mpemba into frozen and active relaxation","Higher-order Mpemba in systems with charge and dipole conservation"]},"model":"grok-4.3","cost_usd":0.003491,"raw_usage":{"total_tokens":1837,"prompt_tokens":666,"num_sources_used":0,"completion_tokens":61,"cost_in_usd_ticks":34912000,"prompt_tokens_details":{"text_tokens":666,"audio_tokens":0,"image_tokens":0,"cached_tokens":256},"completion_tokens_details":{"audio_tokens":0,"reasoning_tokens":1110,"accepted_prediction_tokens":0,"rejected_prediction_tokens":0}},"tokens_in":666,"tokens_out":61,"duration_ms":8602,"temperature":1.0,"reasoning_tokens":1110,"cache_read_input_tokens":256,"cache_creation_input_tokens":0},"cache_creation_input_tokens":0},"created_at":"2026-06-28T00:26:34.249035+00:00","model_set":{"reader":"grok-4.3"},"falsifier":"A calculation or simulation in which active sectors are removed or suppressed yet the asymmetry crossings still appear, or one in which the crossings disappear when frozen sectors are eliminated.","supporting_citations":[],"review_version":1}