{"id":"1e2e7a6c-04ca-4ed8-8c6b-dd61b13c8716","arxiv_id":"1908.11773","paper_version":2,"verdict":"CONDITIONAL","confidence":"HIGH","novelty_score":5.0,"correctness_risk":"medium","formal_verification":"none","parameter_count":0,"one_line_summary":"For a correlated quench with a single excitation, local observable dynamics equals the survival probability, giving IPR squared fluctuation scaling and suppressed scrambling.","lead":"This paper shows that in quantum systems with one conserved excitation, a simple local measurement can behave non-thermally: its fluctuations and information scrambling differ from the standard eigenstate thermalization hypothesis. The analytical results apply to rotating-wave-approximation experiments, such as trapped ions and superconducting circuits, and provide a way to measure survival probabilities.","discovery_kind":"new_application","skeptic_critique":{"model":"deepseek-v4-flash","headline":"The correlated-quench mechanism is exact only in an extremal single-excitation sector; the paper's own Appendix D shows the non-ergodic scaling degrades with system size once number conservation is broken, so the claimed robustness and genericity are not established.","rationale":"The reader's CONDITIONAL verdict is appropriate: the exact derivation of Eq. (22) is correct under the stated single-excitation, non-degenerate-bath-state conditions, and the numerical checks in Figs. 2-4 support the ideal-case predictions. My stress-test pass does not find an internal inconsistency in the exact conservation-law argument. The load-bearing concern is about the scope of the central claim. The protocol requires the bath to start in an extremal eigenstate of the conserved number (zero excitations, or analogously the fully polarized state), so the mechanism is not a generic finite-density phenomenon. More importantly, the paper's own Appendix D shows that when the conservation law is only approximate, the non-ergodic scaling weakens with increasing system size, while the abstract asserts robustness to perturbations that break the approximation. This is a concrete, self-identified limitation that should be front and center in any acceptance decision. It does not overturn the exact result, but it converts the headline from a broadly applicable ETH violation to a precisely conditioned single-excitation effect. The reader identified the non-degenerate bath state and single-excitation restriction as the weakest assumption; my concern extends that to the perturbation-robustness claim and its finite-size trend, so my agreement is partial. A single scaling experiment at larger N in the Appendix D model would settle whether the robustness claim survives in the thermodynamic limit.","tokens_in":16118,"tokens_out":29477,"duration_ms":277518,"concrete_test":"Rerun the non-conserving model of Appendix D (Eqs. D1-D3) for N=10,12,14,16,18,20, computing the diagonal-ensemble fluctuations delta^2_O and the IPR of the correlated initial state, and fit log(delta^2_O) versus log(IPR). If the fitted slope flows from approximately 2 toward approximately 1 as N increases, the non-ergodic IPR^2 scaling is a finite-size effect and the abstract's robustness claim fails; if the slope remains near 2, the concern is resolved.","verdict_should_be":"UNCHANGED","load_bearing_attack":"The central result, Eq. (22), follows exactly because the initial bath state is the unique eigenstate of N_B with N_B=0, so the sum in Eq. (20) collapses to a single term. This is a special, extremal charge sector: in any finite-density sector the eigenspace of N_B is degenerate, the sum does not collapse, and the rank-one off-diagonal structure—and with it the IPR^2 scaling, Eq. (23)—is lost. The paper's own Appendix D quantifies the price of relaxing exact number conservation: in the non-conserving model (D1)-(D3), the authors state that the non-ergodic scaling 'gets worse as the system size increases' (Fig. 7a). That admission directly undercuts the abstract's claim that 'predictions are robust to perturbations that break this approximation.' For the central claim to hold as a generic statement about non-integrable systems, the deviation from ETH must survive in the thermodynamic limit under small perturbations; the evidence provided shows the opposite trend. The exact conservation-law case is internally sound, but the paper's broader applicability claim rests on a finite-size effect whose scaling direction is unfavorable.","agreement_with_reader":"partial"},"referee_report":{"model":"deepseek-v4-flash","summary":"The paper studies quantum thermalization in the presence of a single conserved charge, focusing on initial states with exactly one excitation localized on a system qubit while the bath starts in a non-degenerate eigenstate of its local conserved quantity. Under these conditions, the authors derive a rank-one off-diagonal structure for system-local observable matrix elements, Eq. (22), which leads to three deviations from standard ETH expectations: equilibrium fluctuations that scale as IPR^2 (Eq. (23)), a time-dependent decay proportional to the survival probability (Eq. (28)), and a long-time OTOC that need not vanish (Eq. (29)). The analytical results are supported by exact diagonalization in a non-integrable spin chain and in the spin-boson model under the rotating-wave approximation. The paper also discusses the robustness of the effect when the conservation law is only approximate, and outlines a possible extension to larger system Hilbert spaces.","tokens_in":16330,"tokens_out":11334,"duration_ms":79375,"significance":"The central observation is valuable: in a single-excitation sector with an extremal bath state, the standard ETH ansatz for off-diagonal matrix elements is replaced by a deterministic rank-one form, and this yields concrete, testable predictions for fluctuations, correlation functions, and scrambling. The derivations of Eqs. (22), (23), and (28) are straightforward and internally consistent, and the numerical checks in Figs. 2, 3, and 4 and in the spin-boson appendix support the formulas. The identification of the survival probability as governing the observable's time evolution is a clean and useful result. However, the paper's broader claims about robustness and generality go beyond what the evidence establishes, as detailed in the major comments. The exact conservation-law mechanism is a special, although physically relevant, situation rather than a generic feature of non-integrable systems.","major_comments":[{"comment":"The abstract states that predictions are 'robust to perturbations that break this approximation,' but Appendix D explicitly says that the non-ergodic scaling 'gets worse as the system size increases' (Fig. 7a). This is a finite-size effect whose scaling direction is unfavorable: for a fixed perturbation, the deviation grows with system size and would destroy the effect in the thermodynamic limit. The robustness claim is therefore not supported by the numerical evidence, and the abstract and discussion should be tempered accordingly, or additional evidence should be provided that the deviation remains bounded for a given perturbation strength as N increases.","section":"Appendix D and Abstract"},{"comment":"The central collapse of the sum in Eq. (20) to a single term, Eq. (21), relies critically on the initial bath state being a unique eigenstate of N_B, which occurs only in extremal charge sectors (e.g., vacuum or fully filled states). The paper's own Appendix C shows that the extension to larger system Hilbert spaces introduces a correction term, Eq. (C2), that can dominate when N_S is large, and the subsequent translational-invariance assumption, Eq. (C5), is not generally justified for a finite system coupled to a bath. The paper should state more precisely the domain of applicability of Eq. (22) and avoid implying that the mechanism is generic for arbitrary system sizes or initial states.","section":"Section III.B and Appendix C"}],"minor_comments":[{"comment":"The caption says 'all qubits up' for panel (a), but the text in Section VI describes the correlated initial state as '|↓,↓,...>_B (All down)'. This inconsistency should be corrected.","section":"Figure 2 caption"},{"comment":"There is a typo: 'transnationally invariant' should be 'translationally invariant'.","section":"Appendix C"},{"comment":"The derivation of the long-time OTOC uses I_n := sum_mu c_mu^n without complex conjugation, which implicitly assumes real eigenvector coefficients. The paper should state this assumption, since the final expression Eq. (29) is not valid for complex coefficients without modification, although the numerical model has a real Hamiltonian.","section":"Appendix B and Eq. (29)"},{"comment":"In the second line, the term O_downarrow downarrow sum_mu c_mu^2(k0,uparrow) should be written as O_downarrow downarrow sum_mu |c_mu|^2 = O_downarrow downarrow if complex coefficients are allowed; the current notation silently assumes real c_mu.","section":"Equation (27)"},{"comment":"The penultimate line indicates that <O(t)O> equals O_uparrow uparrow O_downarrow downarrow, but the equality is only approximate after dropping IPR-weighted terms; using 'approximately equals' at that step would be clearer.","section":"Section V, Eq. (24)"}],"recommendation":"major_revision","confidential_remarks":"The paper presents a correct but rather special mechanism. The main issue for the editor is the overstatement in the abstract: the robustness claim is contradicted by the paper's own Appendix D data, which show the effect degrading with system size. If the authors revise the abstract and discussion to accurately reflect the restricted domain of validity, the paper could be suitable for publication. The novelty is moderate: the core result is that for a single-excitation sector with an extremal bath state, the survival probability governs local observable dynamics, which is a clean observation but not a broad revision of ETH. The numerical verification is adequate. I would not recommend rejection, as the exact results are sound and the limitations can be fixed with careful rewriting."},"author_rebuttal":null,"desk_editor":{"model":"deepseek-v4-flash","letter":"Dear colleague,\n\nThe one thing to know: the core derivation is right. Under a correlated quench in a single-excitation sector, Eq. (22) is a genuine non-random off-diagonal structure for a local observable, and the consequences — IPR^2 fluctuations, time evolution following the survival probability, and a non-scrambling OTOC — follow cleanly. The paper earns its central claim in the regime where it is exact.\n\nWhat is actually new: the explicit form of the observable matrix element in terms of the initial-state amplitudes, Eq. (22), is not in the prior literature. The identification of the local system observable with the survival probability is immediate once stated, but the paper works through the consequences carefully. The spin-boson example in the RWA and the exact-diagonalization checks in Figs. 2–4 support the formulas. The self-citations to your own RMT work are relevant, not padding.\n\nWhere it gets soft: the advertised generality is overstated. Equation (22) is exact because the initial bath state is the unique eigenstate of N_B in its charge sector with one excitation; the sum over bath states collapses to a single term. In any finite-density sector the eigenspace is degenerate and the rank-one structure is lost. That is not a mistake, but it means the effect lives in an extremal slice of Hilbert space. More important, the abstract says predictions are robust to perturbations that break the conservation law. Appendix D shows the opposite scaling trend: for the non-conserving model, the non-ergodic scaling \"gets worse as the system size increases\" (their words, Fig. 7a). So the robustness claim is not established; if anything, the deviation from ETH looks like a finite-size effect once number conservation is relaxed. The multi-excitation generalization in Appendix C also needs translational-invariance assumptions that are not generic.\n\nMinor: the OTOC expansion in Appendix B is cumbersome and hard to follow, but the final expression matches ED in Fig. 4, so I trust it.\n\nOverall: the exact-conservation-law result is solid and worth publishing. The paper deserves a serious referee. For peer review, I would push for a revised abstract that states the exact conditions up front and softens the robustness claim, and for a clearer discussion of why Appendix D does not support the perturbation-robustness wording.\n\nBest, [you]","headline":"Correct core result in an extremal regime; the robustness claim is not supported by the paper's own Appendix D.","tokens_in":16851,"tokens_out":2526,"would_cite":true,"duration_ms":23973,"reading_group":"maybe","serious_thinker":"yes","would_accept_peer_review":true},"rs_alignment":null,"lean_confirmation":null,"pith_extraction":{"msc":[],"pacs":[],"model":"deepseek-v4-flash","headline":"Correlated quenches—one excitation on a system qubit, bath in a single number eigenstate—make local observables deviate from ETH predictions for fluctuations, time evolution, and scrambling.","keywords":["eigenstate thermalization hypothesis","non-ergodic thermalization","single excitation subspace","correlated quench","survival probability","out-of-time-ordered correlator","quantum scrambling","long-time fluctuations"],"falsifier":"A numerical exact-diagonalization experiment on the NN-XXX chain (Eqs. 25–26) can settle the claim: for initial states $|\\!\\uparrow\\rangle_S|\\downarrow\\cdots\\downarrow\\rangle_B$ at increasing chain length $N$, compute the long-time variance $\\delta^2_{\\sigma_z^{(S)}}(\\infty)$ and the IPR, and fit $\\log\\delta^2$ versus $\\log \\mathrm{IPR}$. The paper predicts an asymptotic slope of 2 ($\\delta^2\\propto \\mathrm{IPR}^2$), while the ETH/RMT prediction is a slope of 1; observing slope 1 (or a crossover toward it at large $N$) would refute the correlated-quench scaling. The analogous test can be done for the long-time OTOC average $\\overline{\\langle W(t)VW(t)V\\rangle}$: Eq. (29) predicts it saturates to the finite value of Eq. (30) for $W=V=\\sigma_z^{(S)}$, whereas scrambling would give a vanishing average.","tokens_in":15895,"feed_emoji":"⚛️","tokens_out":14215,"duration_ms":121119,"temperature":0.7,"pith_summary":"The paper shows that a closed, non-integrable quantum system can thermalize in a way that visibly violates the standard signatures of the eigenstate thermalization hypothesis (ETH), provided the dynamics stays inside a single-excitation sector and the bath starts in a non-degenerate eigenstate of a conserved number. Under this 'correlated quench', the energy-basis matrix elements of a local observable are not random: $O_{\\mu\\nu} = \\Delta O\\, c_\\mu(\\alpha_0)c_\\nu(\\alpha_0) + O_{\\downarrow\\downarrow}\\delta_{\\mu\\nu}$, with off-diagonals fixed by the initial-state amplitudes. The paper derives three concrete consequences: equilibrium fluctuations scale as $\\delta^2_O(\\infty) \\approx \\Delta O^2\\, \\mathrm{IPR}(|\\psi(0)\\rangle)^2$ rather than the ETH's $1/D_{\\rm eff}$ scaling; the time-dependent expectation value follows the survival probability $P_0(t)$; and the long-time out-of-time-ordered correlator stays finite, meaning local information does not scramble. These results matter because they give analytic, checkable predictions for when 'thermalization without ETH universality' appears—for example, in rotating-wave approximation settings—and they explain earlier numerical observations of initial-state-dependent scrambling.","feed_headline":"One conserved charge breaks ETH fluctuation scaling","feed_subtitle":"In a one-excitation quench, fluctuations shrink far faster than the ETH predicts—and information does not scramble.","key_machinery":"The load-bearing identity is the collapse of the overlap sum $\\eta = \\sum_k c_\\mu(k,\\uparrow)c_\\nu(k,\\uparrow)$ to the single term $c_\\mu(\\alpha_0)c_\\nu(\\alpha_0)$. This collapse is forced by the structure of the Hilbert space: with $[H,\\hat N]=0$, $\\hat N=\\hat N_S+\\hat N_B$ local, and the initial state $|\\psi(0)\\rangle=|\\!\\uparrow\\rangle_S|k_0\\rangle_B$ with $|k_0\\rangle_B$ a non-degenerate eigenstate of $\\hat N_B$, the only basis state in which the system qubit is excited has the bath in the fixed state $|k_0\\rangle_B$. A local observable $O_S$ that commutes with $\\hat N_S$ and $H_S$ is then identified with the survival probability up to a constant, so its matrix elements inherit the initial-state amplitude products. The inverse participation ratio, $\\mathrm{IPR}(|\\psi(0)\\rangle)=\\sum_\\mu |c_\\mu(\\alpha_0)|^4$, enters as the natural measure of effective Hilbert-space dimension and controls both the fluctuation scaling and the size of finite-$N$ corrections to the OTOC.","core_discovery":"The central claim is Eq. (22): for a correlated quench, observable matrix elements in the energy eigenbasis collapse to $O_{\\mu\\nu} = \\Delta O\\, c_\\mu(\\alpha_0)c_\\nu(\\alpha_0) + O_{\\downarrow\\downarrow}\\delta_{\\mu\\nu}$, where $\\alpha_0$ indexes the initial state $|\\!\\uparrow\\rangle_S|k_0\\rangle_B$. The off-diagonal part is therefore not a random matrix element but a product of the initial state's overlap amplitudes with the two eigenstates; this is what the paper calls an ETH-like relation with non-random off-diagonals. Substituting this form into the diagonal-ensemble formula gives $\\delta^2_O(\\infty) \\approx \\Delta O^2\\,\\mathrm{IPR}(|\\psi(0)\\rangle)^2$ (Eq. 23), the time dependence $\\langle O(t)\\rangle = \\Delta O\\,P_0(t)+O_{\\downarrow\\downarrow}$ (Eq. 28), and a long-time OTOC average $\\overline{F(t)} = \\overline{\\langle W(t)VW(t)V\\rangle}$ that does not vanish when $W=V=\\sigma_z^{(S)}$ (Eqs. 29–30). The system still reaches the diagonal-ensemble expectation in the sense of Eq. (3), so it thermalizes, but it fails the ergodicity condition of Eq. (2) and does not scramble. Numerical exact-diagonalization calculations on a non-integrable NN-XXX spin chain and on a spin-boson model under the rotating-wave approximation match the analytic predictions.","pith_inferences":["Editorial inference: The same mechanism should appear for any conserved quantity that links a local observable to a projection onto the initial state (particle number, magnetization, momentum sectors), so one could look for $\\mathrm{IPR}^2$ fluctuation scaling in Hubbard or lattice-gauge models prepared with one particle on a vacuum-like bath.","Editorial inference: The OTOC result implies that in single-excitation sectors, late-time OTOC decay is not a reliable chaos diagnostic for charge-diagonal operators; scrambling tests should instead use operators with support transverse to the conserved charge or multi-excitation initial states to avoid false negatives.","Editorial inference: Appendix D suggests the non-ergodic scaling survives weak breaking of the conservation law at finite sizes but degrades as the system grows; a systematic finite-size crossover study could map how much symmetry breaking is tolerable before the ETH scaling is restored."],"forward_implications":["Under a correlated quench, equilibrium fluctuations of a local charge-diagonal observable scale as $\\mathrm{IPR}^2$, an extra factor of the inverse participation ratio smaller than the ETH scaling $\\propto \\mathrm{IPR}$; in a Hilbert space of effective dimension $D_{\\rm eff}$, fluctuations are suppressed as $1/D_{\\rm eff}^2$ rather than $1/D_{\\rm eff}$.","The time dependence of the local observable after the quench is exactly (up to a constant offset) the survival probability, $\\langle O(t)\\rangle = \\Delta O\\,P_0(t)+O_{\\downarrow\\downarrow}$; hence measuring local spin polarization gives a direct, experimentally accessible readout of $P_0(t)$ and, by Fourier transform, of the local density of states.","The long-time average of the out-of-time-ordered correlator does not vanish for charge-diagonal operators: for $W=V=\\sigma_z^{(S)}$, $\\overline{\\langle W(t)VW(t)V\\rangle}\\to 1$ in the large-system limit, so local information about that observable is not scrambled even though the Hamiltonian is non-integrable.","The survival probability itself shows the non-ergodic $\\mathrm{IPR}^2$ fluctuation scaling for both correlated and degenerate (e.g., Néel) initial bath states, whereas a local system observable shows it only when the bath state is non-degenerate; this difference is what makes scrambling initial-state dependent.","In the rotating-wave approximation, the spin-boson model realizes exactly the correlated-quench condition, so the analytic predictions for fluctuations, dynamics, and OTOC apply to that familiar open-system setting."],"supporting_citations":[{"why":"States the standard ETH ansatz for diagonal matrix elements that the paper's Eq. (22) modifies in the correlated-quench setting.","marker":"[14]"},{"why":"Supplies Srednicki's ansatz for off-diagonal matrix elements, with random $R_{\\mu\\nu}$, which the paper replaces by the correlated product $c_\\mu(\\alpha_0)c_\\nu(\\alpha_0)$.","marker":"[18]"},{"why":"Earlier work deriving the ETH/RMT scaling $\\delta^2_O \\propto \\mathrm{IPR}$, the baseline that Eq. (23) overturns.","marker":"[20]"},{"why":"Provides the claim that $\\delta^2\\propto\\mathrm{IPR}$ scaling follows from the ETH; this is the standard fluctuation expectation the correlated quench deviates from.","marker":"[12]"},{"why":"Gives the quantum ergodicity condition Eq. (2) that the paper shows is violated while the weaker Eq. (3) still holds.","marker":"[35]"},{"why":"Reports the numerical observation of initial-state-dependent scrambling that the paper's long-time OTOC calculation explains.","marker":"[45]"},{"why":"Shows that the survival probability is not self-averaging, which contextualizes the non-ergodic $\\mathrm{IPR}^2$ scaling of $P_0$ fluctuations.","marker":"[48]"}],"fun_headline_variants":["Single-excitation quench: thermalization but no scrambling","Survival probability sets decay, not ETH fluctuations","Nonrandom off-diagonals break ETH fluctuation scaling","Long-time correlations deviate from ETH in one-excitation quench"],"cache_read_input_tokens":3200,"weakest_assumption_plain":"The argument depends on the bath starting in exactly one definite configuration with no extra excitations, so that when the system qubit is found excited the bath must be in that single configuration; if the bath starts with several possible configurations, the collapse that produces the non-random matrix elements fails.","fun_headline_variants_meta":{"raw":{"variants":["Single-excitation quench: thermalization but no scrambling","Survival probability sets decay, not ETH fluctuations","Nonrandom off-diagonals break ETH fluctuation scaling","Long-time correlations deviate from ETH in one-excitation quench"]},"model":"deepseek-v4-flash","effort":"low","cost_usd":0.000307,"raw_usage":{"total_tokens":1815,"prompt_tokens":1063,"completion_tokens":752,"prompt_tokens_details":{"cached_tokens":384},"prompt_cache_hit_tokens":384,"prompt_cache_miss_tokens":679,"completion_tokens_details":{"reasoning_tokens":687}},"tokens_in":679,"tokens_out":752,"duration_ms":8183,"temperature":1.0,"reasoning_tokens":687,"cache_read_input_tokens":384,"cache_creation_input_tokens":0},"cache_creation_input_tokens":0},"created_at":"2026-08-14T10:08:05.015362+00:00","model_set":{"reader":"deepseek-v4-flash"},"falsifier":"A numerical exact-diagonalization experiment on the NN-XXX chain (Eqs. 25–26) can settle the claim: for initial states $|\\!\\uparrow\\rangle_S|\\downarrow\\cdots\\downarrow\\rangle_B$ at increasing chain length $N$, compute the long-time variance $\\delta^2_{\\sigma_z^{(S)}}(\\infty)$ and the IPR, and fit $\\log\\delta^2$ versus $\\log \\mathrm{IPR}$. The paper predicts an asymptotic slope of 2 ($\\delta^2\\propto \\mathrm{IPR}^2$), while the ETH/RMT prediction is a slope of 1; observing slope 1 (or a crossover toward it at large $N$) would refute the correlated-quench scaling. The analogous test can be done for the long-time OTOC average $\\overline{\\langle W(t)VW(t)V\\rangle}$: Eq. (29) predicts it saturates to the finite value of Eq. (30) for $W=V=\\sigma_z^{(S)}$, whereas scrambling would give a vanishing average.","supporting_citations":[{"cited_title":"Srednicki, Journal of Physics A: Mathematical and General 29, 75 (1996), 9511001 [chao-dyn]","cited_arxiv_id":null,"evidence_quote":"States the standard ETH ansatz for diagonal matrix elements that the paper's Eq. (22) modifies in the correlated-quench setting."},{"cited_title":"Srednicki, J","cited_arxiv_id":null,"evidence_quote":"Supplies Srednicki's ansatz for off-diagonal matrix elements, with random $R_{\\mu\\nu}$, which the paper replaces by the correlated product $c_\\mu(\\alpha_0)c_\\nu(\\alpha_0)$."},{"cited_title":"Nation and D","cited_arxiv_id":null,"evidence_quote":"Earlier work deriving the ETH/RMT scaling $\\delta^2_O \\propto \\mathrm{IPR}$, the baseline that Eq. (23) overturns."},{"cited_title":null,"cited_arxiv_id":null,"evidence_quote":"Provides the claim that $\\delta^2\\propto\\mathrm{IPR}$ scaling follows from the ETH; this is the standard fluctuation expectation the correlated quench deviates from."},{"cited_title":"Iyoda and T","cited_arxiv_id":null,"evidence_quote":"Reports the numerical observation of initial-state-dependent scrambling that the paper's long-time OTOC calculation explains."},{"cited_title":"Self-averaging in many-body quantum systems out of equilibrium: Chaotic systems","cited_arxiv_id":"1906.11856","evidence_quote":"Shows that the survival probability is not self-averaging, which contextualizes the non-ergodic $\\mathrm{IPR}^2$ scaling of $P_0$ fluctuations."}],"review_version":1}