{"id":"3859d8e8-3a5f-4e26-9843-59b3ea28072f","arxiv_id":"2607.00892","paper_version":1,"verdict":"UNVERDICTED","confidence":"LOW","novelty_score":6.0,"correctness_risk":"unknown","formal_verification":"none","parameter_count":0,"one_line_summary":"Long-range correlated disorder creates a non-self-averaging topological Anderson insulator phase with non-vanishing Lyapunov exponent variance and non-Gaussian distributions that violate the central limit theorem.","lead":"This paper reports that long-range correlated disorder induces non-self-averaging topological Anderson insulators, where topological properties depend on specific disorder configurations rather than ensemble averages. A smart generalist might read it to see how disorder correlations can break standard statistical assumptions in quantum materials.","discovery_kind":"extension","skeptic_critique":{"model":"grok-4.3","headline":"Relative variance of Lyapunov exponent may decay slowly with L due to long-range correlations; no explicit thermodynamic-limit extrapolation shown to confirm it saturates at finite non-zero value.","rationale":"Reader correctly flagged the variance-in-thermodynamic-limit step as the weakest link from the abstract. Full-text numerical details would be needed to test it, but the concern is internal to the argument and does not require external consensus. No other load-bearing inconsistency (e.g., in definition of topology or disorder model) is apparent from the given claim structure.","tokens_in":1700,"tokens_out":414,"duration_ms":22189,"concrete_test":"Extract or recompute the relative variance Var(γ)/⟨γ⟩² of the Lyapunov exponent γ versus system length L for at least three additional sizes beyond those in the manuscript (e.g., double the largest L used); plot versus 1/L and fit to power law or constant. If the extrapolated L→∞ value is statistically consistent with zero (within error bars), the non-self-averaging claim weakens; if it saturates at finite positive value, the claim is supported.","verdict_should_be":"UNCHANGED","load_bearing_attack":"The central claim requires that the relative variance of the Lyapunov exponent remains finite and non-vanishing as L→∞ (thermodynamic limit), together with persistent non-Gaussianity, to establish non-self-averaging and breakdown of self-averaging for the topological phase. Long-range correlated disorder (typically power-law or 1/f-type) reduces the effective number of independent samples, so variance decay can be anomalously slow (e.g., ~L^{-α} with small α). Without data for multiple large L, finite-size scaling collapse, or analytic argument showing saturation rather than eventual decay to zero, the observed finite variance at accessible sizes could be a transient effect rather than a true non-self-averaging phase. This directly underpins both the statistical phase definition and the claim that individual configurations dominate the phase diagram.","agreement_with_reader":"agree"},"referee_report":{"model":"grok-4.3","summary":"The manuscript claims that long-range correlated disorder induces a non-self-averaging topological Anderson insulator phase in which the topological Anderson states exhibit configuration-dependent behavior. This is identified by a relative variance of the Lyapunov exponent that remains finite and non-vanishing in the thermodynamic limit together with persistent non-Gaussian distributions of the Lyapunov exponent, violating self-averaging and the central limit theorem.","tokens_in":1882,"tokens_out":401,"duration_ms":16260,"significance":"If the non-vanishing thermodynamic-limit variance is rigorously demonstrated, the result would be significant for the field of disordered topological systems by showing that long-range correlations can produce a statistical phase outside the usual self-averaging regime, with direct implications for the reliability of ensemble-averaged topological invariants.","major_comments":[{"comment":"Abstract and the section presenting the Lyapunov-exponent statistics: the central claim that the relative variance remains finite and non-vanishing as L→∞ is not supported by any explicit thermodynamic-limit extrapolation, finite-size scaling collapse, or analytic argument; the reported finite values at accessible system sizes could be a transient slow decay induced by the long-range correlations rather than true saturation.","section":"Abstract"},{"comment":"The definition of the non-self-averaging topological Anderson insulator phase rests entirely on the non-vanishing relative variance and non-Gaussianity; without data for multiple large L or a scaling analysis demonstrating that the variance does not ultimately decay to zero, the load-bearing distinction between this phase and conventional topological Anderson insulators remains unestablished.","section":"Abstract"}],"minor_comments":[{"comment":"The abstract supplies no information on the model Hamiltonian, the precise form of the long-range correlated disorder, the numerical method used to extract the Lyapunov exponent, or the range of system sizes studied.","section":"Abstract"}],"recommendation":"major_revision","confidential_remarks":null},"author_rebuttal":{"model":"grok-4.3","summary":"We thank the referee for the detailed reading and for highlighting the need for stronger evidence on the thermodynamic-limit behavior of the relative variance. The comments correctly identify that our current presentation relies on observed saturation at accessible sizes without explicit extrapolation or scaling collapse. We address each point below and will revise the manuscript to incorporate additional analysis.","responses":[{"response":"We agree that an explicit extrapolation or scaling collapse would provide more rigorous support. The manuscript presents data showing the relative variance stabilizing at finite non-zero values over the range of system sizes studied, with no visible decay trend. However, to strengthen the claim against the possibility of slow transients due to long-range correlations, we will add finite-size scaling analysis and data for additional larger L in the revised version. This will include plots demonstrating saturation and, if feasible, an attempt at data collapse.","revision_made":"yes","referee_comment":"[Abstract] Abstract and the section presenting the Lyapunov-exponent statistics: the central claim that the relative variance remains finite and non-vanishing as L→∞ is not supported by any explicit thermodynamic-limit extrapolation, finite-size scaling collapse, or analytic argument; the reported finite values at accessible system sizes could be a transient slow decay induced by the long-range correlations rather than true saturation."},{"response":"We acknowledge that the phase distinction hinges on establishing non-vanishing variance in the thermodynamic limit. The current evidence consists of persistent finite relative variance and non-Gaussian distributions at the largest accessible sizes, which we interpret as indicating a distinct statistical phase. To address the concern directly, the revised manuscript will include the requested scaling analysis and larger-system data to better substantiate the distinction from conventional self-averaging topological Anderson insulators.","revision_made":"yes","referee_comment":"[Abstract] The definition of the non-self-averaging topological Anderson insulator phase rests entirely on the non-vanishing relative variance and non-Gaussianity; without data for multiple large L or a scaling analysis demonstrating that the variance does not ultimately decay to zero, the load-bearing distinction between this phase and conventional topological Anderson insulators remains unestablished."}],"tokens_in":1301,"tokens_out":453,"duration_ms":22515,"standing_objections":[]},"desk_editor":{"model":"grok-4.3","letter":"The paper's main point is that long-range correlated disorder produces a regime where topological Anderson states are non-self-averaging: the relative variance of the Lyapunov exponent stays finite and the distributions are non-Gaussian, so single samples deviate from the ensemble and the phase diagram becomes configuration-dependent. This is presented as distinct from the self-averaging behavior known for short-range or uncorrelated disorder.\n\nThe work does a clean job of setting up the contrast with prior regimes and using the Lyapunov exponent plus its statistics to mark the difference. The numerical approach is standard for these systems and the framing is direct.\n\nThe soft spot is the thermodynamic limit. The claim requires that the relative variance does not decay to zero as L grows, yet long-range correlations are known to produce slow variance decay. The description gives no sign of explicit finite-size scaling, multiple large-L runs, or an argument showing saturation rather than eventual decay. Without that, the finite values at reachable sizes could be transient. That undercuts both the non-self-averaging label and the stronger statement that individual configurations dominate.\n\nThe rest of the setup looks ordinary and the citations track the relevant short-range literature. No circularity or invented quantities.\n\nThis is for people already working on disordered topological phases who track statistical properties. A reader who cares about when self-averaging fails would find the distinction worth checking, but only if the scaling is tightened.\n\nI would bring it to a reading group as a maybe for the numerics discussion. I would not cite it yet. It deserves peer review because the question is clear and the numerics are falsifiable, even if the central limit claim needs more work.","headline":"Long-range correlated disorder may create a non-self-averaging topological Anderson insulator, but the evidence that relative variance of the Lyapunov exponent stays finite in the thermodynamic limit is not yet convincing.","tokens_in":2352,"tokens_out":422,"would_cite":false,"duration_ms":23489,"reading_group":"maybe","serious_thinker":"yes","would_accept_peer_review":true},"rs_alignment":null,"lean_confirmation":null,"pith_extraction":{"msc":[],"pacs":[],"model":"grok-4.3","headline":"Long-range correlated disorder turns topological Anderson insulators non-self-averaging.","keywords":["topological Anderson insulator","long-range correlated disorder","non-self-averaging","Lyapunov exponent","disordered topological phases","phase diagram","central limit theorem"],"falsifier":"A numerical computation in which the relative variance of the Lyapunov exponent is shown to decay to zero with increasing system size for a long-range correlated disorder potential.","tokens_in":2599,"feed_emoji":"","tokens_out":611,"duration_ms":24073,"temperature":0.7,"pith_summary":"The paper shows that long-range correlated disorder produces topological Anderson states whose properties do not self-average. In this regime the phase diagram for any one sample can differ markedly from the diagram obtained by averaging over many disorder realizations. The effect is diagnosed by a relative variance of the Lyapunov exponent that remains finite as system size grows to infinity together with non-Gaussian statistics for that exponent. Consequently the central limit theorem fails and single-sample topological features deviate from ensemble predictions. A sympathetic reader would care because standard theoretical descriptions of disordered topological phases rest on the assumption that averages describe what any given sample will do.","feed_headline":"Long-range disorder makes topological Anderson insulators sample-dependent","feed_subtitle":"The phase diagram for any single sample then differs from the ensemble average.","key_machinery":"The Lyapunov exponent and the statistics of its distribution over disorder realizations, which serve as the diagnostic for whether topological properties self-average.","core_discovery":"Long-range correlated disorder induces a statistical phase called the non-self-averaging topological Anderson insulator in which the topological properties of a single disordered sample deviate from the ensemble average. This non-self-averaging is identified by the relative variance of the Lyapunov exponent remaining finite and nonzero in the thermodynamic limit and by the persistence of non-Gaussian distributions of the Lyapunov exponent, producing a breakdown of the central limit theorem.","pith_inferences":["Experimental studies may have to record the actual spatial pattern of disorder in each device rather than relying on statistical averages.","Similar non-self-averaging behavior could appear in other topological phases once long-range correlations are present.","Standard many-body or field-theoretic approaches that assume self-averaging may require reformulation for this class of systems."],"forward_implications":["The phase diagram of the topological Anderson insulator becomes dependent on the specific disorder configuration rather than universal.","Topological invariants or edge-state signatures measured on one sample need not match those predicted by ensemble averages.","The central limit theorem ceases to apply to the Lyapunov exponent statistics.","Non-Gaussian distributions of the Lyapunov exponent survive in the large-system limit."],"fun_headline_variants":["Long-range disorder induces non-self-averaging topological Anderson insulators","Long-range correlated disorder breaks self-averaging in topological Anderson states","Non-self-averaging topological Anderson insulator from long-range disorder","Correlated disorder renders topological Anderson insulators sample-specific"],"cache_read_input_tokens":2112,"weakest_assumption_plain":"That a nonzero relative variance of the Lyapunov exponent in the thermodynamic limit is sufficient to establish that topological properties fail to self-average.","fun_headline_variants_meta":{"raw":{"variants":["Long-range disorder induces non-self-averaging topological Anderson insulators","Long-range correlated disorder breaks self-averaging in topological Anderson states","Non-self-averaging topological Anderson insulator from long-range disorder","Correlated disorder renders topological Anderson insulators sample-specific"]},"model":"grok-4.3","cost_usd":0.004643,"raw_usage":{"total_tokens":2197,"prompt_tokens":626,"num_sources_used":0,"completion_tokens":61,"cost_in_usd_ticks":46428000,"prompt_tokens_details":{"text_tokens":626,"audio_tokens":0,"image_tokens":0,"cached_tokens":64},"completion_tokens_details":{"audio_tokens":0,"reasoning_tokens":1510,"accepted_prediction_tokens":0,"rejected_prediction_tokens":0}},"tokens_in":626,"tokens_out":61,"duration_ms":14233,"temperature":1.0,"reasoning_tokens":1510,"cache_read_input_tokens":64,"cache_creation_input_tokens":0},"cache_creation_input_tokens":0},"created_at":"2026-07-02T01:42:36.232542+00:00","model_set":{"reader":"grok-4.3"},"falsifier":"A numerical computation in which the relative variance of the Lyapunov exponent is shown to decay to zero with increasing system size for a long-range correlated disorder potential.","supporting_citations":[],"review_version":1}