{"id":"b60588ad-1c87-4409-8311-2aff1bc303a9","arxiv_id":"2606.03426","paper_version":1,"verdict":"UNVERDICTED","confidence":"LOW","novelty_score":7.0,"correctness_risk":"unknown","formal_verification":"none","parameter_count":0,"one_line_summary":"At the Anderson transition in a Chern insulator the system shows non-zero conductance and a critical length scale in the local Chern marker, with excitation density failing to follow Kibble-Zurek scaling during quenches.","lead":"The paper examines the critical properties of the topological Anderson transition in a disordered Chern insulator, finding non-zero conductance and a critical length scale from the local Chern marker, plus quench dynamics that deviate from Kibble-Zurek scaling. Smart generalists might read it to learn how disorder and rapid changes affect topological states in quantum materials.","discovery_kind":"extension","skeptic_critique":{"model":"grok-4.3","headline":"Local Chern marker profile may not yield the true correlation length for exponent extraction at the disordered Anderson transition","rationale":"The reader's weakest assumption identifies precisely the same point—the reliability of the marker-derived length and finite-size control—and this remains the single most load-bearing assumption even after the abstract is supplemented by the claim of consistency with IQHE exponents. No other internal inconsistency is visible from the given material.","tokens_in":1732,"tokens_out":362,"duration_ms":14748,"concrete_test":"For the same disorder realizations and system sizes used in the paper, recompute the length scale both from the local Chern marker decay and from the disorder-averaged inverse participation ratio (or Thouless conductance) versus disorder strength; if the extracted \nu differs by more than the quoted uncertainty, the marker-based scaling does not capture the standard critical length.","verdict_should_be":"CONDITIONAL","load_bearing_attack":"The central claim rests on the real-space profile of the local Chern marker developing a length scale whose finite-size scaling directly supplies the correlation-length exponent \nu and dynamical exponent z, asserted to match the non-interacting IQHE class. For this extraction to be load-bearing, the marker length must track the diverging correlation length of the Anderson transition (rather than a disorder-specific or boundary-dominated quantity), and the simulations must be large enough that size effects do not masquerade as criticality. Standard diagnostics in Anderson localization (IPR, Thouless conductance, level statistics) are not mentioned as cross-checks in the abstract; if the marker length scales differently from these, the reported consistency with IQHE exponents would be an artifact of the chosen observable rather than evidence of universality. The quench-dynamics claim (decoupling of marker length from excitation density) inherits the same uncertainty.","agreement_with_reader":"agree"},"referee_report":{"model":"grok-4.3","summary":"The manuscript examines the topological Anderson transition separating the Chern insulator phase from the trivial Anderson insulator in a strongly disordered model. It reports that the transition features non-zero electrical conductance together with the appearance of a critical length scale in the real-space profile of the local Chern marker; finite-size scaling of this length is used to extract the correlation-length exponent ν and dynamical exponent z, which are stated to agree with the non-interacting integer quantum Hall universality class. The authors then drive the disorder strength across the transition and analyze the resulting quench dynamics, finding that the excitation density deviates from Kibble-Zurek scaling while the marker-derived length scale remains decoupled from the production of excitations (close to the KZ prediction only for the topological-to-trivial direction).","tokens_in":1897,"tokens_out":463,"duration_ms":16999,"significance":"If the local Chern marker length is shown to track the true diverging correlation length of the Anderson transition, the work would establish a real-space diagnostic for criticality in disordered topological systems and demonstrate that non-equilibrium scaling can decouple from equilibrium exponents in a manner absent from clean topological quenches. Such a result would be of interest to both the Anderson localization and topological matter communities.","major_comments":[{"comment":"Abstract: The central claim that the extracted ν and z match the IQHE class rests on the real-space profile of the local Chern marker supplying the correlation length of the Anderson transition. Standard Anderson diagnostics (inverse participation ratio, Thouless conductance, or level statistics) are not referenced as cross-checks; without explicit comparison showing that the marker length scales identically to these observables at the same critical disorder strength, the reported universality could be an artifact of the chosen quantity rather than evidence of the underlying fixed point.","section":"Abstract"},{"comment":"Abstract: The assertion that the non-equilibrium marker length is decoupled from excitation generation inherits the same uncertainty. If the marker profile does not faithfully represent the diverging correlation length (as questioned above), the reported deviation from Kibble-Zurek scaling for the excitation density cannot be unambiguously attributed to a decoupling of length scales at the Anderson critical point.","section":"Abstract"}],"minor_comments":[],"recommendation":"major_revision","confidential_remarks":null},"author_rebuttal":{"model":"grok-4.3","summary":"We thank the referee for their thorough review and valuable feedback on our manuscript. We address each of the major comments point by point below.","responses":[{"response":"The local Chern marker is a natural choice for probing the correlation length at the topological Anderson transition because it encodes the real-space distribution of the topological invariant. Its critical scaling yields exponents consistent with the integer quantum Hall universality class, and this is further supported by the observation of non-zero conductance at the transition point. While standard localization measures such as the inverse participation ratio could provide additional confirmation, they primarily characterize the localization length rather than the topological criticality. We therefore maintain that the marker-based length is the appropriate diagnostic here. If the editor deems it necessary, we are prepared to include a supplementary comparison in a revised version.","revision_made":"partial","referee_comment":"[Abstract] Abstract: The central claim that the extracted ν and z match the IQHE class rests on the real-space profile of the local Chern marker supplying the correlation length of the Anderson transition. Standard Anderson diagnostics (inverse participation ratio, Thouless conductance, or level statistics) are not referenced as cross-checks; without explicit comparison showing that the marker length scales identically to these observables at the same critical disorder strength, the reported universality could be an artifact of the chosen quantity rather than evidence of the underlying fixed point."},{"response":"Given our justification for the marker length as the correlation length in the equilibrium case, the reported decoupling in the quench dynamics stands as a key finding of the work. This decoupling appears to be a distinctive feature of the disordered topological transition, as opposed to clean systems where Kibble-Zurek scaling holds more directly. The direction-dependent behavior further underscores the non-equilibrium peculiarities at this critical point.","revision_made":"no","referee_comment":"[Abstract] Abstract: The assertion that the non-equilibrium marker length is decoupled from excitation generation inherits the same uncertainty. If the marker profile does not faithfully represent the diverging correlation length (as questioned above), the reported deviation from Kibble-Zurek scaling for the excitation density cannot be unambiguously attributed to a decoupling of length scales at the Anderson critical point."}],"tokens_in":1402,"tokens_out":466,"duration_ms":27721,"standing_objections":[]},"desk_editor":{"model":"grok-4.3","letter":"The one or two things to know are that this paper finds the topological Anderson transition characterized by non-zero conductance and a critical length from the local Chern marker, yielding exponents matching the integer quantum Hall effect, and that in quenches the excitation density deviates from Kibble-Zurek scaling with the marker length decoupled from excitations.\n\nThe new element is extending this analysis to the disordered Chern insulator and highlighting the non-equilibrium behavior that differs from clean systems. The numerics appear to make a connection to established criticality classes in a disordered setting. It does well in examining both the equilibrium critical properties and the dynamics after crossing the transition by ramping disorder.\n\nThe soft spots are around the use of the local Chern marker to define the correlation length. If this length does not correspond to the actual diverging length at the Anderson transition, or if the simulations are not large enough to avoid size effects, the reported consistency with IQHE exponents could be an artifact. The abstract does not mention checks against other common diagnostics for Anderson transitions, so that is a point to verify. The dynamics results depend on this as well. Since the full details are not in the abstract, the robustness of the finite-size scaling would need to be assessed from the paper itself.\n\nThis paper is for people studying disordered topological insulators and critical phenomena in quenches. A reader focused on numerical studies of Chern insulators would likely get something out of the quench part.\n\nIt shows honest engagement with the literature on the topic. I recommend sending it for peer review to allow detailed examination of the methods and scaling analysis.","headline":"Extracts IQHE-like exponents from local Chern marker at topological Anderson transition and shows KZ deviations in quenches, but marker length needs cross-checks to confirm it tracks true correlation length.","tokens_in":2392,"tokens_out":399,"would_cite":false,"duration_ms":26372,"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":"Disorder-driven transition in a Chern insulator shows non-zero conductance and a critical length scale from the local Chern marker.","keywords":["topological Anderson transition","Chern insulator","local Chern marker","critical exponents","Kibble-Zurek scaling","quench dynamics","disorder","integer quantum Hall effect"],"falsifier":"A calculation or measurement in which the length extracted from the local Chern marker scales with disorder in a manner inconsistent with the correlation-length and dynamical exponents of the integer quantum Hall universality class.","tokens_in":2643,"feed_emoji":"","tokens_out":687,"duration_ms":23844,"temperature":0.7,"pith_summary":"The paper studies the topological Anderson phase transition separating a Chern insulator from a trivial Anderson insulator in the presence of strong disorder. It establishes that this transition is marked by non-zero electrical conductance together with the appearance of a critical length scale visible in the real-space profile of the local Chern marker. Critical exponents for the correlation length and dynamics are then read off from the scaling of that length and found to agree with those known from clean integer quantum Hall models. When the disorder is ramped across the transition, the resulting quench dynamics differ from clean topological systems: the density of excitations fails to follow Kibble-Zurek scaling and the non-equilibrium length scale extracted from the Chern marker is decoupled from the creation of those excitations.","feed_headline":"Chern insulator Anderson transition yields IQHE-like exponents","feed_subtitle":"Non-zero conductance and critical length scale appear, yet excitations decouple from Kibble-Zurek scaling in quenches.","key_machinery":"The real-space profile of the local Chern marker, which develops a critical length scale whose scaling supplies the correlation-length and dynamical exponents.","core_discovery":"The transition is characterized by a non-zero electrical conductance and by the emergence of a critical length scale in the real-space profile of the local Chern marker. From this, we extract the correlation-length and the dynamical critical exponents, which are consistent with those of non-interacting models of the integer quantum Hall effect. We then ramp the disorder strength across the transition and study the ensuing dynamics. In contrast to clean topological systems, we find that the excitation density does not follow the Kibble-Zurek scaling. The non-equilibrium length scale associated with the local Chern marker is decoupled from the generation of excitations.","pith_inferences":["The observed decoupling implies that topological markers and particle excitations can respond independently when disorder is varied dynamically.","Similar decoupling may appear in other disordered topological transitions where a local invariant can be tracked in real space.","The finite-size results invite direct comparison with larger-scale or continuum-limit simulations to test whether the decoupling persists in the thermodynamic limit."],"forward_implications":["Critical exponents extracted from the local Chern marker match those of the integer quantum Hall effect.","Excitation density after a disorder quench does not obey Kibble-Zurek scaling.","The non-equilibrium length scale from the local Chern marker is decoupled from the generation of excitations.","For the system sizes studied, the length scale remains close to the Kibble-Zurek prediction for topological-to-trivial quenches but deviates for the reverse direction."],"fun_headline_variants":["Chern insulator Anderson transition matches IQHE exponents","Critical length scale emerges in local Chern marker","Excitations decouple from Kibble-Zurek in Chern quenches","Non-zero conductance defines Chern Anderson transition"],"cache_read_input_tokens":64,"weakest_assumption_plain":"The real-space profile of the local Chern marker supplies a correlation length whose scaling with disorder strength yields the true critical exponents without being dominated by finite-size or boundary effects.","fun_headline_variants_meta":{"raw":{"variants":["Chern insulator Anderson transition matches IQHE exponents","Critical length scale emerges in local Chern marker","Excitations decouple from Kibble-Zurek in Chern quenches","Non-zero conductance defines Chern Anderson transition"]},"model":"grok-4.3","cost_usd":0.004611,"raw_usage":{"total_tokens":2278,"prompt_tokens":652,"num_sources_used":0,"completion_tokens":58,"cost_in_usd_ticks":46112000,"prompt_tokens_details":{"text_tokens":652,"audio_tokens":0,"image_tokens":0,"cached_tokens":256},"completion_tokens_details":{"audio_tokens":0,"reasoning_tokens":1568,"accepted_prediction_tokens":0,"rejected_prediction_tokens":0}},"tokens_in":652,"tokens_out":58,"duration_ms":10181,"temperature":1.0,"reasoning_tokens":1568,"cache_read_input_tokens":256,"cache_creation_input_tokens":0},"cache_creation_input_tokens":0},"created_at":"2026-06-28T08:22:25.242473+00:00","model_set":{"reader":"grok-4.3"},"falsifier":"A calculation or measurement in which the length extracted from the local Chern marker scales with disorder in a manner inconsistent with the correlation-length and dynamical exponents of the integer quantum Hall universality class.","supporting_citations":[],"review_version":1}