{"id":"b153fbea-7e6f-4aad-970f-d739227b7d34","arxiv_id":"2608.11186","paper_version":1,"verdict":"REJECT","confidence":"MODERATE","novelty_score":4.0,"correctness_risk":"high","formal_verification":"none","parameter_count":5,"one_line_summary":"Changing the asymmetry of inter-chain hopping in a disordered two-leg ladder drives a skin-to-Anderson-to-skin localization transition, with edge pile-up reappearing in a line-gap spectral regime.","lead":"This paper studies a disordered two-leg ladder made of one non-Hermitian chain and one ordinary chain, connected by hopping that is stronger in one direction than the other. It reports that tuning this directional hopping switches the electron states between piling at the edge, spreading out in a disordered pattern, and piling at the edge again.","discovery_kind":"extension","skeptic_critique":{"model":"deepseek-v4-flash","headline":"Line-gap claim is visually asserted without a topological invariant; if the a>t spectrum actually has point-gap winding, the central 'beyond point-gap' result collapses.","rationale":"The reader's weakest_assumption identifies exactly the same load-bearing concern: the line-gap claim is asserted from visual inspection of Fig. 2 without computing any topological invariant. My independent reading confirms that this is the decisive issue. The abstract and conclusion make the central claim depend on the coexistence of skin localization with a line-gap spectrum; if that spectral-topology read is wrong, the novelty of the paper is gone. The paper provides no computation of the point-gap winding number, the non-Bloch winding, or a generalized Brillouin zone analysis, so the claim is unsupported. The local spectral analysis in Sec. V is not a substitute: it treats each site independently, predicts a different critical value (a_c = sqrt(t^2 + Delta_j^2) versus a=t), and explicitly neglects the intra-chain hopping terms that generate the dispersive bands whose topology matters. The internal inconsistency in the IPR interpretation in Sec. III further weakens confidence in the numerical evidence, but it is secondary to the missing topological invariant. A concrete, feasible test is to compute the point-gap winding of the clean PBC spectrum (and, if possible, a real-space winding for the disordered periodic ring) at the parameters of Fig. 2. If that winding is non-zero, the central claim collapses; if it is zero, the paper would present a genuinely surprising result, but the current manuscript does not provide that evidence. Therefore the reader's REJECT verdict is appropriate, and my stress-test does not change it.","tokens_in":8323,"tokens_out":4611,"duration_ms":46511,"concrete_test":"For the clean limit of Hamiltonian (1) with the Fig. 2 parameters (gamma=1, lambda=1.5, J=1, t=28, a=50), compute the periodic-boundary spectrum E(k), k in [0,2pi), and evaluate the point-gap winding W(E_ref) = (1/2pi i) integral_0^{2pi} dk d/dk log det[H(k)-E_ref] for a reference energy E_ref in the purported line gap. Repeat at a=0 and a=28 to map the winding transitions. If W(E_ref) is non-zero for any a>t reference point, the spectrum has a point gap and the claimed 'beyond point-gap' skin effect is not established. For the disordered case, the same check can be performed on a large periodic ring with disorder, using the real-space winding number or by monitoring the OBC spectrum for encirclement of a reference point.","verdict_should_be":"UNCHANGED","load_bearing_attack":"Section III and Fig. 2 assert that for a>t the spectrum 'develops an imaginary line-gap instead of a point gap', but no winding number, non-Bloch band invariant, or generalized Brillouin zone calculation is provided. In non-Hermitian systems the NHSE is tied to non-zero point-gap winding of the Bloch or non-Bloch spectrum; a line-gapped spectrum does not by itself preclude a non-zero point-gap winding around a reference point if the spectrum encircles it. The local 2x2 analysis in Sec. V predicts the transition at a_c = sqrt(t^2 + Delta_j^2), not at a=t, and neglects the intra-chain hoppings (gamma +/- lambda) and J, so it cannot substantiate the spectral-topology classification of the full ladder. The IPR discussion in Sec. III is also internally inconsistent: an increasing IPR is described as 'less localized' and the maximum IPR is called the 'weakest' localization, which inverts the standard definition. The most load-bearing issue is the unsupported line-gap/point-gap classification: if the a>t spectrum actually has non-zero point-gap winding, the central claim that skin localization persists beyond the point-gap regime collapses.","agreement_with_reader":"agree"},"referee_report":{"model":"deepseek-v4-flash","summary":"The manuscript studies a two-leg ladder composed of a disordered Hatano–Nelson chain coupled to a Hermitian chain by asymmetric inter-chain hopping (parameter a). It reports that tuning a drives the eigenstates from boundary (skin) localization to an Anderson-localized regime at a=t and back to skin localization for a>t, and it claims that the re-entrant skin effect occurs although the spectrum is line-gapped, i.e., beyond the conventional point-gap regime. The evidence is based on complex-energy spectra, inverse participation ratios, mean center of mass, and finite-size scaling, supplemented by a local 2x2 spectral analysis that exhibits an exceptional point at a_c = sqrt(t^2 + Delta_j^2).","tokens_in":8586,"tokens_out":6159,"duration_ms":53957,"significance":"If the central claim were established, the result would be significant because it would challenge the prevalent point-gap-topology criterion for the non-Hermitian skin effect in disordered systems and could motivate new invariants for line-gapped skin modes. The paper has concrete strengths: the model is simple, no parameters are fitted, the local exceptional-point calculation is transparent and exact, and the disorder-averaged observables are clearly defined. However, the headline result is not currently supported by the evidence presented.","major_comments":[{"comment":"The statement that for a>t \"the spectrum develops an imaginary line-gap instead of a point gap\" is made from visual inspection of the complex-energy plot. No winding number of the spectrum around a reference point, non-Bloch band invariant, or generalized Brillouin zone calculation is provided. Because the abstract's central claim is precisely that skin localization persists without point-gap topology, this classification must be demonstrated, e.g., by computing the point-gap winding number of the non-Bloch or disorder-averaged spectrum as a function of a. As it stands, the line-gap claim is an assumption, not a result.","section":"Section III, Fig. 2"},{"comment":"The IPR narrative is internally inconsistent. Equation (4) defines IPR as the sum of fourth powers of the normalized wavefunction amplitudes, so a larger IPR corresponds to more localized eigenstates. The text says \"the average IPR increases steadily with increasing a, indicating that the skin modes become progressively less localized\" and \"the localization reaches its weakest, reflected by the maximum value of the average IPR.\" These statements invert the standard meaning of IPR. The identification of a=t as the Anderson-localization point and the claimed non-monotonicity of localization therefore rest on an incorrect reading of the numerical quantity. The authors should either reinterpret the data with the standard IPR convention or use a different diagnostic, such as a participation-number-based measure.","section":"Section III, Fig. 3 and text after Eq. (6)"},{"comment":"The local 2x2 analysis predicts the transition at a_c = sqrt(t^2 + Delta_j^2), which depends on the local disorder Delta_j and exceeds t whenever Delta_j is nonzero, whereas the numerical transition is stated to occur at a=t (the unidirectional-coupling condition t-a=0). The local Hamiltonian in Eq. (14) also neglects the intra-chain hoppings (gamma +/- lambda) and J. The paper does not explain how the local exceptional point at a_c leads to the global transition at a=t; as written, the analytical derivation is not connected to the numerical transition point and cannot be used to support it. A derivation of the full-chain spectral/gap condition, or an explicit argument that the local analysis applies to the ladder, is needed.","section":"Section V, Eq. (21)"},{"comment":"The finite-size scaling contains only 10 disorder realizations and no error bars. The claim that the IPR at a=28 is \"nearly independent of the system size\" whereas at other a values it decreases is the key evidence for Anderson localization at the critical point; with N_r=10 and no statistical uncertainty, this distinction is not convincing. The authors should report the standard error over disorder realizations and preferably increase N_r for the scaling plot.","section":"Section III, Fig. 4"},{"comment":"The phase diagram is built on mcom, the mean center of mass, which discriminates boundary-localized from bulk-centered states but does not by itself discriminate extended states from Anderson-localized ones. A bulk-centered Anderson-localized state and a bulk-centered extended state both produce large mcom. The V-shaped high-mcom region therefore does not establish Anderson localization; additional diagnostics, such as IPR with the correct orientation or spectral statistics, are required to support the phase boundary.","section":"Section IV, Figs. 5 and 6"}],"minor_comments":[{"comment":"The first sentence reads \"disorder verses t\"; this should be \"disorder versus t.\"","section":"Section IV"},{"comment":"The notation is inconsistent: Eq. (8) uses mcom for the disorder-averaged quantity, while Eq. (12) uses xcom for an individual eigenstate. The notation should be harmonized.","section":"Eqs. (8) and (12)"},{"comment":"References [3] and [26] are duplicates (Gong et al., Physical Review X 8, 031079 (2018)).","section":"References"},{"comment":"The phrase \"an local exceptional point\" should read \"a local exceptional point.\"","section":"Section V"},{"comment":"The text \"2Neigenstates\" needs a space; minor typographical errors of this kind should be corrected throughout.","section":"After Eq. (5)"}],"recommendation":"major_revision","confidential_remarks":"The paper addresses an interesting question, but the current version does not support the central claim. The missing topological invariant and the IPR inversion are the most serious issues. I recommend major revision rather than outright rejection because the model and the phenomenon may be salvageable with additional analysis; however, if the required computations, such as the point-gap winding number, reveal that the a>t spectrum does have point-gap winding, the central claim will have to be withdrawn."},"author_rebuttal":null,"desk_editor":{"model":"deepseek-v4-flash","letter":"Colleague,\n\nQuick read on arXiv:2608.11186. The paper takes the two-leg disordered non-Hermitian ladder from Ref [19] and adds an asymmetry parameter in the vertical coupling. Tuning that asymmetry drives a skin-Anderson-skin reentrant transition, which is a legitimate extension and, as far as I can tell, not in the earlier literature. The local 2x2 spectral analysis is standard but correctly done, and the identification of the unidirectional coupling point a=t as a special point is reasonable.\n\nThe problems start with the interpretation of the numerics. The text in Sec. III explicitly says that for a<t the IPR increases with a, 'indicating that the skin modes become progressively less localized.' That is backwards: larger IPR means more localized. The same paragraph calls the maximum IPR 'the weakest' localization. That is not a typo, it is repeated. It undercuts the reader's trust in the localization claims.\n\nMore load-bearing: the central 'beyond point-gap' claim rests on a visual assertion that for a>t the spectrum is line-gapped. No winding number, non-Bloch invariant, or generalized Brillouin zone calculation is given. A line-gapped spectrum does not by itself rule out point-gap winding around some reference point, and the paper does not show that the relevant topological invariant is zero. The local analysis in Sec. V predicts an exceptional point at a_c = sqrt(t^2 + Delta_j^2), which is not equal to t for any finite disorder, so it does not explain the transition at a=t that drives the numerics. The local analysis also drops the intra-chain hoppings, which may or may not matter, but the connection to the full ladder is never made.\n\nThere are smaller issues: Fig. 4 uses only 10 disorder realizations, no error bars anywhere, and the disorder distribution is not specified. No code or data is shipped. These are fixable but they are part of why the current evidence is not persuasive.\n\nWho is this for? Someone working on non-Hermitian localization in coupled chains might find the model and the phase diagram useful as a starting point. But the paper in its current form does not support the headline claim. It deserves a serious referee because the underlying idea is plausible and the model is clean, but the referee should insist on a proper spectral-topology analysis and corrected IPR interpretation.\n\nI would not cite it yet, and I wouldn't bring it to the reading group without a warning label, but it is not a crank submission. Send it out, but expect heavy revision.","headline":"Modest model extension with a reentrant transition, but the line-gap skin-effect claim is asserted, not shown, and the IPR text is inverted.","tokens_in":9059,"tokens_out":3426,"would_cite":false,"duration_ms":30462,"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":"In a disordered two-leg ladder, tuning the inter-chain asymmetry drives a skin-effect-to-Anderson-to-skin-effect sequence, and the returning skin localization appears with a line-gap spectrum instead of the point-gap spectrum usually…","keywords":["non-Hermitian skin effect","Anderson localization","Hatano-Nelson model","asymmetric inter-chain coupling","line-gap topology","point-gap topology","exceptional point","disordered ladder"],"falsifier":"Compute the non-Bloch winding number or generalized Brillouin zone for the full disordered ladder at $a>t$: if the winding around every reference energy is zero and open-boundary eigenstates still pile at the boundary, the paper's core observation stands; if no skin mode appears under periodic boundary conditions or the winding is nonzero, the line-gap-versus-point-gap reading is wrong. A second decisive check is whether the Anderson-to-skin return occurs exactly at $a=t$ independent of disorder realization, since the local analysis predicts a disorder-dependent transition at $a_c=\\sqrt{t^2+\\Delta_j^2}$.","tokens_in":8104,"feed_emoji":"🔄","tokens_out":13823,"duration_ms":103593,"temperature":0.7,"pith_summary":"The paper studies a two-leg ladder: one chain has non-reciprocal (directional) hopping, the other is Hermitian, and the two are coupled vertically with amplitudes $t-a$ and $t+a$ while strong disorder is present on both legs. It claims that increasing the asymmetry $a$ drives two successive localization transitions: for $a<t$ the eigenstates accumulate at the boundary (non-Hermitian skin effect), at $a=t$ the skin effect is suppressed and disorder produces Anderson-localized states, and for $a>t$ boundary localization returns. The distinctive claim is that the returning skin effect coexists with a line-gap spectrum rather than the point-gap spectrum normally associated with skin modes. If correct, this means boundary localization in disordered non-Hermitian lattices is not controlled by point-gap winding alone and points to a more general mechanism.","feed_headline":"Skin localization persists beyond point-gap topology","feed_subtitle":"Tuning one coupling parameter switches boundary pile-up into Anderson localization and back again","key_machinery":"The central object is the asymmetric inter-chain coupling parameter $a$, which makes the vertical hopping amplitudes $t_\\uparrow=t-a$ and $t_\\downarrow=t+a$ unequal; at $a=t$ the upward hopping vanishes and the coupling becomes unidirectional. The paper analyzes each site pair through the local $2\\times2$ Hamiltonian $H_j=\\begin{pmatrix} \\Delta_j & t+a \\\\ t-a & -\\Delta_j \\end{pmatrix}$, whose eigenvalues $E_\\pm=\\pm\\sqrt{\\Delta_j^2+t^2-a^2}$ predict a site-dependent exceptional point at $a_c=\\sqrt{t^2+\\Delta_j^2}$. This local spectral analysis carries the explanation of how the gap closes and reopens along the imaginary axis, while the global transition observed in the numerics sits at $a=t$ where one inter-chain hopping amplitude vanishes. The spectral-topology language used throughout is the distinction between a point gap (the spectrum winds around a reference point) and a line gap (the spectrum is separated along a line), with the claimed skin phase at $a>t$ assigned to the latter.","core_discovery":"The central claim, stated on the paper's own terms, is that robust non-Hermitian skin localization can persist beyond the conventional point-gap regime in a strongly coupled disordered ladder. The authors show that at $a=0$ the complex spectrum has point-gap topology and eigenstates pile at the left boundary; as $a$ grows the point gap closes, and at the unidirectional coupling point $a=t$ one inter-chain hopping amplitude vanishes, the skin effect is destroyed, and the eigenstates become Anderson localized across the lattice. For $a>t$ the spectrum is described as line-gapped, yet the eigenstates again accumulate at the boundary, which the authors take as evidence that boundary localization is not solely dictated by point-gap topology. The evidence includes disorder-averaged inverse participation ratios, mean center of mass, finite-size scaling showing $O(1)$ IPR at $a=t$, and a V-shaped Anderson region in the $(t,W)$ phase diagram around $a=t$.","pith_inferences":["Editorial inference: if the line-gap skin phase survives a genuine generalized Brillouin zone calculation, the standard non-Bloch bulk-boundary correspondence needs a new disorder-averaged invariant that does not rely on point-gap winding.","Editorial inference: the mismatch between the numerical transition at $a=t$ and the local exceptional point $a_c=\\sqrt{t^2+\\Delta_j^2}$ suggests the full ladder's transition may be controlled by the vanishing of the $t-a$ hopping rather than by the local degenerate point; calculating the disorder-resolved spectrum near $a=t$ would separate these mechanisms.","Editorial inference: the ladder maps naturally onto electrical-circuit and photonic-platform experiments, where boundary impedance or transmission measurements for $a>t$ could test whether boundary accumulation persists with a line-gapped spectrum.","Editorial inference: the disorder-broadened V-shaped Anderson region hints at possible mobility edges inside the ladder; a direct IPR-versus-energy study would test whether a critical energy separates skin and Anderson states."],"forward_implications":["For $a<t$, the skin effect is robust and is transferred from the non-reciprocal chain into the Hermitian chain through the inter-chain coupling.","At $a=t$, the inter-chain coupling becomes unidirectional, the skin effect is suppressed, and disorder-driven Anderson localization takes over, as shown by an IPR that stays $O(1)$ with system size.","For $a>t$, boundary localization returns even though the spectrum is line-gapped, so in this model the skin effect is not a consequence of point-gap winding.","In the $(t,W)$ phase diagram, stronger disorder broadens the high-center-of-mass region around $t=a$, meaning disorder enlarges the parameter range in which Anderson localization wins.","The mean center of mass has a sharp peak at $a=t$, marking a sudden redistribution of eigenstate weight away from the boundary and back."],"supporting_citations":[{"why":"Supplies the strongly coupled disordered non-Hermitian two-chain setting and the Anderson delocalization phenomenon this ladder builds on and contrasts with.","marker":"[19]"},{"why":"Introduces the non-reciprocal chain used as one leg of the ladder and the disorder-driven localization transition it exhibits.","marker":"[32]"},{"why":"Establishes point-gap topology as the standard topological origin of the skin effect, the paradigm the paper claims to go beyond.","marker":"[9]"},{"why":"Provides the non-Bloch bulk-boundary correspondence and edge-state topological invariants that the line-gap result would extend or challenge.","marker":"[16]"},{"why":"Formulates biorthogonal bulk-boundary correspondence for non-Hermitian systems, the framework for assessing boundary localization beyond point gaps.","marker":"[18]"},{"why":"Supplies non-Bloch band theory whose point-gap winding is the conventional condition the paper argues is bypassed.","marker":"[6]"},{"why":"Gives the winding-number-to-skin-mode correspondence whose point-gap condition is the comparison baseline for the $a>t$ regime.","marker":"[8]"},{"why":"Classifies non-Hermitian topological phases by point-gap and line-gap symmetries, the language in which the paper frames its spectral-topology claim.","marker":"[14]"}],"fun_headline_variants":["Skin modes survive beyond point-gap topology","Disorder drives skin-to-Anderson-to-skin switches","One coupling knob toggles skin and Anderson phases","Skin localization outlives point-gap protection","Beyond point gap: robust boundary pile-up"],"cache_read_input_tokens":3200,"weakest_assumption_plain":"The load-bearing premise is the visual classification of the $a>t$ spectrum as line-gapped rather than point-gapped; if that classification is wrong, the claim of skin localization beyond the point-gap regime collapses, and the paper supplies no winding number or generalized Brillouin zone invariant to confirm it while its local analytic transition $a_c=\\sqrt{t^2+\\Delta_j^2}$ differs from the numerical transition at $a=t$.","fun_headline_variants_meta":{"raw":{"variants":["Skin modes survive beyond point-gap topology","Disorder drives skin-to-Anderson-to-skin switches","One coupling knob toggles skin and Anderson phases","Skin localization outlives point-gap protection","Beyond point gap: robust boundary pile-up"]},"model":"deepseek-v4-flash","effort":"low","cost_usd":0.000184,"raw_usage":{"total_tokens":1296,"prompt_tokens":901,"completion_tokens":395,"prompt_tokens_details":{"cached_tokens":384},"prompt_cache_hit_tokens":384,"prompt_cache_miss_tokens":517,"completion_tokens_details":{"reasoning_tokens":323}},"tokens_in":517,"tokens_out":395,"duration_ms":3826,"temperature":1.0,"reasoning_tokens":323,"cache_read_input_tokens":384,"cache_creation_input_tokens":0},"cache_creation_input_tokens":0},"created_at":"2026-08-12T04:27:38.332185+00:00","model_set":{"reader":"deepseek-v4-flash"},"falsifier":"Compute the non-Bloch winding number or generalized Brillouin zone for the full disordered ladder at $a>t$: if the winding around every reference energy is zero and open-boundary eigenstates still pile at the boundary, the paper's core observation stands; if no skin mode appears under periodic boundary conditions or the winding is nonzero, the line-gap-versus-point-gap reading is wrong. A second decisive check is whether the Anderson-to-skin return occurs exactly at $a=t$ independent of disorder realization, since the local analysis predicts a disorder-dependent transition at $a_c=\\sqrt{t^2+\\Delta_j^2}$.","supporting_citations":[{"cited_title":null,"cited_arxiv_id":null,"evidence_quote":"Supplies the strongly coupled disordered non-Hermitian two-chain setting and the Anderson delocalization phenomenon this ladder builds on and contrasts with."}],"review_version":1}