{"id":"fa5b1294-9b43-41e4-a9b2-7becb48a2699","arxiv_id":"2508.14724","paper_version":1,"verdict":"UNVERDICTED","confidence":"LOW","novelty_score":6.0,"correctness_risk":"unknown","formal_verification":"none","parameter_count":0,"one_line_summary":"In an interacting non-Hermitian quasiperiodic chain with power-law hopping, the authors report a topologically trivial intermediate regime with real spectrum and multifractal states, and show that long-range hopping weakens the skin effect.","lead":"This paper numerically studies a one-dimensional quantum chain with asymmetric long-range hopping, a quasiperiodic potential, and interactions. It reports a middle phase where wavefunctions are multifractal yet the energy spectrum is fully real, and finds that long-range hopping suppresses the non-Hermitian skin effect at open boundaries.","discovery_kind":"extension","skeptic_critique":{"model":"deepseek-v4-flash","headline":"Power-law hopping amplifies finite-size effects: the intermediate multifractal phase may be a small-system artifact.","rationale":"The reader identified finite-size scaling as the weakest assumption; I agree. The provided material does not contain the model Hamiltonian or numerical methods, so I cannot verify the computation, but the abstract's claims make specific phase distinctions that depend on extrapolation. Power-law hopping exacerbates usual ED limitations because the interaction range is not finite; for exponents σ near 1, the system is effectively non-local and conventional finite-size scaling may not converge. The proposed test directly measures whether the intermediate regime survives larger sizes and different σ. Since the reader's verdict was UNVERDICTED and my concern reinforces rather than overrides that assessment, the verdict should remain UNCHANGED.","tokens_in":5630,"tokens_out":6483,"duration_ms":78564,"concrete_test":"Re-run exact diagonalization for the interacting model at L=10,12,14,16 (or the largest feasible) at parameters inside the claimed intermediate regime. Compute (i) the Fock-space fractal dimension d2 from the participation entropy of mid-spectrum eigenstates, and (ii) the fraction of eigenstates with |Im E|<10^-8, as functions of L. Extrapolate d2 vs 1/L using a power-law fit; if the extrapolated d2 is not distinct from 0 (NHMBL) or 1 (ergodic), the intermediate phase is not established. Also vary the hopping exponent σ=1.0,1.5,2.0 and check whether the size dependence of the phase boundary changes qualitatively. If the real-spectrum region vanishes or the fractal dimension extrapolates to a trivial value with increasing L, the central claim fails.","verdict_should_be":"UNCHANGED","load_bearing_attack":"The central claim is that a topologically trivial intermediate regime exists with multifractal many-body eigenstates and a fully real spectrum, distinct from NHMBL. All sub-claims (intermediate phase, destruction of mobility edges, robust real spectrum) rely on exact-diagonalization data on chains that are necessarily small for interacting long-range models (typically L ≲ 16). With power-law hopping of the form t_ij ~ |i-j|^-σ, the effective coupling range grows with L, so the thermodynamic limit cannot be captured by adding a few sites. A state that appears multifractal in Fock space at L=12 may be either ergodic or localized at L→∞, and the 'real spectrum' region can shrink because the spectral transition moves with L. The abstract itself describes a crossover sequence ('restoring the TRS before crossing over'), but nothing in the visible text rules out that this intermediate region is a finite-size crossover rather than a genuine phase. The phase classification is thus only as secure as the finite-size scaling, which is the load-bearing assumption.","agreement_with_reader":"agree"},"referee_report":{"model":"deepseek-v4-flash","summary":"The paper claims to study one-dimensional interacting non-Hermitian quasiperiodic chains with asymmetric power-law hopping. The central claims are: (i) a fully real eigenspectrum does not necessarily imply non-Hermitian many-body localization (NHMBL); (ii) there exists a topologically trivial intermediate regime with multifractal eigenstates and a real spectrum; (iii) interactions destroy the multifractal and mobility edges seen in the non-interacting counterpart; and (iv) due to long-range hopping, a topologically non-trivial ergodic phase under periodic boundary conditions does not always yield boundary-localized skin modes under open boundary conditions. The manuscript as provided contains only the abstract, the introduction, and a reference list. No model Hamiltonian, parameter definitions, numerical results, finite-size scaling analysis, or error estimates are included.","tokens_in":5890,"tokens_out":3916,"duration_ms":53747,"significance":"The questions addressed are timely and potentially important for the understanding of non-Hermitian many-body localization, the interplay of topology, time-reversal symmetry, and long-range hopping. If the claims are substantiated, they would challenge the common identification of a real eigenspectrum with a trivial NHMBL phase and would clarify the fate of multifractality and skin effects in interacting long-range models. The paper also frames a falsifiable prediction: interactions destroy single-particle multifractal and mobility edges in the proposed intermediate regime. However, because the visible manuscript contains no technical content, the significance is entirely conditional on evidence that is not currently available.","major_comments":[{"comment":"The paper never defines the Hamiltonian. The claims require a precise specification of the quasiperiodic potential, the non-Hermitian asymmetric hopping amplitude, the power-law exponent σ, the interaction term, and the boundary conditions. Without an explicit model, none of the reported phenomena—intermediate multifractal phase, real-spectrum region, destruction of mobility edges, or absent skin effect—can be reproduced or checked. A complete model section with the Hamiltonian and all parameter definitions is essential.","section":"Entire manuscript / no model section"},{"comment":"The central claims are numerical, but the manuscript contains no data, figures, or finite-size scaling analysis. In particular, the claimed intermediate multifractal phase with a fully real spectrum is a small-system-sensitive statement. With power-law hopping, the effective range grows with system size, so a crossover at L ≲ 16 can easily be mistaken for a genuine phase. The abstract's own phrase 'before crossing over' underscores this risk. The authors must provide scaling collapse of multifractal exponents (e.g., IPR or D_q), spectral statistics, and spectral-reality fraction across several system sizes, with a clear criterion distinguishing a phase from a finite-size crossover.","section":"Abstract / Results (missing)"},{"comment":"The paper repeatedly distinguishes 'topologically trivial' and 'topologically non-trivial' regimes but never defines the topological invariant used. The central claim that a real spectrum does not imply a trivial NHMBL phase requires simultaneous measurement of a topological quantity (e.g., winding number, spectral flow under twisted boundary conditions, or an equivalent many-body invariant) and the spectral reality. Without this definition, the claim is not falsifiable. The topology diagnostic and its relation to TRS must be stated explicitly.","section":"Phase classification / topology (Abstract, §I)"},{"comment":"The claim that the entire topologically non-trivial ergodic regime under PBC does not always give rise to OBC skin modes is not supported by any boundary-condition comparison. To establish this, the authors need to show OBC eigenstate density or participation ratio as a function of parameters and system size, and ideally identify the threshold in the hopping exponent where the skin effect disappears. No such analysis is present in the submitted text.","section":"Skin effect claim (Abstract)"}],"minor_comments":[{"comment":"Typo: 'Our findings thus advances' should be 'Our findings thus advance'. Also 'quaisperiodic' in §I should be 'quasiperiodic'.","section":"Abstract"},{"comment":"The introduction references several models and results (e.g., Refs. [37,41,44,65,67]) without defining the corresponding Hamiltonians; adding a brief model orientation in the introduction would help the reader.","section":"§I / References"},{"comment":"The text ends after the introduction and references; no conclusions or summaries of numerical findings are present. The manuscript appears truncated or incomplete in its current form.","section":"Manuscript completeness"},{"comment":"The reference list mentions software and diagnostics such as QuSpin [80] and complex spacing ratios [81], but the methods are never described. If these tools are used, the relevant definitions and statistical procedures must appear in the main text.","section":"References / Methods"}],"recommendation":"major_revision","confidential_remarks":"The submitted manuscript as provided is essentially an abstract plus introduction; the entire technical content is missing. This is not a standard 'minor revision' situation because not a single load-bearing equation or result is available. I recommend major revision, with the understanding that the authors must supply the full model, numerical data, scaling analysis, and topological diagnostics. If, in fact, the full manuscript was intended to be submitted and the missing sections are an artifact of the review package, then I ask the editor to obtain the complete version before further evaluation."},"author_rebuttal":null,"desk_editor":{"model":"deepseek-v4-flash","letter":"Here's the quick take: this is a numerical exact-diagonalization paper with a nice twist—reality of the eigenspectrum does not necessarily mean the system is in the NHMBL phase. The authors report an intermediate phase with multifractal states, fully real spectrum, and trivial topology, plus two additional results (interaction destroying mobility edges and long-range hopping suppressing skin modes). If correct, that's a useful addition to the non-Hermitian quasiperiodic phase-diagram literature. The question is well motivated and they cite the relevant prior work, including Xu et al. (2021) and Peng et al. (2023, 2025) on power-law hopping and skin-effect weakening.\n\nWhat's new is the specific combination: interactions + power-law hopping + non-Hermitian AAH potential. That combination hasn't been studied before, as far as the abstract and references suggest. The abstract is honest about the claims and doesn't oversell.\n\nNow the soft spots. The version I can see stops at the introduction and references—no Hamiltonian, no parameters, no finite-size scaling, no error bar. So the reader's low soundness score is a reflection of missing evidence, not a judgment on the work. The central claims are all numerical and all depend on extrapolating from chains that are necessarily small because ED with long-range interactions is expensive. The stress-test worry is on point: power-law hopping of the form t_ij ~ |i-j|^{-σ} means the effective range grows with L, so adding a few sites changes the model more than it would for short-range hopping. A Fock-space multifractal at L=12 might be ergodic or localized at L→∞. The abstract itself says the restoration of TRS happens 'before crossing over'—the word 'crossover' is exactly the finite-size phenomenon that needs to be shown to sharpen into a phase. None of this is visible in the excerpt. It's possible that the full paper does careful scaling and the intermediate phase holds up, but I can't verify that.\n\nOne more point: the claims about interactions destroying mobility edges and about skin modes not appearing are also prone to finite-size artifacts. The interaction destruction is particularly delicate because interactions mix Fock-space sectors in ways that may not stabilize until larger L.\n\nBottom line: give it to a referee. The question is important enough and the combination is new enough to warrant a careful look, but the referee should push hard on the finite-size scaling and ask for the explicit model and the definitions of the observables. If the intermediate phase survives scaling, this is a solid contribution to the non-Hermitian MBL literature. If it doesn't, it's still a useful documentation of a crossover, but the abstract should say so.","headline":"Numerical claim that a real spectrum can coexist with multifractal many-body states in a non-Hermitian quasiperiodic chain with power-law hopping; plausible but unverifiable from the available text, and finite-size scaling is the main risk.","tokens_in":6304,"tokens_out":2413,"would_cite":false,"duration_ms":25210,"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":"A fully real eigenspectrum can coexist with multifractal states in an interacting non-Hermitian quasiperiodic chain, so real spectrum alone does not indicate many-body localization.","keywords":["non-Hermitian many-body localization","quasiperiodic potential","power-law hopping","multifractality","time-reversal symmetry","non-Hermitian skin effect","mobility edge","exact diagonalization"],"falsifier":"A larger-scale numerical study (e.g., tensor-network or density-matrix renormalization group) that measures the many-body inverse participation ratio scaling in the intermediate regime: if it approaches ergodic or localized scaling as system size grows, the intermediate phase is an artifact; likewise, computing the open-boundary density profile for the topologically non-trivial ergodic regime could reveal whether skin modes appear at larger sizes.","tokens_in":5600,"feed_emoji":"⚛️","tokens_out":10475,"duration_ms":95739,"temperature":0.7,"pith_summary":"The paper studies a one-dimensional chain of interacting particles moving in a quasiperiodic potential, with asymmetric hopping that decays as a power of distance—a non-Hermitian system that does not conserve probability. The authors show that the common shortcut of identifying the many-body localized phase by checking whether the energy spectrum is fully real is not reliable in this model. Instead, they find a topologically trivial intermediate phase in which the eigenstates are multifractal—neither fully delocalized nor localized—while the spectrum is real, sitting between the ergodic and the localized phases. They also find that interactions erase the mobility edges and multifractal structure that exist in the non-interacting version of the model. Finally, because of the long-range hopping, the topologically non-trivial regime under periodic boundaries does not always produce the boundary-localized skin modes expected under open boundaries.","feed_headline":"A real spectrum can hide a multifractal phase in non-Hermitian chains","feed_subtitle":"Interactions and long-range hopping open an intermediate phase that breaks the spectrum–localization link.","key_machinery":"The paper's model combines (i) asymmetric hopping whose amplitude decays as a power of distance, (ii) a quasiperiodic potential, and (iii) a particle–particle interaction. The phase identification uses two complementary many-body diagnostics: the complex spacing ratio, which distinguishes real from complex spectra and ergodic from localized statistics, and the scaling of the many-body inverse participation ratio, which quantifies multifractality. The key mechanism is the competition between long-range hopping (which delocalizes and can create skin modes) and the quasiperiodic potential plus interactions (which localize and restore time-reversal symmetry); in the intermediate regime this comp","core_discovery":"The central claim is that in an interacting non-Hermitian quasiperiodic chain with asymmetric power-law hopping, the reality of the eigenspectrum is not sufficient to conclude that the system is in the non-Hermitian many-body localized (NHMBL) phase. The paper identifies an intermediate, topologically trivial regime in which the many-body eigenstates are multifractal—neither fully delocalized nor localized—while the spectrum is entirely real, thus respecting time-reversal symmetry. In this intermediate regime, interactions completely suppress the multifractal and mobility edges that are present in the non-interacting model. Additionally, the paper shows that the long-range nature of the hopp","pith_inferences":["If the intermediate multifractal phase is robust at larger sizes, analogous phases may appear in other non-Hermitian models with power-law interactions, and they could be sought in experiments with dissipative cold atoms or photonic waveguides.","The suppression of skin modes by long-range hopping suggests that transport measurements in open systems with power-law couplings will not reveal the topological character of the bulk; a direct probe of the complex winding number or the density profile may be needed instead.","The interaction-driven destruction of mobility edges could be a general mechanism: sufficiently strong interactions may erase the energy separation that produces mobility edges in single-particle spectra, so this effect may be testable in clean quasiperiodic systems."],"forward_implications":["A purely real spectrum is no longer a reliable witness for non-Hermitian many-body localization; eigenstate structure must be checked as well.","The newly identified intermediate phase with multifractal states and real spectrum is a distinct phase of interacting non-Hermitian quasiperiodic matter that any comprehensive phase diagram must include.","Interactions can destroy mobility edges in long-range non-Hermitian systems, so the non-interacting phase diagram does not survive the addition of interactions.","The non-Hermitian skin effect is not guaranteed in long-range hopping models even when the periodic-boundary spectrum is topologically non-trivial; open-boundary observables must be computed explicitly."],"supporting_citations":[{"why":"Supplies the asymmetric hopping model that forms the non-Hermitian backbone of the Hamiltonian.","marker":"[37]"},{"why":"Representative prior work identifying the real-spectrum regime with non-Hermitian many-body localization; the paper's first claim overturns this identification.","marker":"[41]"},{"why":"Introduces the quasiperiodic chain with power-law hopping in the non-interacting limit, the starting point the interacting model extends.","marker":"[61]"},{"why":"Earlier non-interacting study of the non-Hermitian quasiperiodic model with power-law hopping; its mobility-edge structure is what interactions are shown to destroy.","marker":"[65]"},{"why":"Directly established that long-range hopping weakens the non-Hermitian skin effect, supporting the paper's result on absent skin modes under open boundaries.","marker":"[67]"},{"why":"Provides the complex-spacing-ratio diagnostic used to detect the spectral transition and identify the intermediate phase.","marker":"[81]"}],"fun_headline_variants":["Real spectrum no longer guarantees localization in non-Hermitian chains","Interactions spawn a hidden multifractal phase in non-Hermitian chains","Long-range hopping breaks the spectrum-localization link","Multifractal order emerges with a fully real spectrum","Non-Hermitian chains reveal a new intermediate phase"],"cache_read_input_tokens":2688,"weakest_assumption_plain":"The classification of the intermediate phase depends on extrapolating exact-diagonalization results from short chains, so the finite-size data must faithfully represent the thermodynamic limit.","fun_headline_variants_meta":{"raw":{"variants":["Real spectrum no longer guarantees localization in non-Hermitian chains","Interactions spawn a hidden multifractal phase in non-Hermitian chains","Long-range hopping breaks the spectrum-localization link","Multifractal order emerges with a fully real spectrum","Non-Hermitian chains reveal a new intermediate phase"]},"model":"deepseek-v4-flash","effort":"low","cost_usd":0.00062,"raw_usage":{"total_tokens":2731,"prompt_tokens":783,"completion_tokens":1948,"prompt_tokens_details":{"cached_tokens":256},"prompt_cache_hit_tokens":256,"prompt_cache_miss_tokens":527,"completion_tokens_details":{"reasoning_tokens":1865}},"tokens_in":527,"tokens_out":1948,"duration_ms":14718,"temperature":1.0,"reasoning_tokens":1865,"cache_read_input_tokens":256,"cache_creation_input_tokens":0},"cache_creation_input_tokens":0},"created_at":"2026-08-05T18:17:34.117736+00:00","model_set":{"reader":"deepseek-v4-flash"},"falsifier":"A larger-scale numerical study (e.g., tensor-network or density-matrix renormalization group) that measures the many-body inverse participation ratio scaling in the intermediate regime: if it approaches ergodic or localized scaling as system size grows, the intermediate phase is an artifact; likewise, computing the open-boundary density profile for the topologically non-trivial ergodic regime could reveal whether skin modes appear at larger sizes.","supporting_citations":[{"cited_title":null,"cited_arxiv_id":null,"evidence_quote":"Representative prior work identifying the real-spectrum regime with non-Hermitian many-body localization; the paper's first claim overturns this identification."},{"cited_title":null,"cited_arxiv_id":null,"evidence_quote":"Introduces the quasiperiodic chain with power-law hopping in the non-interacting limit, the starting point the interacting model extends."},{"cited_title":null,"cited_arxiv_id":null,"evidence_quote":"Earlier non-interacting study of the non-Hermitian quasiperiodic model with power-law hopping; its mobility-edge structure is what interactions are shown to destroy."},{"cited_title":null,"cited_arxiv_id":null,"evidence_quote":"Directly established that long-range hopping weakens the non-Hermitian skin effect, supporting the paper's result on absent skin modes under open boundaries."},{"cited_title":null,"cited_arxiv_id":null,"evidence_quote":"Provides the complex-spacing-ratio diagnostic used to detect the spectral transition and identify the intermediate phase."}],"review_version":1}