{"id":"25a0d515-f570-48e8-8ab7-eaf4ac4052eb","arxiv_id":"2606.06466","paper_version":1,"verdict":"UNVERDICTED","confidence":"LOW","novelty_score":5.0,"correctness_risk":"unknown","formal_verification":"none","parameter_count":0,"one_line_summary":"In the interacting non-Hermitian SSH model the real-space topological marker remains robust while non-Hermiticity amplifies staggered charge correlations near exceptional points under open boundary conditions.","lead":"The paper numerically studies an interacting non-Hermitian Su-Schrieffer-Heeger chain and reports that a real-space topological marker stays reliable while non-Hermiticity strongly boosts staggered charge correlations near exceptional points under open boundaries. A smart generalist might read it to see how topology, interactions, and non-Hermitian physics combine in one-dimensional models that appear in open quantum systems and engineered lattices.","discovery_kind":"extension","skeptic_critique":{"model":"grok-4.3","headline":"Finite-size effects in ED may drive the reported OBC amplification of charge correlations near EPs","rationale":"The reader's weakest assumption already flags finite-size artifacts in ED; the load-bearing concern is exactly that point, now made concrete by noting the missing scaling for the OBC correlation enhancement that underpins the 'pronounced amplification' claim.","tokens_in":1676,"tokens_out":304,"duration_ms":11982,"concrete_test":"Recompute the staggered charge correlation vs. non-Hermiticity strength (Fig. corresponding to OBC data) for at least three consecutive even lengths (e.g., L=8,10,12) at fixed interaction U; if the peak height near the EP decreases by >20% or its position moves by more than the EP width when L increases, the enhancement is a finite-size artifact.","verdict_should_be":"UNCHANGED","load_bearing_attack":"The central claim that non-Hermiticity produces a pronounced, physically meaningful amplification of staggered charge correlations under OBC (due to low-energy state accumulation near EPs) rests on exact diagonalization of finite chains. No system-size scaling is shown for the correlation peak height or its location relative to the EP; on small L the non-Hermitian skin effect plus discrete spectrum can artificially pile up weight at the boundary, inflating the CDW signal. If the enhancement shrinks or shifts with increasing L, the attribution to EPs and the claim of interaction enhancement become unreliable.","agreement_with_reader":"agree"},"referee_report":{"model":"grok-4.3","summary":"The manuscript investigates the interacting non-Hermitian Su-Schrieffer-Heeger model using exact diagonalization on finite chains. It maps the phase diagram under periodic and open boundary conditions via a real-space topological marker, staggered charge correlations, and the complex many-body spectrum. The central claims are that the topological marker remains a robust diagnostic of non-Hermitian topological phases even with interactions and signals their breakdown at the CDW onset, while non-Hermiticity enhances interaction effects, producing a pronounced amplification of staggered charge correlations near exceptional points under open boundary conditions due to accumulation of low-energy states.","tokens_in":1790,"tokens_out":393,"duration_ms":21253,"significance":"If the reported OBC amplification and marker robustness hold after addressing finite-size concerns, the work would establish a concrete example of non-Hermiticity amplifying interaction-driven charge ordering in a topological chain and validate real-space markers for interacting non-Hermitian systems. The absence of system-size scaling data leaves the physical attribution of the enhancement open to reinterpretation as a numerical artifact.","major_comments":[{"comment":"The central claim of pronounced amplification of staggered charge correlations near EPs under OBC (abstract and numerical results section) rests on ED of finite chains with no system-size scaling shown for the correlation peak height or its location relative to the EP. This is load-bearing because the non-Hermitian skin effect plus discrete spectrum on small L can artificially pile up boundary weight, potentially inflating the CDW signal and undermining the attribution to low-energy state accumulation near EPs.","section":"Numerical results on OBC charge correlations"}],"minor_comments":[{"comment":"The abstract does not specify the range of interaction strengths, non-Hermiticity parameters, or chain lengths L used in the ED calculations.","section":null}],"recommendation":"major_revision","confidential_remarks":null},"author_rebuttal":{"model":"grok-4.3","summary":"We thank the referee for their careful reading and constructive comments. Below we respond point-by-point to the major comment.","responses":[{"response":"We agree that the lack of explicit system-size scaling for the OBC staggered charge correlation peak constitutes a genuine limitation of the present study. Exact diagonalization of the interacting non-Hermitian model restricts us to modest chain lengths, and the non-Hermitian skin effect can indeed concentrate weight near the boundaries on small systems. Our attribution of the enhancement to low-energy state accumulation rests on the observed correlation between the correlation peak and the closing of the many-body gap near exceptional points; however, without scaling data this link remains suggestive rather than conclusive. We will revise the manuscript to include an explicit discussion of finite-size caveats and to qualify the strength of the physical interpretation accordingly.","revision_made":"partial","referee_comment":"[Numerical results on OBC charge correlations] The central claim of pronounced amplification of staggered charge correlations near EPs under OBC (abstract and numerical results section) rests on ED of finite chains with no system-size scaling shown for the correlation peak height or its location relative to the EP. This is load-bearing because the non-Hermitian skin effect plus discrete spectrum on small L can artificially pile up boundary weight, potentially inflating the CDW signal and undermining the attribution to low-energy state accumulation near EPs."}],"tokens_in":1279,"tokens_out":302,"duration_ms":19666,"standing_objections":[]},"desk_editor":{"model":"grok-4.3","letter":"The paper adds interactions to the non-Hermitian SSH chain and tracks both a real-space topological marker and staggered charge correlations. It compares periodic and open boundaries and reports that the marker still identifies the topological phases and drops when charge-density-wave order appears.\n\nThe clearest new piece is the observation that non-Hermiticity produces a stronger amplification of charge correlations under open boundaries near exceptional points, which the authors tie to low-energy state accumulation. The work is a direct numerical extension of earlier non-Hermitian SSH studies into the interacting regime, and the phase diagrams under both boundary conditions are useful to see.\n\nThe soft spot is the reliance on exact diagonalization of finite chains. The stress-test concern about skin-effect artifacts inflating the open-boundary signal is reasonable; without system-size scaling of the correlation peak height or its position relative to the exceptional point, it is hard to judge whether the reported enhancement survives in the thermodynamic limit or is mainly a small-L effect. That does not invalidate the rest of the numerics, but it does make the central amplification claim the part that needs the most scrutiny.\n\nThis is a paper for people already working on non-Hermitian many-body topology or 1D topological markers. Readers who want concrete phase diagrams and a check that the marker survives interactions will get something from it. It is coherent on its own terms and deserves a serious referee, mainly so the finite-size question can be settled in review.","headline":"The paper's main addition is the OBC-specific boost to staggered charge correlations near EPs in the interacting non-Hermitian SSH, but finite-size ED leaves that claim provisional.","tokens_in":2294,"tokens_out":373,"would_cite":false,"duration_ms":16316,"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":"A real-space topological marker stays reliable for non-Hermitian topological phases even after interactions trigger charge density waves.","keywords":["non-Hermitian SSH model","topological marker","charge density wave","exceptional points","interacting fermions","open boundary conditions","staggered charge correlations"],"falsifier":"A calculation on longer chains that shows the staggered charge-correlation peak near exceptional points disappearing or moving away from the reported location would falsify the claimed amplification.","tokens_in":2600,"feed_emoji":"⚛️","tokens_out":654,"duration_ms":11192,"temperature":0.7,"pith_summary":"The paper examines an interacting version of the non-Hermitian Su-Schrieffer-Heeger chain and tracks how topology and charge ordering compete. It finds that the real-space topological marker continues to identify the topological phases and correctly flags their disappearance when a charge density wave sets in. Non-Hermiticity strengthens the effect of interactions, producing a clear increase in staggered charge correlations near exceptional points when the chain has open boundaries. This increase is traced to the pile-up of low-energy states that favors electronic instabilities. The results are obtained by comparing the many-body spectrum and correlation functions under periodic and open boundary conditions.","feed_headline":"Topological marker survives interactions in non-Hermitian SSH chains","feed_subtitle":"It flags the breakdown into charge density waves and reveals stronger staggered correlations near exceptional points under open boundaries.","key_machinery":"Real-space topological marker that evaluates local winding or polarization on finite chains and detects the transition to charge-density-wave order.","core_discovery":"The topological marker remains a robust diagnostic of non-Hermitian topological phases in the presence of interactions and consistently signals their breakdown at the onset of a charge density wave. Non-Hermiticity enhances interaction effects, leading to pronounced amplification of staggered charge correlations near exceptional points under open boundary conditions due to accumulation of low-energy states.","pith_inferences":["Similar amplification of ordering tendencies may appear in other one-dimensional non-Hermitian models with exceptional points, such as extended Kitaev chains.","Cold-atom or photonic realizations could test the boundary-condition dependence by comparing periodic and open geometries in the same device.","The marker's robustness suggests it could serve as a starting point for diagnosing topology in driven or dissipative many-body systems."],"forward_implications":["The marker can be used to map phase boundaries in other interacting non-Hermitian models without needing periodic-boundary winding numbers.","Open-boundary charge correlations become a practical experimental probe for exceptional-point physics once non-Hermiticity is tuned.","Charge-density-wave order is expected to appear at weaker interaction strengths near exceptional points than far from them.","The complex many-body spectrum under open boundaries should exhibit level clustering that correlates with the observed correlation enhancement."],"fun_headline_variants":["Topological marker holds amid interactions in non-Hermitian SSH","Non-Hermiticity strengthens charge correlations near exceptions in SSH","CDW onset breaks topological marker in interacting non-Hermitian SSH","Staggered charge correlations amplify at exceptional points under open boundaries"],"cache_read_input_tokens":64,"weakest_assumption_plain":"Exact diagonalization on finite chains with the chosen interaction and non-Hermiticity strengths captures the spectrum and correlations without large finite-size effects that would change the reported enhancement near exceptional points.","fun_headline_variants_meta":{"raw":{"variants":["Topological marker holds amid interactions in non-Hermitian SSH","Non-Hermiticity strengthens charge correlations near exceptions in SSH","CDW onset breaks topological marker in interacting non-Hermitian SSH","Staggered charge correlations amplify at exceptional points under open boundaries"]},"model":"grok-4.3","cost_usd":0.004452,"raw_usage":{"total_tokens":2098,"prompt_tokens":581,"num_sources_used":0,"completion_tokens":69,"cost_in_usd_ticks":44515500,"prompt_tokens_details":{"text_tokens":581,"audio_tokens":0,"image_tokens":0,"cached_tokens":64},"completion_tokens_details":{"audio_tokens":0,"reasoning_tokens":1448,"accepted_prediction_tokens":0,"rejected_prediction_tokens":0}},"tokens_in":581,"tokens_out":69,"duration_ms":9289,"temperature":1.0,"reasoning_tokens":1448,"cache_read_input_tokens":64,"cache_creation_input_tokens":0},"cache_creation_input_tokens":0},"created_at":"2026-06-27T23:13:57.344750+00:00","model_set":{"reader":"grok-4.3"},"falsifier":"A calculation on longer chains that shows the staggered charge-correlation peak near exceptional points disappearing or moving away from the reported location would falsify the claimed amplification.","supporting_citations":[],"review_version":1}