{"id":"5c4b7d6f-d469-4379-aca1-cad8decc6719","arxiv_id":"2606.03124","paper_version":1,"verdict":"UNVERDICTED","confidence":"LOW","novelty_score":7.0,"correctness_risk":"unknown","formal_verification":"none","parameter_count":0,"one_line_summary":"A GBZ transformation produces a quasi-reciprocal Hamiltonian that encodes open-boundary non-Hermitian many-body physics under periodic boundaries, with phases distinguished by Zak phase, CDW structure factor, and low-lying entanglement spectrum degeneracy.","lead":"The authors map an interacting non-Hermitian model with circular generalized Brillouin zone to a quasi-reciprocal many-body Hamiltonian whose periodic-boundary physics reproduces the original open-boundary behavior. This enables numerical study of phases via exact diagonalization and entanglement spectra.","discovery_kind":"unclear","skeptic_critique":{"model":"grok-4.3","headline":"GBZ transformation from non-interacting case may acquire interaction-dependent corrections not ruled out by the construction","rationale":"The reader's weakest_assumption directly identifies the same load-bearing step. Because the manuscript performs all numerics on the transformed model only, the equivalence remains an untested assumption rather than a demonstrated result; confirming or refuting the spectral match on small lattices would resolve the uncertainty without requiring larger-system extrapolations.","tokens_in":1779,"tokens_out":383,"duration_ms":11414,"concrete_test":"For the smallest system size (e.g., L=6 or 8 sites) where ED is feasible, compute the full many-body spectrum of the original non-Hermitian interacting Hamiltonian under OBC and of the quasi-reciprocal Hamiltonian under PBC; check whether the lowest 10 eigenvalues (and their degeneracies) agree to within 10^{-4} (in units of the hopping) after the GBZ rescaling. If they diverge systematically with interaction strength, the transformation requires corrections.","verdict_should_be":"CONDITIONAL","load_bearing_attack":"The strongest claim requires that the GBZ similarity transformation (originally derived for single-particle non-Hermitian Hamiltonians with circular GBZ) maps the many-body OBC spectrum and eigenstates of the original non-Hermitian interacting model onto the PBC spectrum of the constructed quasi-reciprocal Hamiltonian without additional many-body renormalization. The paper performs ED only on the quasi-reciprocal model and extracts Zak phase, CDW structure factor, and entanglement spectrum; it does not report a direct side-by-side comparison of low-lying eigenvalues or order parameters between the two formulations on the same finite-size lattice. If interaction-induced shifts in the effective non-reciprocity or in the many-body GBZ radius exist, the mapping fails while the reported phase diagram remains internally consistent.","agreement_with_reader":"agree"},"referee_report":{"model":"grok-4.3","summary":"The manuscript claims that for an interacting non-Hermitian model with circular GBZ, a GBZ transformation can be used to construct a quasi-reciprocal many-body Hamiltonian. Under PBC this Hamiltonian reproduces the OBC physics (including spectrum and eigenstates) of the original non-Hermitian interacting system. Exact diagonalization on the quasi-reciprocal model is used to obtain a phase diagram from the Zak phase and CDW structure factor; the degeneracy pattern of the low-lying entanglement spectrum is shown to label each phase.","tokens_in":1944,"tokens_out":511,"duration_ms":20095,"significance":"If the mapping holds without interaction-dependent corrections, the construction supplies a concrete route to many-body non-Hermitian physics that re-uses standard PBC numerics and entanglement diagnostics. The numerical extraction of Zak phase, CDW order, and entanglement spectrum on the transformed model is a tangible contribution that could be extended to other circular-GBZ models.","major_comments":[{"comment":"The central mapping asserts that the single-particle GBZ similarity transformation extends unmodified to the interacting regime. No derivation or explicit check is supplied to exclude interaction-induced renormalization of the GBZ radius or effective non-reciprocity; the construction therefore rests on an untested assumption that is load-bearing for the claim that the quasi-reciprocal PBC Hamiltonian captures the original OBC physics.","section":"GBZ transformation and construction of the quasi-reciprocal Hamiltonian"},{"comment":"ED results (Zak phase, CDW structure factor, entanglement spectrum) are reported exclusively for the quasi-reciprocal model. No side-by-side comparison of low-lying eigenvalues, order parameters, or eigenstate overlaps between the original non-Hermitian OBC system and the transformed PBC system on identical finite-size lattices is presented, leaving the mapping unvalidated.","section":"Numerical results and phase diagram"}],"minor_comments":[{"comment":"The model Hamiltonian (hopping amplitudes, interaction strength, non-reciprocity parameter) should be written explicitly in the main text rather than referenced only by name.","section":"Model definition"},{"comment":"Figure captions for the phase diagram and entanglement spectra should state the system sizes used and the precise definition of the entanglement cut.","section":"Figures"}],"recommendation":"major_revision","confidential_remarks":null},"author_rebuttal":{"model":"grok-4.3","summary":"We thank the referee for the careful reading and constructive comments. We address the two major points below and will revise the manuscript to strengthen the derivation of the mapping and provide direct numerical validation.","responses":[{"response":"We agree that an explicit derivation is required. In the revised manuscript we will add a dedicated subsection deriving the many-body quasi-reciprocal Hamiltonian. For the circular-GBZ class the similarity transformation is a uniform rescaling of all hoppings that commutes with density-density interactions; consequently the GBZ radius remains interaction-independent and no renormalization of non-reciprocity appears. This property follows directly from the single-particle GBZ equation being unchanged by the interaction term.","revision_made":"yes","referee_comment":"[GBZ transformation and construction of the quasi-reciprocal Hamiltonian] The central mapping asserts that the single-particle GBZ similarity transformation extends unmodified to the interacting regime. No derivation or explicit check is supplied to exclude interaction-induced renormalization of the GBZ radius or effective non-reciprocity; the construction therefore rests on an untested assumption that is load-bearing for the claim that the quasi-reciprocal PBC Hamiltonian captures the original OBC physics."},{"response":"We accept that direct validation is necessary. In the revision we will include finite-size benchmarks (L=4 and L=6) comparing the original non-Hermitian OBC spectrum, CDW structure factor, and eigenstate overlaps with the corresponding quantities of the quasi-reciprocal PBC Hamiltonian. These comparisons will be added as a new figure and accompanying text.","revision_made":"yes","referee_comment":"[Numerical results and phase diagram] ED results (Zak phase, CDW structure factor, entanglement spectrum) are reported exclusively for the quasi-reciprocal model. No side-by-side comparison of low-lying eigenvalues, order parameters, or eigenstate overlaps between the original non-Hermitian OBC system and the transformed PBC system on identical finite-size lattices is presented, leaving the mapping unvalidated."}],"tokens_in":1452,"tokens_out":445,"duration_ms":14422,"standing_objections":[]},"desk_editor":{"model":"grok-4.3","letter":"The core advance is a concrete construction: take an interacting non-Hermitian chain whose single-particle GBZ is circular, apply the GBZ similarity transform to obtain a quasi-reciprocal many-body Hamiltonian, and then study that Hamiltonian under ordinary PBC with standard ED. They extract a phase diagram from the Zak phase and CDW structure factor, and they note that low-lying entanglement-spectrum degeneracy tracks the phases.\n\nThat route is useful because it lets people reuse existing many-body codes instead of inventing new OBC solvers for non-Hermitian interactions. The entanglement-spectrum diagnostic is a reasonable extension of what is already done in Hermitian topological models.\n\nThe soft spot is exactly where the stress-test note flags it. The abstract and the reported numerics only show results on the transformed Hamiltonian; there is no side-by-side comparison of low-lying eigenvalues or order parameters between the original non-Hermitian OBC problem and the quasi-reciprocal PBC problem on the same finite lattice. Without that check, it remains possible that interaction-induced shifts in the effective non-reciprocity or GBZ radius spoil the mapping. The paper also gives no derivation steps or checks against known non-interacting limits.\n\nThis is therefore a paper for people already working on dissipative many-body systems who want a practical workaround. It is worth sending to referees because the open problem it targets is real and the proposed workaround is simple enough to test, but any referee will have to insist on the missing direct validation before the claim can be trusted.","headline":"The paper gives a workable numerical route for many-body non-Hermitian systems via a GBZ-transformed quasi-reciprocal model, but the central mapping is asserted without the direct spectral comparisons needed to confirm it survives interactions.","tokens_in":2452,"tokens_out":399,"would_cite":false,"duration_ms":12686,"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 GBZ transformation yields a quasi-reciprocal Hamiltonian whose periodic-boundary physics matches the open-boundary behavior of an interacting non-Hermitian model.","keywords":["non-Hermitian systems","generalized Brillouin zone","many-body interactions","entanglement spectrum","topological phases","open boundary conditions","periodic boundary conditions","quasi-reciprocal Hamiltonian"],"falsifier":"Direct numerical comparison in which the energy levels, correlation functions, or entanglement spectrum of the quasi-reciprocal periodic Hamiltonian fail to match the open-boundary spectrum of the original non-Hermitian model at the same parameters.","tokens_in":2679,"feed_emoji":"⚛️","tokens_out":640,"duration_ms":15932,"temperature":0.7,"pith_summary":"The paper extends the generalized Brillouin zone framework to many-body interacting non-Hermitian systems that have a circular GBZ. It constructs a quasi-reciprocal many-body Hamiltonian via the GBZ transformation; when this new Hamiltonian is studied with periodic boundary conditions, its properties reproduce those of the original non-Hermitian model with open boundaries. Exact diagonalization on the transformed model produces the phase diagram through the Zak phase and charge-density-wave structure factor. The degeneracy structure of the low-lying entanglement spectrum distinguishes the phases and thereby encodes the topological information of the original system.","feed_headline":"Transformed Hamiltonian captures non-Hermitian open-boundary physics","feed_subtitle":"A quasi-reciprocal periodic model reproduces the original open-boundary states, with phases labeled by entanglement-spectrum degeneracy.","key_machinery":"The GBZ transformation that converts the non-Hermitian model into a quasi-reciprocal many-body Hamiltonian studied under periodic boundaries.","core_discovery":"Based on a GBZ transformation, a quasi-reciprocal many-body Hamiltonian can be constructed which, under periodic boundary conditions, captures the physics of the original non-Hermitian model under open boundary conditions. The topological properties in the interacting non-Hermitian system are encoded in the entanglement spectrum of the quasi-reciprocal model.","pith_inferences":["The same mapping may extend to other interacting non-Hermitian models provided their GBZ is circular.","Models with non-circular GBZs would require checking whether additional corrections are needed.","The approach supplies a concrete route for computing many-body invariants without explicit open-boundary simulations."],"forward_implications":["The phase diagram is obtained by computing the Zak phase and the charge-density-wave structure factor via exact diagonalization under periodic boundaries.","Degeneracy of the low-lying entanglement spectrum labels each phase in the diagram.","Topological properties of the interacting non-Hermitian system become accessible through standard periodic-boundary calculations on the transformed Hamiltonian."],"fun_headline_variants":["GBZ maps non-Hermitian OBC to quasi-reciprocal PBC many-body model","Quasi-reciprocal PBC Hamiltonian reproduces original non-Hermitian OBC states","Entanglement spectrum degeneracy labels phases in many-body GBZ systems","Transformed periodic Hamiltonian captures many-body non-Hermitian GBZ physics"],"cache_read_input_tokens":2112,"weakest_assumption_plain":"The generalized Brillouin zone transformation developed for non-interacting systems applies unchanged to interacting many-body models when the GBZ remains circular.","fun_headline_variants_meta":{"raw":{"variants":["GBZ maps non-Hermitian OBC to quasi-reciprocal PBC many-body model","Quasi-reciprocal PBC Hamiltonian reproduces original non-Hermitian OBC states","Entanglement spectrum degeneracy labels phases in many-body GBZ systems","Transformed periodic Hamiltonian captures many-body non-Hermitian GBZ physics"]},"model":"grok-4.3","cost_usd":0.004572,"raw_usage":{"total_tokens":2282,"prompt_tokens":691,"num_sources_used":0,"completion_tokens":85,"cost_in_usd_ticks":45724500,"prompt_tokens_details":{"text_tokens":691,"audio_tokens":0,"image_tokens":0,"cached_tokens":256},"completion_tokens_details":{"audio_tokens":0,"reasoning_tokens":1506,"accepted_prediction_tokens":0,"rejected_prediction_tokens":0}},"tokens_in":691,"tokens_out":85,"duration_ms":8567,"temperature":1.0,"reasoning_tokens":1506,"cache_read_input_tokens":256,"cache_creation_input_tokens":0},"cache_creation_input_tokens":0},"created_at":"2026-06-28T08:34:33.670982+00:00","model_set":{"reader":"grok-4.3"},"falsifier":"Direct numerical comparison in which the energy levels, correlation functions, or entanglement spectrum of the quasi-reciprocal periodic Hamiltonian fail to match the open-boundary spectrum of the original non-Hermitian model at the same parameters.","supporting_citations":[],"review_version":1}