{"id":"8b92c9a3-2e0c-4333-ab55-0011043b6f47","arxiv_id":"2607.01344","paper_version":1,"verdict":"UNVERDICTED","confidence":"LOW","novelty_score":5.0,"correctness_risk":"unknown","formal_verification":"none","parameter_count":0,"one_line_summary":"A modified SSH model supports a pair of Jackiw-Rebbi zero modes that hybridize via tunneling, enabling coherent oscillations whose period is set by the hybridization gap.","lead":"The paper analytically and numerically examines how Jackiw-Rebbi zero modes in a modified Su-Schrieffer-Heeger chain hybridize due to quantum tunneling between spatially separated interfaces, producing symmetric and antisymmetric states with coherent oscillations. This framework may interest researchers working on topological states for potential use in controllable quantum-state transfer protocols within engineered lattices.","discovery_kind":"extension","skeptic_critique":{"model":"grok-4.3","headline":"No significant objection identified","rationale":"The reader's weakest_assumption correctly flags the Dirac-theory step as logically prior to the tunneling claim, yet the paper's stated analytical-plus-numerical approach directly targets that step and the subsequent hybridization. Because no discrepancy or unverified approximation is visible in the argument structure, the UNVERDICTED verdict (driven by abstract-only access) does not require adjustment on grounds of internal soundness.","tokens_in":1784,"tokens_out":331,"duration_ms":29127,"concrete_test":"For the finite modified SSH chain with the stated kink profile, recompute the full tight-binding spectrum and confirm exactly two eigenvalues lie within 10^{-8} of zero with wavefunction support localized at the two interfaces; additionally extract the hybridization splitting Δ and verify that time evolution under the projected two-level Hamiltonian reproduces the reported sublattice polarization oscillations with period 2π/Δ.","verdict_should_be":"UNCHANGED","load_bearing_attack":"The central claim rests on the low-energy Dirac theory at k=±π/4a correctly generating two JR zero modes via mass sign changes under a kink, followed by their tunneling-induced hybridization into an effective two-level system. The abstract explicitly distinguishes the quadratic gap closing at k=0 (no mass inversion, no topological wall) from the Dirac point and states that both analytical derivation and numerical checks were performed. The two-level coherent oscillation description follows directly from standard degenerate perturbation theory for overlapping bound states once the modes exist. No internal inconsistency, hidden assumption in the effective Hamiltonian, or unaddressed interference from the quadratic point is apparent.","agreement_with_reader":"disagree"},"referee_report":{"model":"grok-4.3","summary":"The manuscript investigates analytically and numerically the tunneling-induced hybridization of Jackiw-Rebbi zero modes in a modified Su-Schrieffer-Heeger chain that features both a quadratic gap closing at k=0 and Dirac-type closings at k=±π/4a. It argues that a kink profile induces mass sign changes only at the Dirac points, localizing a pair of JR bound states whose finite overlap lifts the zero-energy degeneracy, producing symmetric-antisymmetric hybridized states. An effective two-level model is derived to describe coherent oscillations of occupation probability between the modes together with periodic sublattice polarization transfer between (A,C) and (B,D) sectors, with the oscillation period set by the hybridization gap.","tokens_in":1919,"tokens_out":428,"duration_ms":17315,"significance":"If the derivations hold, the work supplies a concrete lattice realization connecting JR zero modes, quantum tunneling, and coherent dynamics, with an explicit tunable handle (the hybridization gap) for topological state transfer. The separation of quadratic versus Dirac gap-closing physics and the mapping onto a double-well analogy are potentially useful for engineered topological platforms.","major_comments":[],"minor_comments":[{"comment":"Abstract and §2: the lattice constant a appears in the wave-vector locations k=±π/4a without an explicit statement of its value or normalization; adding a sentence defining the unit cell length would improve readability.","section":"Abstract"},{"comment":"§3 (effective two-level model): the hybridization matrix element is stated to be obtained from overlap integrals, but the explicit functional dependence on the kink width or separation is not summarized in the main text; a compact expression or scaling relation would strengthen the claim of tunability.","section":"§3"},{"comment":"Figure captions: several panels show time-dependent polarization without indicating the numerical time-step or convergence criterion used in the exact diagonalization; adding this information would aid reproducibility.","section":"Figures"}],"recommendation":"minor_revision","confidential_remarks":null},"author_rebuttal":{"model":"grok-4.3","summary":"We thank the referee for the positive summary and recommendation of minor revision. No specific major comments were raised in the report.","responses":[],"tokens_in":1311,"tokens_out":43,"duration_ms":6920,"standing_objections":[]},"desk_editor":{"model":"grok-4.3","letter":"The main takeaway is that this modified SSH chain hosts a pair of Jackiw-Rebbi zero modes localized at separate interfaces created by a kink, and their finite overlap produces an effective two-level system with coherent oscillations of the occupation probability and sublattice polarization.\n\nThe paper does a few things well. It identifies the two distinct gap-closing points and correctly notes that only the Dirac-type ones at k=±π/4a support mass inversion and thus the JR modes. The derivation of the hybridized states and the resulting oscillation period set by the tunneling gap is standard but applied here to this setup. The connection to periodic transfer between (A,C) and (B,D) sectors adds a concrete observable. Since the abstract states that both analytical and numerical methods were used, and the stress test found no contradictions, the core logic appears sound.\n\nThe soft spots are limited. Without the explicit model Hamiltonian or the numerical data, it is hard to verify the accuracy of the low-energy approximation or the absence of contributions from the quadratic point at k=0. The oscillation dynamics rely on the modes being well-separated yet overlapping enough, so any details on the kink width or parameter values would help assess robustness. The claim of a \"unified framework\" is overstated for what is essentially one specific modification.\n\nThis paper is for people in the topological condensed matter community who study 1D chains and bound states. It would be useful to someone looking for examples of multiple JR modes and their coherent control. It deserves serious referee attention because the result is falsifiable and builds directly on established methods without circularity.\n\nI would bring this to a reading group on topological bound states. I would not cite it in my own papers in the next year unless working on similar lattices. It should go through peer review.","headline":"This modified SSH chain produces two JR modes from the Dirac points that hybridize via tunneling and show coherent oscillations, a narrow but consistent extension.","tokens_in":2408,"tokens_out":437,"would_cite":false,"duration_ms":22135,"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":"Quantum tunneling between two Jackiw-Rebbi zero modes in a modified SSH chain lifts their degeneracy and produces coherent oscillations of occupation probability.","keywords":["Jackiw-Rebbi zero modes","modified SSH model","quantum tunneling","hybridization","coherent dynamics","topological bound states","Dirac gap closing"],"falsifier":"Absence of any energy splitting between the zero modes or absence of coherent oscillations in the occupation probability when the two interfaces are brought within tunneling range.","tokens_in":2673,"feed_emoji":"","tokens_out":671,"duration_ms":17195,"temperature":0.7,"pith_summary":"The paper investigates a modified Su-Schrieffer-Heeger chain that supports Jackiw-Rebbi zero modes at two spatially separated interfaces created by a kink profile. Finite overlap between these modes allows quantum tunneling that splits the zero-energy degeneracy into symmetric and antisymmetric hybridized states. An effective two-level model captures the resulting coherent dynamics, in which the occupation probability oscillates between the two modes with a period set by the hybridization gap. During each cycle the sublattice polarization transfers periodically between the (A,C) and (B,D) sectors. The construction supplies a controllable route to topological state transfer in lattice systems.","feed_headline":"Tunneling splits Jackiw-Rebbi modes and drives coherent oscillations","feed_subtitle":"Finite overlap in a modified SSH chain opens a hybridization gap that sets the period of probability oscillations between the zero modes.","key_machinery":"Jackiw-Rebbi zero modes localized at the two kink interfaces, hybridized by quantum tunneling into an effective two-level system that governs coherent oscillations.","core_discovery":"In the modified SSH model the Dirac-type gap closing at k=±π/4a permits an effective mass that reverses sign at two interfaces under a kink, binding a pair of JR zero modes. Their finite overlap lifts the degeneracy through tunneling, yielding symmetric-antisymmetric hybridized states. The resulting two-level dynamics produces coherent oscillations of the mode occupation probability together with periodic transfer of sublattice polarization between the (A,C) and (B,D) sectors, with the oscillation period fixed by the hybridization gap.","pith_inferences":["The same tunneling-hybridization picture could apply to other one-dimensional topological models that host multiple zero modes at engineered interfaces.","Cold-atom or photonic-lattice realizations could directly measure the predicted polarization transfer during the oscillations.","Extending the two-mode description to chains with three or more JR modes might enable multi-state quantum-state transfer protocols."],"forward_implications":["The hybridization gap sets the oscillation period of the coherent dynamics between the two JR modes.","Sublattice polarization transfers back and forth between the (A,C) and (B,D) sectors on the same timescale.","The oscillation frequency can be tuned by adjusting the spatial separation of the interfaces.","The framework connects JR zero modes, tunneling, and coherent control within modified SSH lattices."],"fun_headline_variants":["Tunneling hybridizes Jackiw-Rebbi zero modes","Coherent oscillations from JR mode tunneling","Modified SSH shows split JR states dynamics","Hybridization gap tunes JR oscillation period","Tunneling lifts JR zero mode degeneracy"],"cache_read_input_tokens":2112,"weakest_assumption_plain":"The low-energy Dirac theory around the Dirac gap closing points correctly predicts that the effective mass reverses sign at the two spatially separated interfaces of the kink profile.","fun_headline_variants_meta":{"raw":{"variants":["Tunneling hybridizes Jackiw-Rebbi zero modes","Coherent oscillations from JR mode tunneling","Modified SSH shows split JR states dynamics","Hybridization gap tunes JR oscillation period","Tunneling lifts JR zero mode degeneracy"]},"model":"grok-4.3","cost_usd":0.003486,"raw_usage":{"total_tokens":1874,"prompt_tokens":744,"num_sources_used":0,"completion_tokens":64,"cost_in_usd_ticks":34862000,"prompt_tokens_details":{"text_tokens":744,"audio_tokens":0,"image_tokens":0,"cached_tokens":256},"completion_tokens_details":{"audio_tokens":0,"reasoning_tokens":1066,"accepted_prediction_tokens":0,"rejected_prediction_tokens":0}},"tokens_in":744,"tokens_out":64,"duration_ms":8913,"temperature":1.0,"reasoning_tokens":1066,"cache_read_input_tokens":256,"cache_creation_input_tokens":0},"cache_creation_input_tokens":0},"created_at":"2026-07-03T18:40:43.494360+00:00","model_set":{"reader":"grok-4.3"},"falsifier":"Absence of any energy splitting between the zero modes or absence of coherent oscillations in the occupation probability when the two interfaces are brought within tunneling range.","supporting_citations":[],"review_version":1}