{"id":"1ff76345-766e-4977-811b-eb055bf0b584","arxiv_id":"2608.08105","paper_version":1,"verdict":"CONDITIONAL","confidence":"MODERATE","novelty_score":7.0,"correctness_risk":"medium","formal_verification":"none","parameter_count":1,"one_line_summary":"Opposite complex leg potentials cancel for same-rung pairs, so composite pairs can stay extended while unpaired particles localize, and breaking the antisymmetry reverses the effect.","lead":"A two-leg quasiperiodic ladder with opposite complex potentials can keep bound particle pairs extended while single particles localize, and switching the potential balance flips the hierarchy. This gives internal pair configuration a role as a reversible control knob for localization.","discovery_kind":"new_application","skeptic_critique":{"model":"deepseek-v4-flash","headline":"The claimed localization inversion may be an artifact of using the right-eigenvector density IPR; the paper never checks the U1-model hierarchy against a biorthogonal or left-eigenvector diagnostic.","rationale":"The reader correctly identifies the diagnostic as the load-bearing point, and no code, data, or independent derivation is provided to rule it out. However, the specific worry that the Eq. (4) denominator ⟨ψR|ψR⟩ can become small is not correct: for a right eigenvector this is the sum of squared component moduli and is strictly positive. The substantive issue is right-vector versus biorthogonal density, not denominator degeneracy. The paper's own Appendix D shows that a biorthogonal pair weight is needed to separate sectors in the EIC model; the absence of the analogous check in the U1 model of Secs. III-IV is exactly the gap that should be closed before the inversion can be accepted. Because the central mechanism (first-order potential cancellation and second-order effective pair landscape) is plausible and internally consistent, the right outcome remains conditional acceptance pending this numerical check, not rejection.","tokens_in":16243,"tokens_out":11961,"duration_ms":133943,"concrete_test":"Recompute the main Fig. 2(a) curves for L=55, U1/J=20, V/J=1, t/J=2, Δφ=0, replacing Eq. (5) with the biorthogonal density IPR I_B(m)=Σ_j |⟨L_m|(n_a,j+n_b,j)|R_m⟩/⟨L_m|R_m⟩|^2 and also with the left-eigenvector IPR, and additionally evaluate the paired-sector weight w^LR_{p,m} of Eq. (D1) for all states with Re E≈U1. If the states identified as extended pairs for h≈2 no longer have I_B∼L^{-1} while unpaired states have I_B=O(1), the inversion is not robust; if the hierarchy persists, the central claim survives this check.","verdict_should_be":"UNCHANGED","load_bearing_attack":"The central claim rests on Eqs. (4)-(5): the right-eigenvector rung density IPR is used to declare paired states extended for h<h3 while unpaired states are localized for h>h2. The self-overlap denominator in Eq. (4) is not itself ill-conditioned (it is the Euclidean norm of the right vector), but the right-vector density is a biased observable in a non-Hermitian problem: because right eigenvectors are not orthogonal and can be nearly parallel near exceptional points, the right-vector density can differ arbitrarily from the biorthogonal density ⟨L_m|n|R_m⟩/⟨L_m|R_m⟩. A large right-vector IPR can coexist with a biorthogonally extended state, and vice versa. The only biorthogonal check in the paper, Eq. (D1), is applied to the U2/EIC model, not to the U1 model of Fig. 2, and the effective-Hamiltonian benchmark (Fig. 8) compares only energies, not eigenvectors or IPRs. If the paired/unpaired classification in Secs. III-IV is not stable under a biorthogonal IPR or a left-eigenvector IPR, the demonstrated inversion would be a diagnostic artifact rather than a property of the spectrum.","agreement_with_reader":"partial"},"referee_report":{"model":"deepseek-v4-flash","summary":"The paper studies a two-leg ladder of hard-core bosons with opposite complex quasiperiodic potentials, onsite same-rung repulsion U1, and a separate model with nearest-rung interaction U2. For antisymmetric leg potentials (Δϕ=0) the first-order potential on a same-rung pair cancels, so pair motion is generated by second-order virtual excursions into the unpaired sector; the resulting effective pair Hamiltonian is argued to be a much weaker non-Hermitian quasicrystal, allowing extended composite pairs to persist for h<h3 even when unpaired states have localized for h>h2. For finite Δϕ a direct first-order pair modulation is restored, which localizes the narrow pair band while the unpaired sector remains extended. In the U2 model, an engineered configuration-space barrier stabilizes an extended composite band embedded in a localized continuum (EIC). The main evidence is exact diagonalization of two-particle sectors for L=34 and L=55, the density inverse participation ratio (IPR) of right eigenvectors, and a second-order quasi-degenerate perturbation theory benchmarked against exact energies in Appendix B.","tokens_in":16492,"tokens_out":6899,"duration_ms":72515,"significance":"If the localization inversion is genuine, the paper makes a useful conceptual contribution: internal configuration is promoted from a passive label to a reversible control parameter for localization, and the EIC phase is an interesting inverse of the standard bound-state-in-the-continuum scenario. The analytic effective pair Hamiltonian of Eqs. (6)-(8) and Appendix B is a parameter-free, internally consistent derivation rather than a fit, and its energy spectra are benchmarked against exact diagonalization in Fig. 8. The paper also includes finite-size comparisons and a biorthogonal sector-weight check, although only for the U2/EIC model. The main weakness is that the central U1 phase diagram rests on a single localization diagnostic, the right-eigenvector density IPR, whose interpretation in a non-Hermitian system with non-orthogonal eigenvectors requires additional validation.","major_comments":[{"comment":"The paired/unpaired classification and the localization inversion in the U1 model are established entirely through the right-eigenvector density IPR defined in Eq. (4). Because H1 is non-Hermitian, the right eigenvectors can be nearly parallel near exceptional points, and the Hermitian density extracted from the right vector is not guaranteed to reflect the biorthogonal density ⟨L_m|n_j|R_m⟩/⟨L_m|R_m⟩; a state can appear extended in one diagnostic and localized in the other. The only biorthogonal check in the paper, Eq. (D1) in Appendix D, is applied to the U2/EIC model, not to the U1 model that carries the main inversion claim. Please repeat the IPR analysis with left-eigenvector or biorthogonal densities for the U1 model and show that the h2/h3 hierarchy and the phase diagrams in Figs. 2 and 3 are unchanged, or state explicitly why the right-vector density is the physically correct observable for this setup.","section":"Sec. III, Eqs. (4)-(5) and Fig. 2"},{"comment":"The benchmark of the effective pair Hamiltonian compares only complex-energy spectra. The central claim, however, is about the spatial structure of paired eigenstates being extended while unpaired states are localized. Energy agreement does not validate that the effective model reproduces the eigenvectors or the IPRs of the paired manifold. Please benchmark the effective-model eigenstates against exact diagonalization for the pair-sector densities and IPRs, at least for the values of h used in Figs. 2 and 3 and near h3.","section":"Appendix B, Fig. 8"},{"comment":"The finite-size analysis is limited to L=34 and L=55, and the conclusion that the paired states are extended relies on the IPR decreasing with L over only two sizes. Since the two-particle Hilbert space has dimension ~L^2, L=89 or 144 is computationally accessible and would give a much stronger check of the L^{-1} scaling claimed in the text. The absence of such data weakens the identification of the extended composite phase, especially because finite-size effects can be severe near non-Hermitian transitions.","section":"Appendix C and D, Figs. 9-10"}],"minor_comments":[{"comment":"The title of ref. 39 contains a typo: \"Summetry\" should be \"Symmetry\".","section":"References, ref. 39"},{"comment":"The definition of |ϕ_j⟩ after Eq. (D1) is grammatically incomplete; add a period and complete the sentence before continuing with \"Because this quantity can generally be complex\".","section":"Appendix D, Eq. (D1)"},{"comment":"The effective pair hopping J_eff_j is written in two apparently different forms in Eq. (7) and Eq. (11); they coincide for Δϕ=0, but the relation should be stated explicitly to avoid reader confusion.","section":"Sec. III and IV, Eqs. (7) and (11)"},{"comment":"The vertical dashed lines in Fig. 4(a) are identified as h1 and h2 in the caption, but the text refers to \"the onset of the full EIC phase\" and \"the crossover to the partial EIC regime\"; please make the labeling consistent.","section":"Sec. V and Fig. 4"}],"recommendation":"major_revision","confidential_remarks":"The main unresolved issue is diagnostic robustness of the right-eigenvector IPR for the U1 model. If the authors can add biorthogonal or left-eigenvector IPR checks and at least one additional system size, the paper would be a solid contribution. I do not see grounds for rejection, but the current evidence is insufficient to fully support the central phase diagram without those checks."},"author_rebuttal":null,"desk_editor":{"model":"deepseek-v4-flash","letter":"Here's my read.\n\nThe paper has a genuinely new mechanism: opposite complex quasiperiodic potentials on the two legs cancel at first order for a same-rung pair, so the composite pair moves through a weak effective landscape generated by virtual unpaired configurations. That inversion of the localization hierarchy between bound pairs and unpaired particles is not in the cited literature, and the effective Hamiltonian in Eqs. (6)-(8) is derived rather than fitted. The benchmark against exact diagonalization for the paired spectrum in Fig. 8 is real evidence, and the finite-size checks in Appendix C, though modest, are consistent with the claimed trend.\n\nThe soft spots are not in the derivation. My main concern is the diagnostic. The paper classifies states as extended or localized using the right-eigenvector density IPR, Eq. (4). In a non-Hermitian system with non-orthogonal eigenvectors, right-vector density can be a biased indicator: near exceptional points, or when many right vectors overlap strongly, a state that is extended in the biorthogonal sense can look localized, and vice versa. The paper applies a biorthogonal sector weight in Appendix D, but only to the U2/EIC model, not to the U1 localization inversion in Figs. 2-3. That is a genuine gap. I don't think it overturns the central claim because the density profiles in Fig. 2(f) and the effective-theory argument point the same way, but the phase boundaries and the EIC phase would be much more convincing with a biorthogonal or left-eigenvector IPR check.\n\nSecondary issues: the interacting two-particle sector is only looked at for L=34 and L=55, which is small for an 'extended band in a localized continuum' claim, and no data or code are provided. Neither is fatal. The paper is honest about these limitations in the appendices.\n\nWho this is for: people working on non-Hermitian quasicrystals, doublons, or interaction-induced localization. It deserves a serious referee. I would send it to review, with a request for the biorthogonal IPR check and a scaling analysis before acceptance. If the diagnostic robustness holds, the result is a useful reversible control mechanism.","headline":"A new mechanism—opposite leg potentials cancelling for same-rung pairs—gives a plausible localization inversion; the main caveat is that the right-vector IPR diagnostic needs a biorthogonal check before I'd fully trust the phase diagram.","tokens_in":17001,"tokens_out":3460,"would_cite":true,"duration_ms":35552,"reading_group":"yes","serious_thinker":"yes","would_accept_peer_review":true},"rs_alignment":null,"lean_confirmation":null,"pith_extraction":{"msc":["81Q12","82B44"],"pacs":[],"model":"deepseek-v4-flash","headline":"An interacting non-Hermitian quasiperiodic ladder can keep same-rung composite pairs extended after single particles have localized, and a phase offset between the two legs reverses the ordering.","keywords":["non-Hermitian quasicrystal","localization inversion","composite excitations","doublon","quasiperiodic ladder","extended state in continuum","inverse participation ratio","effective pair Hamiltonian"],"falsifier":"Diagonalise the same two-excitation ladder ($\\Delta\\phi=0$, $U_1/J=20$, $V/J=1$, $t/J=2$) and recompute the inverse participation ratio using the biorthogonal overlap $\\langle L_m|R_m\\rangle$ or the left-eigenvector density, and compare with a generalized Brillouin zone criterion; if the paired-sector extended phase no longer survives past $h\\approx 1.58$ or the effective $h_3$ collapses toward $h_2$, the inversion is a diagnostic effect rather than a property of the spectrum.","tokens_in":2138,"feed_emoji":"⚛️","tokens_out":2671,"duration_ms":115608,"temperature":0.7,"pith_summary":"The paper establishes that in an interacting non-Hermitian quasiperiodic ladder, a composite of two particles bound on the same rung can have a localization behavior opposite to that of the unpaired single-particle states in the same lattice. For antisymmetric complex leg potentials, the quasiperiodic potential cancels at first order for a same-rung pair, while it acts directly on separated particles; the pair instead moves through virtual unpaired configurations, so it experiences a much weaker emergent quasiperiodic landscape. As a result, paired states remain extended up to $h_3\\approx 2.37$ (with $U_1/J=20$, $V/J=1$, $t/J=2$) even after the unpaired sector has localized above $h_2\\approx 1.58$. A finite phase offset $\\Delta\\phi$ between the legs breaks the cancellation and reverses the hierarchy, localizing the pair while single-particle states stay extended, and an interaction-engineered pathway can embed an extended composite band inside a localized continuum. The message is that internal configuration is a reversible control parameter for localization, not just the external potential.","feed_headline":"Pairs stay extended while singles localize; phase shift flips the rule","feed_subtitle":"Opposite leg potentials cancel for same-rung pairs, making internal configuration a reversible localization switch.","key_machinery":"The load-bearing object is the effective paired-sector Hamiltonian obtained by projecting out unpaired configurations, written in Eqs. (B24), (6)-(8), and (11)-(14). Because hard-core bosons cannot hop a same-rung pair directly, the projector satisfies $PTP=0$, so pair propagation is a second-order virtual process. The effective hopping $J_j^{\\mathrm{eff}}$ and renormalized onsite energy $\\epsilon_j^{\\mathrm{eff}}$ encode the emergent non-Hermitian quasicrystal experienced by the composite: for $\\Delta\\phi=0$ the first-order potential cancels and the residual modulation is $O(J^2/U_1)$, while for $\\Delta\\phi\\neq 0$ a direct term $-2V\\sin(2\\pi\\alpha j+ih)\\sin(\\Delta\\phi/2)$ dominates the narrow composite band. The $U_2$ interaction in Eq. (15) plays the same role in configuration space by raising the energy of intermediate interleg configurations, stabilising the extended embedded band. The mechanism therefore turns internal pair configuration into the parameter that selects the effective landscape.","core_discovery":"The central claim is that composite excitations do not inherit the localization of their constituents in this model. In the two-particle sector of the antisymmetric ladder ($\\Delta\\phi=0$), the first-order onsite potential for a same-rung pair vanishes because $V_{a,j}+V_{b,j}=0$, leaving the bare pair energy $U_1$. Pair motion is generated only by virtual excursions into the unpaired sector, and second-order quasi-degenerate perturbation theory yields a one-dimensional effective Hamiltonian for the paired manifold with modulated hopping $J_j^{\\mathrm{eff}}$ and onsite energy $\\epsilon_j^{\\mathrm{eff}}$ (Eqs. 6-8). For $U_1\\gg J,V$ this effective pair quasicrystal has modulations of order $J^2/U_1$, far weaker than the direct landscape seen by unpaired particles, so the pair band survives as extended while the unpaired band localizes. The hierarchy is controlled by $\\Delta\\phi$: a small phase offset restores a first-order pair potential $-2V\\sin(2\\pi\\alpha j+ih)\\sin(\\Delta\\phi/2)$, which, acting on the narrow pair band of width $J^2/U_1$, drives the pair localized while unpaired particles remain extended. The same logic, with a nearest-rung interaction $U_2$, suppresses certain virtual pathways and creates an extended composite band embedded inside a localized unpaired continuum, the inverse of a bound state in the continuum.","pith_inferences":["Inference beyond the paper: if the mechanism is the first-order cancellation rather than the complex phase $h$, a Hermitian ladder with opposite real potentials should show the same inversion as the potential amplitude is increased; this would separate the role of non-Hermiticity from the role of composite structure.","Inference beyond the paper: time-modulating $\\Delta\\phi$ between $0$ and $\\pi/3$ should switch the same lattice between pair-extended and pair-localized regimes, providing a dynamical switch that the paper does not explicitly simulate.","Inference beyond the paper: the same configuration-space pathway suppression could be applied to composite excitations larger than pairs, such as rung trimers, where the virtual intermediate configurations are more numerous and the effective landscape may be even weaker or more tunable."],"forward_implications":["At $\\Delta\\phi=0$ with $U_1/J=20$, $V/J=1$, $t/J=2$, the unpaired sector localizes for $h\\gtrsim 1.58$ but same-rung pairs remain extended up to $h\\approx 2.37$, so the composite band can be used for selective propagation through a localized environment.","Introducing a small phase offset $\\Delta\\phi\\lesssim\\pi/3$ localizes the composite band while the unpaired sector remains extended, demonstrating that the same microscopic lattice can support both ordering regimes.","Because the pair moves via weak $O(J^2/U_1)$ couplings, increasing $U_1$ widens the window in which extended pairs coexist with localized unpaired states; finite-size data for $L=34$ and $55$ show the hierarchy is stable.","Engineering a nearest-rung interleg interaction $U_2$ with $U_2/J=40$ produces a full extended-state-in-continuum phase for $1.56\\lesssim h/J\\lesssim 3.07$, with an extended composite band embedded within a localized unpaired continuum.","These results are all achieved within the same lattice Hamiltonian, so a single experimental setup could switch between composite-selective transport and pair confinement by tuning $\\Delta\\phi$."],"supporting_citations":[{"why":"Supplies the non-Hermitian quasiperiodic single-chain transition $h_c=\\ln(2J/V)$ that frames the ladder's single-particle landscape and the PT transition.","marker":"[31]"},{"why":"Introduces repulsively bound atom pairs (doublons), the composite-excitation concept whose localization the paper contrasts with unpaired particles.","marker":"[5]"},{"why":"Shows that two interacting particles in a random potential propagate differently from single particles, the background assumption that composites can have their own localization behavior.","marker":"[6]"},{"why":"Provides the non-Hermitian two-particle bound-state-in-the-continuum result whose inverse the paper constructs as an extended composite band in a localized continuum.","marker":"[37]"},{"why":"Provides the interaction-induced multiparticle bound-states-in-the-continuum scenario that the extended-state-in-continuum is meant to invert.","marker":"[38]"},{"why":"Supplies the quasi-degenerate perturbation theory used to derive the effective pair Hamiltonian of Eqs. (6)-(8) and (B24).","marker":"[39]"},{"why":"Supplies the symmetrized second-order perturbation treatment used to handle the non-degenerate paired manifold at finite $\\Delta\\phi$.","marker":"[40]"}],"fun_headline_variants":["Pairs stay free while singles localize; phase shift inverts fate","Localization switch: internal phase decides if pairs or singles stay put","Composite pairs shrug off disorder; phase twist reverses the roles","Localization inversion: pairs extended, singles trapped, phase twist flips it","Phase shift flips localization: pairs roam, singles freeze, and back"],"cache_read_input_tokens":19200,"weakest_assumption_plain":"The separation into paired and unpaired sectors assumes that the right-eigenvector density inverse participation ratio with self-overlap normalization correctly labels localized versus extended states; for non-Hermitian eigenstates with tiny self-overlap, that label can fail, and if it fails the claimed inversion could be an artifact of the diagnostic.","fun_headline_variants_meta":{"raw":{"variants":["Pairs stay free while singles localize; phase shift inverts fate","Localization switch: internal phase decides if pairs or singles stay put","Composite pairs shrug off disorder; phase twist reverses the roles","Localization inversion: pairs extended, singles trapped, phase twist flips it","Phase shift flips localization: pairs roam, singles freeze, and back"]},"model":"deepseek-v4-flash","effort":"low","cost_usd":0.000879,"raw_usage":{"total_tokens":3831,"prompt_tokens":1008,"completion_tokens":2823,"prompt_tokens_details":{"cached_tokens":384},"prompt_cache_hit_tokens":384,"prompt_cache_miss_tokens":624,"completion_tokens_details":{"reasoning_tokens":2731}},"tokens_in":624,"tokens_out":2823,"duration_ms":22264,"temperature":1.0,"reasoning_tokens":2731,"cache_read_input_tokens":384,"cache_creation_input_tokens":0},"cache_creation_input_tokens":0},"created_at":"2026-08-12T00:24:52.972718+00:00","model_set":{"reader":"deepseek-v4-flash"},"falsifier":"Diagonalise the same two-excitation ladder ($\\Delta\\phi=0$, $U_1/J=20$, $V/J=1$, $t/J=2$) and recompute the inverse participation ratio using the biorthogonal overlap $\\langle L_m|R_m\\rangle$ or the left-eigenvector density, and compare with a generalized Brillouin zone criterion; if the paired-sector extended phase no longer survives past $h\\approx 1.58$ or the effective $h_3$ collapses toward $h_2$, the inversion is a diagnostic effect rather than a property of the spectrum.","supporting_citations":[{"cited_title":"Longhi ,\\ title title Topological phase transition in non- H ermitian quasicrystals , \\ 10.1103/PhysRevLett.122.237601 journal journal Phys","cited_arxiv_id":null,"evidence_quote":"Supplies the non-Hermitian quasiperiodic single-chain transition $h_c=\\ln(2J/V)$ that frames the ladder's single-particle landscape and the PT transition."},{"cited_title":null,"cited_arxiv_id":null,"evidence_quote":"Shows that two interacting particles in a random potential propagate differently from single particles, the background assumption that composites can have their own localization behavior."},{"cited_title":"Liu \\ and\\ author S","cited_arxiv_id":null,"evidence_quote":"Provides the non-Hermitian two-particle bound-state-in-the-continuum result whose inverse the paper constructs as an extended composite band in a localized continuum."},{"cited_title":"Huang , author Y","cited_arxiv_id":null,"evidence_quote":"Provides the interaction-induced multiparticle bound-states-in-the-continuum scenario that the extended-state-in-continuum is meant to invert."},{"cited_title":null,"cited_arxiv_id":null,"evidence_quote":"Supplies the quasi-degenerate perturbation theory used to derive the effective pair Hamiltonian of Eqs. (6)-(8) and (B24)."},{"cited_title":"Cohen-Tannoudji , author J","cited_arxiv_id":null,"evidence_quote":"Supplies the symmetrized second-order perturbation treatment used to handle the non-degenerate paired manifold at finite $\\Delta\\phi$."}],"review_version":1}