{"id":"ab74efa8-8cc7-471f-9948-2987a1880f86","arxiv_id":"2507.02038","paper_version":1,"verdict":"CONDITIONAL","confidence":"MODERATE","novelty_score":6.0,"correctness_risk":"medium","formal_verification":"none","parameter_count":3,"one_line_summary":"On-site potentials in a 2D non-Hermitian SSH lattice can selectively force real energy spectra under periodic or open boundary conditions, with a line-gap-closing transition at theta = pi/4.","lead":"A two-dimensional lattice model with gain and loss can be tuned so that either its bulk or its boundary modes have purely real energies, controlled by a simple on-site potential. The finding is a step toward selectively controlling lasing in the bulk versus the boundary of non-Hermitian materials.","discovery_kind":"new_method","skeptic_critique":{"model":"deepseek-v4-flash","headline":"The full-OBC reality claim in the 'OBC reality switch' section depends on an unquantified edge-mode loop-shrinking argument; a finite-size scaling check is needed before the β-potential switch can be accepted as proven.","rationale":"I read the paper's central claim as a selective reality switch: α makes the PBC bulk real via PT, β makes the full-OBC spectrum real via the skin effect and non-Bloch RMyT symmetry, and the combined potential interpolates with a gap-closing transition at θ=π/4. The α branch is on solid ground because PT symmetry is explicit and the numerical spectra show the PT transition. The β branch is the load-bearing piece: the bulk under yOBC is argued from non-Bloch RMyT symmetry, but the decisive statement about the full OBC spectrum includes the edge modes, and that argument is only verbal. The reader's weakest assumption identifies exactly this. I agree with the conditional verdict: the paper is a plausible and interesting proposal, with numerical evidence, but the full-OBC reality claim is not yet quantitatively established. A finite-size scaling study or a direct 2D non-Bloch calculation of the edge modes would settle it. Until then, the claim should be treated as conditional, not as a proven theorem. I see no reason to change the reader's verdict.","tokens_in":5655,"tokens_out":8388,"duration_ms":91900,"concrete_test":"Diagonalize the β-only model (β=0.8, γin=0.2, γex=0.4, γ'_in=γ'_ex=0.5γin,ex) on L×L full OBC lattices with L=16, 24, 32, 48, 64 and compute max_{edge} |Im E|, separating edge-localized states by inverse participation ratio. If this maximum decays as a power of L (e.g. L^{-1} or faster) toward zero, the loop-shrinking claim is supported; if it saturates above ~10^{-2}, the 'entire spectrum is real under full OBC' claim fails. Separately, for the same sizes, verify that the yOBC edge-mode eigenvalues evaluated at the allowed k_x=2πn/L_x values approach the real axis as L grows; this directly tests the 'mixing vanishes' step.","verdict_should_be":"UNCHANGED","load_bearing_attack":"The central assertion that βσ_zσ0 makes the entire full-OBC spectrum real for large β rests on the paragraph in 'OBC reality switch' stating: 'the loops shrink under full OBC due to the non-Hermitian skin effect' and 'in the thermodynamic limit, the mixing vanishes.' This is load-bearing because the switch must control boundary spectra, not just the bulk. The yOBC edge modes form complex loop spectra with opposite winding on opposite y-boundaries; the paper argues that under full OBC these loops collapse to real arcs because no additional x-boundary edge modes mix with them. None of the three steps is derived: (i) the claim that no x-direction edge modes appear ignores possible bulk-boundary hybridization; (ii) 'loops shrink' is asserted without an equation of motion for the edge-mode eigenvalues under the second open direction; (iii) 'mixing vanishes' lacks a finite-size scaling or non-Bloch analysis for the 2D generalized Brillouin zone. If any step fails, the full-OBC spectrum retains complex edge eigenvalues, and the OBC reality switch is only a bulk reality switch. Since the α-potential PBC result is supported by the explicit PT symmetry, the unproven edge-mode part is the weakest point of the central claim.","agreement_with_reader":"agree"},"referee_report":{"model":"deepseek-v4-flash","summary":"The paper studies a 2D non-Hermitian Su-Schrieffer-Heeger model and proposes two on-site potentials, ασ0σz and βσzσ0, that act as a boundary-selective 'reality switch': a sufficiently large α makes the PBC bulk spectrum real via PT symmetry, while a sufficiently large β is claimed to make the full OBC spectrum real in the thermodynamic limit via the non-Hermitian skin effect combined with a non-Bloch RMyT symmetry. The authors also study the combined potential cos(θ)σ0σ3 + sin(θ)σ3σ0 and identify a line-gap-closing transition at θ = π/4 that they interpret as a topological transition. The central claim is that the switch can selectively control the reality of bulk versus boundary spectra, with potential implications for bulk-boundary selective lasing.","tokens_in":5931,"tokens_out":3556,"duration_ms":41710,"significance":"If established, the proposal would be a useful, parameter-free mechanism for controlling spectral reality by boundary conditions in a concrete lattice model, and the non-Bloch RMyT symmetry concept could generalize the known non-Bloch PT framework. The paper is concise and the symmetry reasoning is clearly laid out; the numerical spectra are consistent with the stated symmetries, and no parameters are fitted to target spectra. However, the full-OBC reality claim depends on an unproved edge-mode argument and on an undefined non-Bloch symmetry, and the finite-size behavior is not quantified. The result is therefore promising but not yet established at the level of proof required for the paper's central assertion.","major_comments":[{"comment":"The assertion that the edge-mode loops under yOBC 'shrink under full OBC due to the non-Hermitian skin effect' and that 'in the thermodynamic limit, the mixing vanishes' is load-bearing for the central claim that the entire full-OBC spectrum becomes real for large β. Yet this is a verbal argument only: no equation of motion for the edge-mode eigenvalues under the second open direction is given, no non-Bloch analysis of the 2D generalized Brillouin zone is provided, and no finite-size scaling of the maximum imaginary part of the edge eigenvalues is shown. Furthermore, the statement that 'no additional edge mode appears on the boundaries normal to the x-direction' ignores the possibility of bulk-boundary hybridization. If any of these steps fails, the full-OBC spectrum retains complex edge eigenvalues and the switch controls only the bulk. Please either supply a quantitative derivation or present finite-size scaling data that demonstrate the loops collapsing to real arcs.","section":"OBC reality switch (paragraph on edge modes under full OBC)"},{"comment":"The paper introduces 'non-Bloch RMyT symmetry' as the mechanism ensuring the reality of the bulk spectrum under yOBC, but it never defines the symmetry transformation on the non-Bloch Hamiltonian H(kx, βy) nor proves that the non-Bloch RMyT symmetric phase implies real arcs. The statement 'When the non-Hermitian skin effect occurs... the arcs can realize the RMyT symmetry in a manner different from that under PBC... thus their energies become real' is a claim, not a derivation. Please specify the operator action on βy, state the condition under which the arcs are invariant, and demonstrate that this condition holds in the parameter regime of Figs. 2(g)-(h). Without this step, the bulk part of the OBC reality switch is not established.","section":"OBC reality switch, paragraph on non-Bloch RMyT symmetry"},{"comment":"The paper calls the line-gap closing at θ = π/4 a 'topological phase transition', but no topological invariant is computed. A complex-energy line-gap closing is necessary but not sufficient for a topological transition; the accompanying statement about 'redistribution of the signs of the on-site potential' is descriptive rather than topological. Please either compute an appropriate complex-spectrum invariant (e.g., a winding number of the PBC or non-Bloch spectrum) and show that it changes at θ = π/4, or explicitly rephrase the claim as a 'line-gap-closing transition' without the topological label.","section":"On-demand PBC-OBC reality switch, Fig. 3 and following paragraph"},{"comment":"The manuscript does not report the lattice sizes Lx and Ly used in any of the boundary-condition spectra, nor does it provide any finite-size scaling. Since the central thermodynamic-limit statement is that the full-OBC spectrum becomes real for large β, the reader cannot distinguish a genuine thermodynamic effect from a finite-size artifact. Please state the lattice sizes in the captions, show the maximum Im E as a function of system size for fixed β, and demonstrate that the deviations from reality extrapolate to zero in the thermodynamic limit.","section":"All numerical spectra (Figs. 2 and 3)"}],"minor_comments":[{"comment":"The caption states 'Green, red, black, and blue represent PBC, xOBC, yOBC, and full OBC (xyOBC), deceptively, as is shown in the inset of (a).' The word 'deceptively' should be 'respectively'.","section":"Fig. 2 caption"},{"comment":"The text refers to 'the 2D non-Hermitian SSH model in Fig.1(d)', but the lattice is shown in Fig.1(b); this cross-reference should be corrected.","section":"Model section"},{"comment":"There are several typographical errors, including 'Su-Schriffer-Heeger' in the Introduction, 'controlability' in the Introduction, and 'non-Herminian skin effect' in the OBC reality switch section; these should be fixed.","section":"Title and Introduction"},{"comment":"The text uses both 'line-gap' and 'lin-gap' (in 'Upon reopening the lin-gap away from θ = π/4'); the spelling should be made consistent.","section":"On-demand PBC-OBC reality switch"}],"recommendation":"major_revision","confidential_remarks":"The paper is concise and the symmetry-based idea is attractive, but the central full-OBC reality claim is currently supported mainly by verbal arguments and by figures without stated system sizes. I recommend major revision rather than rejection because the missing elements—a definition and proof for non-Bloch RMyT symmetry, an analysis of edge-mode mixing, a topological invariant calculation, and finite-size scaling—are within the scope of the manuscript and can in principle be supplied. I would also ask the editor to require the authors to state lattice sizes explicitly, since the numerical results are otherwise not reproducible from the text."},"author_rebuttal":null,"desk_editor":{"model":"deepseek-v4-flash","letter":"The core idea is real and worth taking seriously: two on-site potentials in the 2D non-Hermitian SSH model give a boundary-selective reality switch, and the symmetry reasoning on the PBC side is clean. What is new is the specific two-potential construction — alpha sigma0 sigma3 forces the PBC bulk real through PT, beta sigma3 sigma0 forces the full-OBC spectrum real through non-Bloch RMyT symmetry plus the skin effect — and the theta = pi/4 line-gap transition that interpolates between them. The numerical spectra in Figs. 2 and 3 are consistent with the stated symmetries, and no parameter is fitted to produce the desired spectrum, so there is no circularity. The PBC reality switch for alpha is essentially proven by the explicit PT symmetry. The non-Bloch bulk argument for beta is also plausible and follows standard theory.\n\nThe soft spot is exactly where the stress-test lands: the full-OBC reality claim for the edge modes. The paper states that under full OBC the edge-mode loops shrink and mixing vanishes in the thermodynamic limit, but there is no finite-size scaling, no equation of motion for the edge eigenvalues, and no non-Bloch analysis with the second open direction. Because the whole point of the beta switch is to make the boundary spectrum real, this is load-bearing, not a side remark. That said, the paper is honest that the result is thermodynamic-limit in spirit — it shows ImE ~ 1e-3 at modest size — so this is a gap in rigor rather than a demonstrated error. I would want a serious referee to ask for finite-size scaling of the maximum imaginary part under full OBC, and ideally a non-Bloch treatment of the edge modes, before calling the claim proven.\n\nTwo smaller issues: the \"topological phase transition\" at theta = pi/4 is inferred from line-gap closing and reopening, but no topological invariant is computed, so that label is premature. And the lasing framing is closer to a suggestion than a demonstrated mechanism; there is no gain model or lasing threshold calculation. These are minor relative to the main mechanism.\n\nWho gets value: people working on non-Hermitian real spectra, skin effect, and selective gain in topological photonic or circuit platforms. It is a short, readable paper with a concrete construction that experimentalists could try. It deserves a serious referee; with a finite-size scaling check added, it would be a solid contribution.\n\nMy recommendation: send it to peer review, with conditions requiring the finite-size and edge-mode analysis. This is not a desk-reject.","headline":"Plausible and interesting boundary-selective reality switch; the PBC side is rigorous, but the full-OBC reality claim needs a finite-size scaling check before it can be taken as proven.","tokens_in":6454,"tokens_out":1635,"would_cite":true,"duration_ms":22667,"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":"This paper shows that in a 2D non-Hermitian SSH lattice, one on-site potential makes the periodic-boundary bulk spectrum real and another makes the full open-boundary spectrum real, with a complex-gap topological transition at the switch.","keywords":["non-Hermitian SSH model","reality switch","PT symmetry","non-Hermitian skin effect","non-Bloch band theory","complex energy gap","topological phase transition","boundary-selective lasing"],"falsifier":"Fix $\\beta$ large and compute the full OBC spectrum for a sequence of system sizes $L_x,L_y$; the paper's claim predicts that the largest imaginary part of any eigenvalue tends to zero and the edge-mode loops collapse to arcs as $L$ grows. If the imaginary parts instead saturate at a finite value or the edge loops continue to enclose finite area, the thermodynamic-limit reality claim fails.","tokens_in":5484,"feed_emoji":"🔀","tokens_out":9338,"duration_ms":94324,"temperature":0.7,"pith_summary":"The paper is trying to establish that a single 2D non-Hermitian SSH model can be switched between having a real bulk spectrum and having a real boundary spectrum just by choosing an on-site potential: $\\alpha\\sigma_0\\sigma_z$ makes the periodic-boundary bulk real through PT symmetry, while $\\beta\\sigma_z\\sigma_0$ makes the full open-boundary spectrum real through the non-Hermitian skin effect and a non-Bloch $RM_yT$ symmetry. A one-parameter combination $\\cos\\theta\\,\\sigma_0\\sigma_3+\\sin\\theta\\,\\sigma_3\\sigma_0$ interpolates between these two regimes, and the switch is accompanied by a line-gap-closing topological phase transition at $\\theta=\\pi/4$. A sympathetic reader would care because a controllable way to turn complex energies real on demand would make non-Hermitian gain and lasing behaviors selectable between bulk and boundary in the same lattice.","feed_headline":"Boundary switch makes a non-Hermitian spectrum real on demand","feed_subtitle":"In one 2D lattice, one potential makes the bulk real and another makes the boundary real — a step toward selective lasing.","key_machinery":"The central objects are the two on-site potentials $\\alpha\\sigma_0\\sigma_z$ and $\\beta\\sigma_z\\sigma_0$, where $\\sigma_\\mu\\sigma_\\nu$ are Kronecker products of Pauli matrices acting on the two sublattice spaces of the four-site unit cell; the first shifts one pair of internal states relative to the other while preserving inversion and PT-related symmetries, and the second shifts a different pair while preserving reciprocal mirror and time-reversal symmetries. The argument is carried by three mechanisms: PT symmetry ensures real PBC bulk energies under the $\\alpha$ term; the non-Hermitian skin effect in the y-direction plus non-Bloch band theory—replacing $e^{ik_y}$ by $\\beta_y$ and imposing the modular condition on $|\\beta_y|$—puts the $\\beta$-term bulk into a non-Bloch $RM_yT$ symmetric phase whose arcs have real energies; and T symmetry with no edge modes on the x-normal boundaries makes the oppositely wound edge-mode loops under yOBC shrink to real arcs under full OBC in the thermodynamic limit. The one-parameter family $\\cos\\theta\\,\\sigma_0\\sigma_3+\\sin\\theta\\,\\sigma_3\\sigma_0$ is the switch that rotates between the two mechanisms, with a line-gap closing at $\\theta=\\pi/4$ marking the topological transition.","core_discovery":"In the 2D non-Hermitian SSH model with asymmetric hoppings, the authors identify two on-site perturbations with opposite boundary selectivity. For sufficiently large $\\alpha$, the perturbation $\\alpha\\sigma_0\\sigma_z$ keeps PT symmetry and drives the PT-broken bulk branches into a PT-unbroken phase, so the full PBC bulk spectrum is real and exhibits arcs rather than areas; the boundary modes remain complex but show no skin effect because oppositely wound edge loops on opposite boundaries cancel. For sufficiently large $\\beta$, the perturbation $\\beta\\sigma_z\\sigma_0$ preserves $RM_yT$ and $T$; under yOBC the non-Hermitian skin effect sets in, the bulk is described by non-Bloch band theory with a modular condition on $\\beta_y$, and the non-Bloch $RM_yT$ symmetric phase makes the bulk arcs real, while the edge-mode loops shrink under full OBC and become real arcs in the thermodynamic limit. The combined potential interpolates between the two regimes and passes through a line-gap-closing topological phase transition at $\\theta=\\pi/4$, where the on-site potential vanishes on one pair of sites; the authors propose that the redistribution of on-site potential signs drives the transition.","pith_inferences":["As an extension, if the central claim holds, the same lattice should show a lasing contrast: pumping the $\\alpha$ regime should favor bulk gain while the edge modes stay complex, and pumping the $\\beta$ regime should favor boundary gain while the bulk is real; the paper points toward this goal but does not compute lasing thresholds.","As an extension, the asserted collapse of edge-mode loops under full OBC lacks a quantitative derivation; an exact or large-scale numerical treatment of the full OBC spectrum as a function of system size would be the natural next step and would fix the crossover scale in $\\beta$.","As an extension, because the on-site potential vanishes on one pair of sites exactly at $\\theta=\\pi/4$, the line-gap-closing transition may be a general sublattice-decoupling mechanism; testing the same combined potential on other two-dimensional non-Hermitian lattices, such as the 2D Hatano-Nelson limit the authors mention, would show whether the transition point is universal."],"forward_implications":["For sufficiently large $\\alpha$, the PBC bulk spectrum becomes entirely real while edge modes remain complex, so an open sample would show boundary-selective spectral complexity even though its bulk is Hermitian-like.","For sufficiently large $\\beta$, the full OBC spectrum becomes real in the thermodynamic limit, so a finite non-Hermitian sample can have an entirely real spectrum despite asymmetric hoppings.","The transition between the two regimes at $\\theta=\\pi/4$ is a line-gap-closing topological phase transition in the complex energy plane, so the reality switch is not a crossover but a phase transition.","The mechanism is not restricted to these two potentials: inter-site perturbations such as $\\sigma_1\\sigma_1+\\sigma_2\\sigma_2$ can also act as a reality switch, and combinations such as $\\sigma_1\\sigma_0+\\sigma_1\\sigma_3$ can induce reality for all boundary conditions simultaneously.","The reality switch persists in the 2D Hatano-Nelson limit $\\gamma_{in}=\\gamma_{ex}$, $\\gamma'_{in}=\\gamma'_{ex}$, suggesting the mechanism is robust to hopping anisotropy."],"supporting_citations":[{"why":"Supplies the standard PT-symmetry criterion for real spectra, which is what makes the $\\alpha$-induced PBC bulk spectrum real.","marker":"[5-7]"},{"why":"The model reference from which the 2D non-Hermitian SSH Hamiltonian with asymmetric hoppings is taken as the platform.","marker":"[10]"},{"why":"Provides the non-Bloch band theory in two dimensions used to analyze the yOBC bulk spectrum through $\\beta_y$.","marker":"[11]"},{"why":"Gives the modular condition on $|\\beta_y|$ that determines the non-Bloch bulk spectrum under the skin effect.","marker":"[12-14]"},{"why":"Establishes the non-Bloch PT symmetric phase and its threshold behavior, the analog used for the non-Bloch $RM_yT$ symmetric phase that guarantees real arcs.","marker":"[15-17]"}],"fun_headline_variants":["Reality switch makes non-Hermitian spectra real, selectively","Boundary-selective real spectra in 2D non-Hermitian SSH model","Switch flips non-Hermitian bulk or boundary to real spectrum","Selective real spectra via boundary switch in non-Hermitian lattice","Real-spectrum control: bulk vs boundary in 2D non-Hermitian system"],"cache_read_input_tokens":3200,"weakest_assumption_plain":"The full open-boundary reality result rests on the assumption that edge-mode loops wound oppositely on opposite boundaries collapse and stop mixing under full open boundaries in the thermodynamic limit, a step the authors state rather than prove.","fun_headline_variants_meta":{"raw":{"variants":["Reality switch makes non-Hermitian spectra real, selectively","Boundary-selective real spectra in 2D non-Hermitian SSH model","Switch flips non-Hermitian bulk or boundary to real spectrum","Selective real spectra via boundary switch in non-Hermitian lattice","Real-spectrum control: bulk vs boundary in 2D non-Hermitian system"]},"model":"deepseek-v4-flash","effort":"low","cost_usd":0.000183,"raw_usage":{"total_tokens":1302,"prompt_tokens":922,"completion_tokens":380,"prompt_tokens_details":{"cached_tokens":384},"prompt_cache_hit_tokens":384,"prompt_cache_miss_tokens":538,"completion_tokens_details":{"reasoning_tokens":283}},"tokens_in":538,"tokens_out":380,"duration_ms":3802,"temperature":1.0,"reasoning_tokens":283,"cache_read_input_tokens":384,"cache_creation_input_tokens":0},"cache_creation_input_tokens":0},"created_at":"2026-08-06T20:39:45.897534+00:00","model_set":{"reader":"deepseek-v4-flash"},"falsifier":"Fix $\\beta$ large and compute the full OBC spectrum for a sequence of system sizes $L_x,L_y$; the paper's claim predicts that the largest imaginary part of any eigenvalue tends to zero and the edge-mode loops collapse to arcs as $L$ grows. If the imaginary parts instead saturate at a finite value or the edge loops continue to enclose finite area, the thermodynamic-limit reality claim fails.","supporting_citations":[{"cited_title":null,"cited_arxiv_id":null,"evidence_quote":"The model reference from which the 2D non-Hermitian SSH Hamiltonian with asymmetric hoppings is taken as the platform."},{"cited_title":"Yokomizo and S","cited_arxiv_id":null,"evidence_quote":"Provides the non-Bloch band theory in two dimensions used to analyze the yOBC bulk spectrum through $\\beta_y$."}],"review_version":1}