{"id":"00038090-e6e5-43f3-8386-ced42e3af402","arxiv_id":"2501.06816","paper_version":2,"verdict":"ACCEPT","confidence":"HIGH","novelty_score":6.0,"correctness_risk":"low","formal_verification":"none","parameter_count":0,"one_line_summary":"Interaction-induced corner localization of doublons in a 2D non-Hermitian Bose-Hubbard model constitutes a second-order skin effect with corner-mode count growing linearly with system size.","lead":"Binding bosons into doublons on a non-Hermitian square lattice makes the pairs collect at corners, an interaction-induced higher-order skin effect. It shows that many-body interactions can create higher-order non-Hermitian boundary phenomena without single-particle nonreciprocity engineering.","discovery_kind":"new_application","skeptic_critique":{"model":"deepseek-v4-flash","headline":"Second-order classification is underdetermined: Fig. 3(b) varies L_y at fixed L_x, so the linear count could also fit a first-order O(L_x L_y) skin effect; a test varying L_x at fixed L_y (plus a bulk IPR check) is needed.","rationale":"The reader identified the bulk-delocalization heuristic as the weakest assumption; I agree that this is the physical condition that separates a second-order skin effect from a first-order one. My stress-test sharpens the concern into a concrete scaling ambiguity: Fig. 3(b) varies only the chain count L_y at fixed chain length L_x, so the displayed linear growth is equally consistent with a first-order volume scaling O(L_x L_y). The missing check is to vary L_x at fixed L_y, which directly tests whether the corner-mode count is a boundary effect (independent of L_x) or a volume effect (growing with L_x). The effective Hamiltonian in Sec. III.B gives good analytic reason to expect N_c ~ L_y, and the numerical spectrum comparison in Fig. 9 supports that effective description, so the flaw is not an internal inconsistency but an insufficient demonstration of the load-bearing hallmark. The reader's ACCEPT verdict is reasonable, but the central quantitative claim would be placed on much firmer ground by the proposed L_x-scaling and bulk-IPR check; hence CONDITIONAL rather than a flat ACCEPT or a rejection.","tokens_in":21490,"tokens_out":14342,"duration_ms":156511,"concrete_test":"Use exact diagonalization in the two-boson sector with P/J = 4, t/J = 2, U/J = 8. Fix L_y = 14 and compute the number N_c of in-gap corner modes for L_x = 9, 11, 13, 15, 17, and 21 under OBCs in both directions; also compute the average inverse participation ratio (IPR) of all doublon bulk states. If N_c remains approximately constant with L_x and the bulk IPR scales as 1/(L_x L_y), the second-order classification is confirmed. If N_c grows with L_x or a macroscopic fraction of bulk states is edge-localized, the corner modes are instead part of a first-order skin effect.","verdict_should_be":"CONDITIONAL","load_bearing_attack":"The central claim (Sec. IV) is that the corner-mode count N_c scales with the linear size, the hallmark of a second-order skin effect. The only quantitative scaling evidence is Fig. 3(b), which plots N_c versus L_y with L_x held fixed (L_x = 15 in the parameter set used). For a conventional first-order skin effect along y, the number of skin states scales as L_x L_y; at fixed L_x this is also linear in L_y, so the plot cannot distinguish the claimed O(L_y) corner-mode count from an O(L_x L_y) first-order skin effect. The analytic effective-doublon model in Sec. III.B predicts one edge state per x-chain, hence N_c ~ L_y independent of L_x, which would settle the issue, but the paper does not report N_c versus L_x. Relatedly, the assertion that bulk doublon states remain extended is supported only by selected density plots (Fig. 2(i-l)) and a heuristic destructive-interference argument; if a macroscopic fraction of doublon states localizes at the top or bottom edge, the corner modes are part of a first-order skin effect rather than a genuine second-order one. This unverified condition is load-bearing for the claimed order of the skin effect.","agreement_with_reader":"partial"},"referee_report":{"model":"deepseek-v4-flash","summary":"The paper studies a two-dimensional non-Hermitian Bose-Hubbard model with nonreciprocal single-boson hopping along y, reciprocal hopping along x, two-boson pairing hopping, and onsite interactions. It claims that, in the two-boson sector, interactions create a band of doublon states with in-gap edge states under x-OBC; when y-OBC is also imposed, these edge states become corner-localized doublon skin modes. The authors derive an effective doublon Hamiltonian by second-order perturbation theory, solve the 1D SSH-like edge problem analytically, obtain the condition P>0 or P<-2J^2/U for edge states, and compute a many-body winding number W=2. They also argue that the corner modes are robust to disorder and propose an ultracold-atom realization. The central claim is an interaction-induced second-order non-Hermitian skin effect whose corner-mode count grows linearly with the linear system size.","tokens_in":21768,"tokens_out":5586,"duration_ms":59657,"significance":"If fully established, the result would be a genuinely new mechanism for higher-order NHSE: many-body interactions, rather than single-particle nonreciprocity, produce corner skin modes in the doublon sector. The paper has clear strengths: the effective doublon Hamiltonian is derived from the original model without fitting and matches exact diagonalization of the full Hamiltonian in Fig. 9; the analytic edge-state condition is explicit and also tested for the negative-P regime in Appendix D; the winding number is computed directly from the interacting Hamiltonian; and the disorder robustness is demonstrated numerically. The main gap is that the scaling evidence that distinguishes a second-order effect from a first-order skin effect is incomplete, and the bulk-delocalization assumption that is load-bearing for the order classification is supported only heuristically.","major_comments":[{"comment":"The central scaling claim is not established by the presented data. Figure 3(b) plots N_c versus L_y at fixed L_x, and the text states that a first-order skin effect would scale as L_x L_y 'regardless of variations in Ly.' At fixed L_x, a first-order skin effect along y also produces a number of localized states proportional to L_y, so the plot cannot distinguish N_c ~ L_y (second order) from N_c ~ L_x L_y (first order along y). The effective model in Sec. III.B predicts one edge state per x-chain, hence N_c ~ L_y independent of L_x, which is a direct and testable consequence. Please add the N_c versus L_x dependence at fixed L_y, or otherwise report the full (L_x, L_y) scaling and compare with the first-order prediction.","section":"Sec. III.A and Fig. 3(b)"},{"comment":"The classification as a second-order skin effect assumes that bulk doublon states remain extended and do not accumulate at a boundary. The paper supports this only by the heuristic destructive-interference argument in Sec. III.B and by selected density plots in Figs. 2(i-l) and 10(g,h); no quantitative measure of localization is given. If a macroscopic fraction of bulk doublon states localized along the top or bottom edge, the corner modes would be part of a first-order skin effect rather than a genuine second-order one. Please compute the inverse participation ratio or participation entropy for the doublon bulk eigenstates as a function of L_x and L_y, and show that the number of non-extended bulk states is O(1), or provide a generalized-Brillouin-zone argument for the effective Hamiltonian in Eq. (8) that proves the absence of bulk skin accumulation.","section":"Sec. III.A and Sec. III.B"},{"comment":"The definition of the integer N_c used in the scaling plot should be stated precisely. It is not clear from the text whether N_c counts all in-gap states in a chosen energy window, all states with density above a corner threshold, or something else. Without a reproducible counting criterion, the scaling plot in Fig. 3(b) cannot be independently verified, and this is directly related to the load-bearing claim of linear scaling.","section":"Sec. III.A, Fig. 3(b)"}],"minor_comments":[{"comment":"The statement that 'the single-boson case ... exhibits no second-order skin effects [see Appendix B]' is not supported by Appendix B, which instead computes the skin corner weight for the two-particle model with U=0 or P=0. Please either add an explicit single-boson analysis or correct the cited appendix.","section":"Sec. III.A"},{"comment":"The wording 'it is disappears when P>0 or P<-2J^2/U' is ungrammatical and the logic of the sentence is hard to parse. Please rephrase to state explicitly which boundary state exists for which parameter range, e.g., 'the higher-energy boundary state is absent, and the lower-energy state is localized, when ...'.","section":"Sec. III.B, around Eq. (19)"},{"comment":"The notation for the effective Hamiltonian would be clearer if the authors stated explicitly that the sum over x runs over sites in the effective lattice and that the boundary modification of U_eff applies only under x-OBC; the transition from Eq. (8) to Eq. (9) is currently abrupt.","section":"Sec. III.B, Eq. (8)"},{"comment":"The many-body winding number is stated to be W=2, but the text gives no numerical illustration of the determinant loop or its winding. Please clarify which subspace (full two-boson Hilbert space or doublon subspace) is used in the determinant, and show the loop or provide the numerical values used.","section":"Eq. (4)"},{"comment":"Reference [88] and reference [109] appear to be the same paper (Brighi and Nunnenkamp, Phys. Rev. A 110, L020201 (2024)). Please deduplicate or cite different sources if both entries were intended.","section":"References"}],"recommendation":"major_revision","confidential_remarks":"The stress-test concern about Fig. 3(b) lands: the published scaling plot cannot discriminate second-order from first-order skin behavior. However, this is a fixable numerical issue, and the effective-model prediction N_c ~ L_y independent of L_x gives a clear way to resolve it. I therefore recommend major revision rather than rejection. The bulk-IPR check is also necessary to justify the order classification, but it is within the scope of the existing numerics."},"author_rebuttal":null,"desk_editor":{"model":"deepseek-v4-flash","letter":"Dear colleague,\n\nThe paper reports a second-order non-Hermitian skin effect induced by interactions in a two-boson system. What's new is the combination: interaction-induced SSH-type edge states for doublons are fed into the hybrid skin-topological mechanism, producing corner-localized doublon modes. The authors back this with a clean effective-doublon Hamiltonian from second-order perturbation theory that matches exact diagonalization, a winding-number computation, a check against Tamm-Shockley states, and disorder robustness. I believe the central physics is right.\n\nWhere it gets soft: the classification as genuinely second-order is underdetermined by the evidence. The only scaling plot, Fig. 3(b), varies L_y at fixed L_x; a first-order skin effect along y would also give N_c ~ L_y at fixed L_x. To rule that out, the authors should show N_c versus L_x (the effective model predicts N_c ~ L_y, independent of L_x) and ideally an inverse participation ratio check that bulk doublon states stay extended. Their argument that bulk states remain extended rests on a heuristic destructive-interference statement and selected density plots. If a macroscopic fraction of doublon states actually localizes at a boundary, the corner modes would be part of a first-order skin effect, and the headline claim would be wrong. This is load-bearing and needs either a proof or a systematic numerical treatment.\n\nMinor issues: no code or data for the exact diagonalization is provided, which would help reproducibility, and the experimental proposal is sketched rather than engineered. Neither is fatal.\n\nWho is this for? Researchers studying interacting non-Hermitian systems, doublon dynamics, or higher-order skin effects. It deserves a serious referee: the question is important, the derivation is self-contained, and the missing checks are addressable in revision. I would send it to review, with the explicit request that the authors add the L_x scaling and a bulk IPR analysis.","headline":"Interaction-induced corner skin modes for doublons are convincingly demonstrated, but the second-order classification needs a stronger scaling check and a less heuristic bulk-delocalization argument.","tokens_in":22257,"tokens_out":3413,"would_cite":true,"duration_ms":34986,"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":"By adding interactions to a non-Hermitian square lattice of bosons, the paper shows that bound boson pairs localize at the corners in a way that scales with system size—a second-order skin effect driven entirely by interactions.","keywords":["non-Hermitian skin effect","higher-order skin effect","many-body interactions","doublons","Bose-Hubbard model","nonreciprocal hopping","corner skin modes","point-gap topology"],"falsifier":"For a range of interaction strengths and hopping parameters, compute the inverse participation ratio of every doublon eigenstate under open boundary conditions in both directions, and plot the corner-mode count $N_c$ versus $L_y$ at fixed $L_x$. If a macroscopic fraction of the bulk doublon states also localizes at an edge, or if $N_c$ grows with the area $L_x L_y$ instead of linearly with $L_y$, then the corner modes are part of a first-order skin effect and the second-order claim fails.","tokens_in":21302,"feed_emoji":"⚛️","tokens_out":7990,"duration_ms":68779,"temperature":0.7,"pith_summary":"This paper sets out to show that many-body interactions, rather than single-particle band engineering, can produce a second-order non-Hermitian skin effect. The authors study a two-dimensional square lattice of bosons with nonreciprocal hopping, onsite interactions, and two-boson pairing hopping, and work in the two-boson sector. They find that bound boson pairs, called doublons, form in-gap states that localize at the lattice corners while the bulk doublon states stay extended, and that the number of corner modes grows linearly with the linear size of the lattice. That linear scaling is the defining signature of a second-order skin effect, so the paper concludes that interactions alone can drive this higher-order phenomenon.","feed_headline":"Boson interactions alone create corner-localized skin modes","feed_subtitle":"Bound boson pairs pile up at lattice corners; mode count grows with system size, no single-particle band engineering needed.","key_machinery":"The engine of the argument is the effective doublon Hamiltonian obtained by quasi-degenerate second-order perturbation theory. In the strong-interaction limit, two bosons bind into a doublon that acts as a single quasiparticle with effective symmetric hopping $J^2/U$ along x, alternating effective unidirectional hopping $t^2/U$ along y, and a direct pairing-hopping term $P$ that staggers the x hoppings into an SSH pattern. That effective model supplies two ingredients: SSH-like edge states localized at the right boundary when the x chain is open, and destructive interference of the alternating y-hopping in the bulk that leaves only the boundary hopping unidirectional. The point-gap topology of the edge states, quantified by the winding number $W=2$, then drives the corner localization when both directions are open.","core_discovery":"The central claim is that interactions alone induce a second-order non-Hermitian skin effect in the two-boson sector of this non-Hermitian Bose-Hubbard model, even though the single-boson model exhibits no such effect. In the strong-interaction limit, second-order perturbation theory maps the two-boson sector onto an effective single-doublon model: the doublon hops symmetrically along x with amplitude $J^2/U$, experiences an additional staggered pairing-hopping term $P$, and undergoes alternating unidirectional hopping along y. In the x direction this effective lattice is an SSH-like chain whose topologically protected edge states sit at the right boundary; along the y direction the alternating unidirectional hopping cancels in the bulk through destructive interference but remains unidirectional at the boundary, pushing those edge states into the top-right corner. The corner modes carry a nonzero many-body winding number ($W=2$), survive a compensating potential that eliminates Tamm-Shockley edge states, remain localized under disorder, and scale in number with the lattice length, which the authors identify as the second-order skin effect.","pith_inferences":["The effective doublon Hamiltonian is a single-particle model, so a classical platform that emulates the doublon hopping, such as an electrical circuit network, could in principle display the same corner skin modes without needing true two-particle quantum dynamics.","The design principle implied by the paper is modular: any one-dimensional chain with interaction-induced edge states, when coupled by boundary-only nonreciprocal hopping, should give corner skin modes. Testing this on other interacting lattice models would show whether the phenomenon is generic rather than specific to this Bose-Hubbard realization.","A stress test beyond the paper's parameter sets is to leave the strong-interaction limit: if the corner modes persist at moderate $U$, the mechanism is robust; if they vanish exactly where the perturbative doublon picture breaks down, the effect hinges on the doublon approximation."],"forward_implications":["The corner skin modes appear for both $P>0$ and $P<-2J^2/U$, and their number $N_c$ grows linearly with the lattice length $L_y$, distinguishing the second-order effect from a first-order volume skin effect.","The in-gap corner states survive a compensating potential that removes Tamm-Shockley edge states, showing that the effect originates from interaction-driven topological edge states rather than trivial surface defects.","The corner modes remain localized under strong disorder in the hopping amplitudes, consistent with the topological point-gap origin claimed by the authors.","The same mechanism produces corner skin modes in the three-excitation subspace, indicating that the effect is not limited to the two-boson sector."],"supporting_citations":[{"why":"Defines the higher-order non-Hermitian skin effect and its linear-size scaling, the benchmark the corner modes are measured against.","marker":"[50]"},{"why":"Shows that pair-hopping chains host interaction-induced topological edge states of photon pairs, the edge-state ingredient reused here.","marker":"[65]"},{"why":"Provides the effective-lattice treatment of doublons via perturbation theory that yields the SSH-like doublon Hamiltonian.","marker":"[66]"},{"why":"Emulates topological edge states of interacting photon pairs in an electrical circuit, supporting the edge-state mechanism and a possible realization route.","marker":"[67]"},{"why":"Supplies the many-body winding-number formula used to characterize the point-gap topology of the edge states.","marker":"[76]"},{"why":"Establishes that repulsively bound pairs can exhibit a non-Hermitian skin effect, a direct precedent for doublon skin behavior.","marker":"[88]"},{"why":"Demonstrates repulsively bound atom pairs in an optical lattice, the physical basis for treating doublons as stable bound states.","marker":"[91]"}],"fun_headline_variants":["Interactions trigger second-order skin effect in bosons","Corner skin modes from boson interactions alone","Interaction-induced corner modes: second-order skin effect","Two-boson bound states create corner skin modes"],"cache_read_input_tokens":3200,"weakest_assumption_plain":"The second-order classification stands on the assumption that bulk doublon states remain extended, and do not also pile up at a boundary, once both directions are open; the paper argues this with a destructive-interference picture and shows density plots for chosen parameters, but does not give a general proof.","fun_headline_variants_meta":{"raw":{"variants":["Interactions trigger second-order skin effect in bosons","Corner skin modes from boson interactions alone","Interaction-induced corner modes: second-order skin effect","Two-boson bound states create corner skin modes"]},"model":"deepseek-v4-flash","effort":"low","cost_usd":0.000236,"raw_usage":{"total_tokens":1542,"prompt_tokens":1022,"completion_tokens":520,"prompt_tokens_details":{"cached_tokens":384},"prompt_cache_hit_tokens":384,"prompt_cache_miss_tokens":638,"completion_tokens_details":{"reasoning_tokens":459}},"tokens_in":638,"tokens_out":520,"duration_ms":5006,"temperature":1.0,"reasoning_tokens":459,"cache_read_input_tokens":384,"cache_creation_input_tokens":0},"cache_creation_input_tokens":0},"created_at":"2026-08-10T20:51:03.398840+00:00","model_set":{"reader":"deepseek-v4-flash"},"falsifier":"For a range of interaction strengths and hopping parameters, compute the inverse participation ratio of every doublon eigenstate under open boundary conditions in both directions, and plot the corner-mode count $N_c$ versus $L_y$ at fixed $L_x$. If a macroscopic fraction of the bulk doublon states also localizes at an edge, or if $N_c$ grows with the area $L_x L_y$ instead of linearly with $L_y$, then the corner modes are part of a first-order skin effect and the second-order claim fails.","supporting_citations":[{"cited_title":null,"cited_arxiv_id":null,"evidence_quote":"Shows that pair-hopping chains host interaction-induced topological edge states of photon pairs, the edge-state ingredient reused here."},{"cited_title":"Salerno , author G","cited_arxiv_id":null,"evidence_quote":"Provides the effective-lattice treatment of doublons via perturbation theory that yields the SSH-like doublon Hamiltonian."},{"cited_title":null,"cited_arxiv_id":null,"evidence_quote":"Emulates topological edge states of interacting photon pairs in an electrical circuit, supporting the edge-state mechanism and a possible realization route."},{"cited_title":"\\ Zhang , author M","cited_arxiv_id":null,"evidence_quote":"Supplies the many-body winding-number formula used to characterize the point-gap topology of the edge states."},{"cited_title":"Winkler , author G","cited_arxiv_id":null,"evidence_quote":"Demonstrates repulsively bound atom pairs in an optical lattice, the physical basis for treating doublons as stable bound states."}],"review_version":1}