{"id":"45d175ec-a486-4bc5-a655-25ac001f610f","arxiv_id":"2607.07801","paper_version":1,"verdict":"ACCEPT","confidence":"HIGH","novelty_score":7.5,"correctness_risk":"low","formal_verification":"none","parameter_count":1,"one_line_summary":"Correlated dephasing noise induces a many-body Lindbladian point-gap topology and asymmetric diffusion that is interaction-driven and vanishes under postselection.","lead":"Decoherence from correlated density-current noise can create topology in an open lattice of fermions, producing a winding number and non-Hermitian skin effect. The result is robust asymmetric diffusion whose direction is fixed by topology and reverses only at a phase transition.","discovery_kind":"new_application","skeptic_critique":{"model":"grok-4.5","headline":"No significant objection identified","rationale":"The manuscript supplies an explicit, solvable interacting Lindbladian whose discrete spectrum of Ĉ carries a point-gap winding induced solely by the correlated Hermitian jumps. The algebraic closure of the correlator hierarchy, the SWAP and weak-translation symmetries that force the point gap once B≠0, the Green-function band for B=0, the non-Bloch localization length, and the topological transition at t=±g are all internally consistent and numerically corroborated. The reader's weakest assumption correctly flags that higher correlators are uncontrolled, yet the paper never claims that every many-body observable is skin-localized—only that two-point densities and currents exhibit robust asymmetric diffusion fixed by the winding of Ĉ. That claim is fully supported by the closed EOM and the spectral analysis. No internal inconsistency or hidden assumption that would falsify the winding or the diffusion was found. The verdict therefore remains ACCEPT; the concrete check above is a straightforward independent verification rather than a potential refutation.","tokens_in":23990,"tokens_out":576,"duration_ms":7051,"concrete_test":"Independently re-derive the closed EOM for C (Eq. 3) from the adjoint action of L (SM I.A) for the model (1), then numerically diagonalize Ĉ for N=20–40 under both PBC and OBC at the parameters of Fig. 1; confirm that the discrete-band winding and the OBC localization of ∑_C ∑_a |C_{i,i+a}|^{2} reverse exactly when t crosses ±AB/2 while the continuous spectrum of Θ does not. If both hold, the central claim is secure within its stated scope.","verdict_should_be":"UNCHANGED","load_bearing_attack":"The reader's weakest assumption (that late-time two-point observables fully capture the many-body Lindbladian skin effect) is real but does not undermine the central claim. The paper's strongest claim is about topology and skin effect in the generator Ĉ of the closed correlator dynamics (Eq. 3 / Methods / SM I), which is algebraically exact for quadratic Hermitian jumps: only O(N^{2}) modes of L have nonzero C, and the discrete spectrum of Ĉ controls the long-time profile of densities and currents. Higher correlators exist and the state becomes non-Gaussian, but they are not needed for the winding number ν(λ), the localization scaling Re(κ)∝(t^{2}-g^{2})|λ|, the bulk-boundary correspondence for Ĉ, or the asymmetric diffusion of n_i shown in Fig. 2. Those results stand on their own. The assumption is therefore a scope limitation rather than a load-bearing flaw in the argument as stated.","agreement_with_reader":"agree"},"referee_report":{"model":"grok-4.5","summary":"The paper shows that environment-induced dephasing generated by correlated density-current jumps K_m = A n_m + B j_m on a 1D free-fermion chain produces, after noise averaging, an interacting Lindbladian whose correlation-matrix generator Ĉ exhibits a point-gap topology in its discrete (decohered) spectrum. The topology is diagnosed by a winding number \nu(\theta) constructed from the momentum-space Bloch matrix C_ab(k), implies a many-body non-Hermitian skin effect under open boundaries, and yields robust asymmetric diffusion of density perturbations whose direction is fixed by the winding and reverses only at the topological transition t = ± AB/2. The effect is interaction-induced (vanishes for B = 0 or under post-selection) and remains analytically tractable via closed equations of motion for the two-point correlator.","tokens_in":24183,"tokens_out":850,"duration_ms":26997,"significance":"If the results hold, the work supplies a concrete, analytically controlled route by which correlated Markovian noise itself generates many-body point-gap topology and a dynamical skin effect, distinct from both free Lindbladians and post-selected non-Hermitian Hamiltonians. The closed EOM for C, the Green’s-function solution of the decohered band at B = 0, the second-order truncation yielding ξ^{-1} ∝ (t^{2} - g^{2})|\theta|, and the explicit bulk-boundary argument for Ĉ constitute genuine technical strengths. The asymmetric-diffusion signature (Fig. 2) is falsifiable and experimentally accessible in ultracold-atom or circuit-QED platforms, making the paper a clear conceptual advance for open-system topology.","major_comments":[],"minor_comments":[{"comment":"Methods, bulk-boundary paragraph: the truncation of the infinite Bloch matrix C_ab(k) to a finite relative-index window is argued via exponential decay of decohered states, but a short numerical check that the winding number \nu(\theta) remains stable under progressive truncation for the parameters of Fig. 1 would make the argument fully self-contained.","section":null},{"comment":"SM Sec. III.C, Eq. (63): the localization scaling is derived near the steady state; a one-sentence remark that the same leading Re(κ) ∝ |\theta| form continues to describe the entire decohered band (as confirmed by the OBC localization plots) would remove any residual ambiguity.","section":null},{"comment":"Fig. 1 caption and main-text discussion of the continuous spectrum: the phrase “fills an entire disk” is correct only in the thermodynamic limit; a parenthetical “in the N \to ∞ limit” would prevent misreading for finite N.","section":null},{"comment":"Introduction, final paragraph: the claim that the model “remains analytically tractable” is accurate, yet a forward reference to the O(N^{2}) complexity of Ĉ (Methods) would help readers immediately appreciate the practical advantage over full Lindbladian diagonalization.","section":null},{"comment":"References: a few recent works on Liouvillian skin effects with non-Hermitian jumps (e.g., Hamanaka et al., Phys. Rev. B 108, 155114) are already cited; adding a brief contrast sentence in the Discussion would further sharpen the distinction drawn in the abstract.","section":null}],"recommendation":"accept","confidential_remarks":"The manuscript is technically solid and the central claim is cleanly supported by the algebra and numerics. Fit for a high-profile quant-ph journal is excellent; the only soft spot is that the many-body character is carried entirely by the two-point sector, which some readers may initially misread as “effectively free.” The authors already address this carefully, so no editorial intervention is needed."},"author_rebuttal":null,"desk_editor":{"model":"grok-4.5","letter":"The punchline is simple: they give an explicit, solvable model where decoherence itself produces a many-body point gap and non-Hermitian skin effect that reverse only at a topological transition, and the effect is invisible under post-selection. That combination is new relative to the free Lindbladian and post-selected non-Hermitian literature they cite.\n\nWhat works well is the technical control. Quadratic Hermitian jumps close the equations of motion for the correlation matrix C, so the N^{2} generator Ĉ is exact for densities and currents. They extract the discrete “decohered” band, prove it must open a point gap once the current term breaks inversion, define the winding number on the Bloch matrix C_ab(k), and derive the localization length scaling Re(κ) ∝ (t^{2} – g^{2})|λ| from a second-order truncation. The asymmetric diffusion in Fig. 2 and the edge localization in OBC follow directly; the transition at t = ±AB/2 is a clean prediction. The SM derivations are explicit enough to re-implement without code. Citations engage the right prior work without overclaiming.\n\nThe soft spot is real but limited: they control only two-point observables. Higher correlators exist (the state becomes non-Gaussian) and are not tracked, so one cannot yet claim the full many-body density matrix exhibits the same skin profile. That is a scope limitation, not a hole in the argument about Ĉ, the winding, or the diffusion of n_i. No other load-bearing gaps appear; the algebra is consistent and the numerics match the analytics.\n\nThis is for people working on open quantum systems, Lindbladian topology, or quantum simulators with engineered noise. The math is solid, the result is new inside that niche, and it deserves a serious referee. I would engage with it and bring it to reading group.","headline":"Clean analytical example of interaction-induced point-gap topology and skin effect generated purely by correlated Hermitian jumps in a full Lindbladian.","tokens_in":24852,"tokens_out":481,"would_cite":true,"duration_ms":12853,"reading_group":"yes","serious_thinker":"yes","would_accept_peer_review":true},"rs_alignment":null,"lean_confirmation":null,"pith_extraction":{"msc":[],"pacs":[],"model":"grok-4.5","headline":"Correlated decoherence alone can open a topological point gap and drive one-way diffusion in an open lattice.","keywords":["decoherence-induced topology","Lindbladian skin effect","non-Hermitian point gap","asymmetric diffusion","correlated quantum noise","open many-body systems","winding number","quadratic jumps"],"falsifier":"Time-evolve the full many-body Lindbladian (or a sufficiently large truncation that includes four-point functions) from a localized density perturbation and check whether the late-time density profile remains asymmetrically biased in the direction predicted by the winding of Ĉ; disappearance or reversal of the bias would refute the claim.","tokens_in":24800,"feed_emoji":"⇄","tokens_out":962,"duration_ms":9994,"temperature":0.7,"pith_summary":"Decoherence is usually treated as the enemy of topological order. This paper shows the opposite can occur: environment-induced dephasing with correlated density and current jumps generates a topological phase in the noise-averaged dynamics of a one-dimensional fermionic lattice. The topology lives in the discrete, long-lived sector of the correlation-matrix generator, is diagnosed by a winding number, and produces a many-body non-Hermitian skin effect. The observable consequence is asymmetric diffusion whose direction is fixed by the winding and reverses only when a topological transition is crossed. The effect is purely interaction-induced, vanishes under post-selection, and has no effective Hamiltonian description, yet the model remains analytically tractable. If correct, the result reframes correlated quantum noise as a constructive resource for topology in open many-body systems.","feed_headline":"Decoherence alone creates one-way diffusion in a lattice","feed_subtitle":"Correlated noise opens a topological gap that forces particles to relax in only one direction","key_machinery":"The N^{2} \times N^{2} correlation-matrix generator Ĉ, obtained by vectorizing the closed linear equation of motion for the two-point matrix C. Its discrete spectrum (the decohered band) is the object that carries the winding number \nu(\theta) and the skin effect; continuous-spectrum modes decay too fast to control late-time diffusion.","core_discovery":"In a lattice of free fermions subject to the Hermitian jumps K_m = A n_m + B j_m, the noise-averaged Lindbladian produces an interaction-induced point gap in the discrete (decohered) spectrum of the correlation-matrix superoperator Ĉ. The gap carries a nonzero winding number that forces a many-body skin effect and long-time asymmetric diffusion whose direction is set by the winding and reverses only at the topological transition t = ± AB/2.","pith_inferences":["If the same mechanism survives in two dimensions, correlated dephasing could generate higher-order skin effects or mixed-state topological order without coherent drive.","The analytic tractability of Ĉ suggests a broader program: classify all quadratic-jump Lindbladians by the topology of their discrete spectra rather than by free-fermion invariants.","Low-temperature or non-Markovian completions of the model may convert the decohered band into a long-lived topological edge current.","The divergence of the localization length at the transition t = ±g offers a sharp experimental signature that is independent of microscopic details."],"forward_implications":["Correlated density-current noise can be deliberately engineered to produce unidirectional relaxation without post-selection.","The direction of asymmetric diffusion can be flipped by tuning only the relative strength of current versus density dephasing, realizing a topological phase transition inside the open system.","Any Lindbladian built from non-commuting Hermitian jumps is a candidate host for analogous interaction-induced point-gap topology.","Experimental platforms already capable of laser-assisted hopping with spontaneous emission (ultracold atoms, superconducting qubits) can test the predicted one-way diffusion.","Post-selection erases the effect, so only noise-averaged protocols will observe it."],"fun_headline_variants":["Decoherence induces winding number and one-way lattice diffusion","Correlated noise opens topological gap forcing asymmetric diffusion","Interactions plus dephasing create skin effect and directed flow","Noise-averaged dynamics yield topology that sets diffusion direction","Decoherence alone drives interaction-induced one-way particle relaxation"],"cache_read_input_tokens":16512,"weakest_assumption_plain":"That late-time spatial profiles of densities and currents are completely fixed by the discrete eigenmodes of Ĉ alone, so that higher-order correlators cannot wash out the observed skin effect or reverse the diffusion direction.","fun_headline_variants_meta":{"raw":{"variants":["Decoherence induces winding number and one-way lattice diffusion","Correlated noise opens topological gap forcing asymmetric diffusion","Interactions plus dephasing create skin effect and directed flow","Noise-averaged dynamics yield topology that sets diffusion direction","Decoherence alone drives interaction-induced one-way particle relaxation"]},"model":"grok-4.5","effort":"low","cost_usd":0.005152,"raw_usage":{"total_tokens":1422,"prompt_tokens":749,"num_sources_used":0,"completion_tokens":83,"cost_in_usd_ticks":51520000,"prompt_tokens_details":{"text_tokens":749,"audio_tokens":0,"image_tokens":0,"cached_tokens":256},"completion_tokens_details":{"audio_tokens":0,"reasoning_tokens":590,"accepted_prediction_tokens":0,"rejected_prediction_tokens":0}},"tokens_in":749,"tokens_out":83,"duration_ms":6426,"temperature":1.0,"reasoning_tokens":590,"cache_read_input_tokens":256,"cache_creation_input_tokens":0},"cache_creation_input_tokens":0},"created_at":"2026-07-10T17:45:45.207441+00:00","model_set":{"reader":"grok-4.5"},"falsifier":"Time-evolve the full many-body Lindbladian (or a sufficiently large truncation that includes four-point functions) from a localized density perturbation and check whether the late-time density profile remains asymmetrically biased in the direction predicted by the winding of Ĉ; disappearance or reversal of the bias would refute the claim.","supporting_citations":[],"review_version":1}