{"id":"32ac0366-5f70-422d-b425-a0d6e28714aa","arxiv_id":"2506.07650","paper_version":3,"verdict":"CONDITIONAL","confidence":"MODERATE","novelty_score":6.0,"correctness_risk":"medium","formal_verification":"none","parameter_count":5,"one_line_summary":"Retaining full momentum-resolved vertices removes the predicted van Hove singularities in CrBr3 magnons and yields T^3 (optical) versus T^2 (acoustic) second-order renormalization.","lead":"This paper recalculates how interacting spin waves (magnons) in the two-dimensional magnet CrBr3 shift with temperature, dropping a shortcut used in an earlier theory, and finds the predicted sharp spectral singularities vanish, matching neutron data. It matters because it clears up a long-standing discrepancy between theory and experiment for a family of two-dimensional magnets and predicts a new, testable temperature scaling difference between the two magnon branches.","discovery_kind":"extension","skeptic_critique":{"model":"deepseek-v4-flash","headline":"The asserted identity K^(2)=K^(3)=K^(4) contradicts Eqs. (14), (17), and (20); the process 3 and 4 results rest on an unsupported shared kinematic factor.","rationale":"The reader's weakest assumption names numerical convergence of the 4D integrals as the load-bearing premise, and that remains a valid concern because no grid sizes, delta-broadening widths, or convergence tests are reported. I agree with that assessment in part. However, the most decisive and checkable problem I find is the asserted equality K^(2)=K^(3)=K^(4), which is contradicted by the paper's own defining equations. This is not a question of convergence or phase regularization; it is an algebraic inconsistency that can be settled by direct evaluation. The false identity appears to have been used to plot one kinematic factor for three distinct scattering channels, so the displayed decay rates and self-energies for processes 3 and 4 do not follow from the stated integrals. Because the upper-band temperature exponent is computed from the sum of processes 2-5, the T^3 result is directly exposed to this error. The absence of van Hove singularities is argued from the same panels, so the central negative claim is also implicated. I would therefore keep the reader's CONDITIONAL verdict: the paper needs a corrected or justified treatment of K^(2), K^(3), K^(4), in addition to the numerical documentation the reader requested. I do not see a basis for REJECT, since the underlying method is plausible and the issue is addressable; I also do not see a basis for ACCEPT in the current form.","tokens_in":38388,"tokens_out":4823,"duration_ms":62766,"concrete_test":"Independently evaluate K^(2)_k, K^(3)_k, and K^(4)_k from Eqs. (14), (17), and (20) using the same numerical delta-broadening scheme on a uniform BZ grid of at least 400x400 points, at the M point and along the Gamma-M-K path. If the three curves are not pointwise identical, the asserted identity and the shared Fig. 4(b) panel are incorrect; then recompute the process 3 and 4 self-energy integrals separately and re-extract the temperature exponents beta_u and beta_d from the summed self-energy.","verdict_should_be":"UNCHANGED","load_bearing_attack":"The central claim that full momentum-resolved second-order self-energies remove van Hove singularities and yield T^3 (up) and T^2 (down) temperature scaling depends on the correctness of the five process-specific integrals in Eqs. (10)-(24). A demonstrable internal inconsistency appears in the assertion that K^(2)_k, K^(3)_k, and K^(4)_k are identical, with a single curve shown for all three in Fig. 4(b). The three delta functions are not equivalent: Eq. (14) conserves epsilon^u_k + epsilon^d_q = epsilon^d_p + epsilon^d_{k+q-p}; Eq. (17) conserves epsilon^u_k + epsilon^d_q = epsilon^u_p + epsilon^d_{k+q-p}; Eq. (20) conserves epsilon^u_k + epsilon^u_q = epsilon^d_p + epsilon^u_{k+q-p}. With epsilon^u_k - epsilon^d_k = 2JS|gamma_k|, these are different energy-conservation surfaces except at isolated points. Consequently, the shared kinematic-factor curve cannot be correct for all three processes, and the decay rates W^(3), W^(4) and real self-energies shown in Fig. 4(e,f,i,k) are not derived from the stated integrals. Since the optical-band exponent beta_u is obtained by summing processes 2-5, this error can directly affect the T^3 claim. The negative result (no van Hove singularities) is also supported by these panels, so the central argument is not secure until the identity is either proven or the integrals are recomputed separately.","agreement_with_reader":"partial"},"referee_report":{"model":"deepseek-v4-flash","summary":"The paper revisits the problem of magnon-magnon interactions in the honeycomb ferromagnet CrBr3 and, as a comparison, the triangular-lattice ferromagnet MnBi2Te4. The authors perform second-order perturbation theory for the magnon self-energy, retaining full momentum-dependent interaction vertices and evaluating the resulting four-dimensional integrals numerically, without the 'thermal magnon approximation' used in earlier work [PRX 8, 011010 (2018)]. They report that the previously predicted van Hove-like singularities in the renormalized spectrum and decay rates are absent, consistent with inelastic neutron scattering data, and that the optical magnon branch renormalizes as T^3 while the acoustic branch renormalizes as T^2. They also claim a distinction between non-Bravais (honeycomb) and Bravais (triangular) lattices in the temperature dependence. The central claims are based on numerical evaluations of five scattering processes, whose self-energy integrals are given in Eqs. (8)-(24).","tokens_in":38692,"tokens_out":9865,"duration_ms":109693,"significance":"If correct, the paper would resolve a longstanding discrepancy between the theoretical prediction of van Hove singularities in interacting Dirac magnons and the smooth spectra measured by inelastic neutron scattering. The branch-dependent T^3 (optical) versus T^2 (acoustic) scaling is a concrete, falsifiable prediction, and the comparison between honeycomb and triangular lattices is a useful contribution. The methodological step of abandoning the thermal magnon approximation and keeping the full momentum dependence in a fully numerical calculation is in principle valuable. However, the paper's numerical evidence is not transparently documented, and at least one internal inconsistency in the presentation of the kinematic factors directly affects the reported results.","major_comments":[{"comment":"The paper states that the kinematic factors for the second, third, and fourth processes are identical and shows a single curve for all three in Fig. 4(b). This is contradicted by the definitions: Eq. (14) conserves epsilon^u_k + epsilon^d_q = epsilon^d_p + epsilon^d_{k+q-p}, Eq. (17) conserves epsilon^u_k + epsilon^d_q = epsilon^u_p + epsilon^d_{k+q-p}, and Eq. (20) conserves epsilon^u_k + epsilon^u_q = epsilon^d_p + epsilon^u_{k+q-p}. Since epsilon^u_k - epsilon^d_k = 2JS|gamma_k| is nonzero except at isolated points, the three energy-conservation surfaces in the four-dimensional integration domain are generically different. The numerical results for processes 2-4, including the decay rates W^(2), W^(3), W^(4) and the real self-energies in Fig. 4(d,e,f,i,j,k), are presented as derived from these integrals. Unless the authors prove a nontrivial identity, for example by a change of variables that maps the band labels, the reported results for these processes are not supported by the stated equations, and the upper-band T^3 exponent (obtained by summing processes 2-5) is not secure.","section":"Sec. II B, Eqs. (14), (17), (20) and Fig. 4"},{"comment":"The four-dimensional integrals in Eq. (8) are the sole basis for the central negative result (absence of van Hove singularities) and the extracted temperature exponents, but the manuscript gives no grid size, no convergence test, and no specification of the delta-function broadening scheme for the on-shell condition (the parameter delta in Eq. (8) is not defined). The claim that the renormalized spectrum and decay rates are free of singular features is a statement about the non-analytic behavior of these integrals; without evidence that the numerical discretization resolves the Brillouin zone sufficiently finely, the smooth profiles in Fig. 4 could be numerical artifacts. The authors should report the numerical parameters and provide convergence checks, for example by varying the Simpson grid size and the broadening delta.","section":"Sec. II B, Eq. (8) and Figs. 4-5"},{"comment":"The vertex amplitudes in Eq. (4) depend on the phase phi_k = arg gamma_k through the angles zeta, theta, and kappa defined in Eq. (5). At the Dirac points K and K', gamma_k = 0 and the phase is ill-defined. The paper presents results along the Gamma-M-K path, including the K point, but does not explain how this phase singularity is regularized in the numerical integration. This is a potential source of error in the matrix elements and could affect the decay rates and self-energies near the Dirac points.","section":"Sec. II, Eq. (5) and Fig. 1"}],"minor_comments":[{"comment":"The caption gives the single-ion anisotropy as A = 0.028 meV, whereas the text and Eq. (1) use A = -0.028 meV; the sign is important for the magnon gap.","section":"Fig. 4 caption"},{"comment":"The manuscript contains a long corrupted passage of unreadable characters immediately after Eq. (B2), interrupting the Matsubara summation derivation; this must be repaired before publication.","section":"Appendix B"},{"comment":"The phrase 'the following Eq. (4)' should be rephrased, for example as 'the following from Eq. (4)'.","section":"Sec. II B(b)"},{"comment":"The word 'Feynmann' should be 'Feynman' in the heading of Section IV A.","section":"Sec. IV A"}],"recommendation":"major_revision","confidential_remarks":"The paper is a revision of a previous arXiv posting (v3, dated 25 Aug 2025). The authors should be asked to provide the numerical details and to either prove the kinematic-factor identity or recompute the integrals separately. The absence of code and data is a concern for a computational paper of this type, and the internal inconsistency in the kinematic factors is a load-bearing issue that must be resolved before the central claims can be accepted."},"author_rebuttal":null,"desk_editor":{"model":"deepseek-v4-flash","letter":"Let me give you the short version: this paper probably does the right thing qualitatively. Dropping the thermal magnon approximation removes the van Hove singularities that one of the authors predicted in PRX 2018, and that did not survive in the 2022 INS data on CrBr3. That is a real and useful correction, and the contrast with the triangular lattice suggests a Bravais vs non-Bravais difference in temperature scaling I have not seen elsewhere. If the numerics hold up, I would want this in the literature.\n\nThe problems are not minor. The paper asserts that the kinematic factors for processes 2, 3, and 4 are identical and shows a single curve in Fig. 4(b). The delta functions in Eqs. (14), (17), and (20) are not equivalent: they put different band energies in the conservation condition, and the up vs down energies differ by a momentum-dependent |gamma| term. I cannot see any symmetry that would make those three four-dimensional integrals equal, and the paper offers no proof. Those kinematic factors feed directly into the decay rates and the real self-energy for the processes that dominate the upper-band renormalization. So the T^3 exponent and even the claimed smooth profiles are not established. This is an internal contradiction with the paper's own equations, and it is load-bearing.\n\nSecond, Appendix B, the derivation of the central self-energy expression in Eq. (8), is corrupted beyond reading—it is full of garbled, machine-generated text. Right now the key equation has no verifiable derivation in the manuscript.\n\nThird, there is no code, no data, no grid sizes, no convergence tests, and no broadening scheme for the delta functions in what is a 4D Simpson quadrature. For a negative result whose entire force is \"we looked everywhere and found no singularity\", that is not acceptable. The reader's conditional verdict is fair.\n\nTwo minor points. The abstract's T^3 claim sits awkwardly with Section III, which correctly says the Hartree T^2 term dominates the observable shift, making T^3 subleading. And the model parameters come from the same experimental paper used for comparison—not fatal for the qualitative claim, but worth flagging.\n\nWho is this for? Anyone who cares about interacting Dirac magnons and the theory-experiment discrepancy in CrBr3. With a careful rewrite—proven or recomputed kinematic factors, a readable appendix, and full numerical documentation—this could become a solid paper. Right now, the quantitative results are not trustworthy.\n\nRecommendation: send it to peer review, because the question is important and the qualitative direction is probably right. A referee should demand that the kinematic factors be recomputed separately and that the numerical evidence be made available.","headline":"A likely correct qualitative retraction of the 2018 Dirac-magnon van Hove prediction, but the paper's numerical core is undermined by an unsupported kinematic-factor identity and missing convergence data.","tokens_in":39321,"tokens_out":4051,"would_cite":false,"duration_ms":48159,"reading_group":"yes","serious_thinker":"no","would_accept_peer_review":true},"rs_alignment":null,"lean_confirmation":null,"pith_extraction":{"msc":["82D40"],"pacs":["75.30.Ds","75.50.Dd","78.70.Nx"],"model":"deepseek-v4-flash","headline":"Second-order magnon self-energy removes the predicted van Hove singularities in CrBr3 and yields distinct $T^3$ (optical) and $T^2$ (acoustic) renormalization.","keywords":["Dirac magnons","CrBr3","magnon-magnon interactions","van Hove singularity","second-order self-energy","thermal magnon approximation","honeycomb lattice","spin-wave renormalization"],"falsifier":"Recompute the kinematic factors and decay rates of Eqs. (11)-(24) with a documented grid-refinement study and explicit delta-function regularization: if van Hove-like peaks reappear or the fitted exponents $\\beta_u=3$ and $\\beta_d=2$ shift with grid size, the central claim fails. Alternatively, a neutron experiment with enough resolution along the optical band near the $M$ point could check directly whether the renormalization scales as $T^3$ rather than $T^2$.","tokens_in":38056,"feed_emoji":"🧲","tokens_out":7098,"duration_ms":70894,"temperature":0.7,"pith_summary":"This paper tries to establish that the van Hove-like singularities previously predicted in the interacting magnon spectrum of the honeycomb ferromagnet CrBr3 are artifacts of the thermal magnon approximation, and that a full second-order perturbation treatment removes them. It also claims that the renormalized optical and acoustic magnon branches obey distinct temperature power laws, $T^3$ and $T^2$ respectively, at second order, while the Hartree term alone is roughly $T^2$ for both. The authors argue that this agrees with recent inelastic neutron scattering, which saw no singular features, and that the same full treatment applied to a triangular-lattice ferromagnet also gives no singularities but a $T^2\\log T$ trend. If the paper is right, earlier predictions need revision and the temperature exponent of each magnon branch becomes a sharper test of interaction theory.","feed_headline":"Full magnon self-energy: no spurious peaks, T^3 optical branch","feed_subtitle":"Neutron data show no singular features; this calculation explains why and tells which band renormalizes how fast.","key_machinery":"The load-bearing object is the second-order (sunset) self-energy $\\Sigma_S(\\omega,\\mathbf{k})$ of Eq. (8), computed from the five momentum-resolved scattering channels of the quartic Holstein-Primakoff Hamiltonian. The crucial step is evaluating the four-dimensional momentum integrals over the full Brillouin zone with Simpson's rule and the full Bose-Einstein occupation factor $F_{\\mathbf{k};\\mathbf{q},\\mathbf{p}}$, without the thermal magnon approximation, and then feeding the Hartree shift back into the bare energies self-consistently. The momentum-dependent vertex phases $\\phi_{\\mathbf{k}}=\\arg\\gamma_{\\mathbf{k}}$ enter through the matrix elements, and the calculation's treatment of the Dirac points, where $\\gamma_{\\mathbf{k}}=0$, is part of what the argument depends on.","core_discovery":"The central claim is that retaining the full momentum-dependent interaction vertices and evaluating the four-dimensional self-energy integrals, rather than assuming one magnon sits thermally near the band bottom, removes the previously predicted van Hove-like singularities near the $M$ points and the Brillouin-zone corners. In this calculation the second-order (sunset) self-energy produces a $T^2$ temperature dependence for the acoustic (down) band and a $T^3$ dependence for the optical (up) band. The absence of singular features is stated to be consistent with the INS data of Ref. [26], and a similar full calculation for the triangular-lattice ferromagnet MnBi$_2$Te$_4$ gives no dip or van Hove features, with a $T^2\\log T$ correction. The paper also finds that the second-order correction can become negative near the $\\Gamma$ point, which limits the validity of perturbation theory to low temperatures.","pith_inferences":["The numerical robustness of the negative result could be checked by repeating the 4D integrals with explicit grid refinement and controlled delta-function broadening; the paper itself reports no such convergence tests.","If the absence of singularities is genuinely caused by full momentum dependence, the same suppression should appear for other honeycomb-lattice magnets, making the effect a generic property of non-Bravais bosonic Dirac systems rather than a CrBr3-specific detail.","The $T^3$ optical exponent is plausibly a generic consequence of the gap in the optical branch, which suppresses its thermal occupancy by one extra power of $T$; comparing with gapped optical branches in other materials would test this."],"forward_implications":["If the central claim is correct, the van Hove singularities predicted for CrBr3 in Ref. [21] are artifacts of assuming one thermally excited magnon, and future spin-wave analyses should retain full momentum-resolved vertices.","The distinct exponents imply that high-resolution neutron scattering on the optical branch could discriminate the $T^3$ prediction from the earlier universal $T^2$ expectation.","For monolayer MnBi$_2$Te$_4$, the full second-order calculation predicts $T^2\\log T$ renormalization with no van Hove dips, a signature that inelastic neutron scattering could test directly.","Because the second-order correction is negative near the $\\Gamma$ point and grows with temperature, the perturbative regime is bounded; at higher temperatures methods beyond second-order perturbation are required."],"supporting_citations":[{"why":"Supplies the prior thermal-magnon-approximation calculation whose van Hove singularities this paper revisits.","marker":"[21]"},{"why":"Provides the inelastic neutron scattering data showing no van Hove features and the scaled-energy data used for comparison.","marker":"[26]"},{"why":"Predicts log corrections and negative renormalization in spin-wave perturbation theory, used to interpret the triangular-lattice behavior and high-temperature breakdown.","marker":"[37]"},{"why":"Gives the earlier thermal-magnon-approximation prediction for monolayer MnBi2Te4 that the full calculation here supersedes.","marker":"[35]"},{"why":"Recent calculation reporting T^3 renormalization in CrI3, compared in the temperature-exponent discussion.","marker":"[36]"},{"why":"Furnishes the single-ion anisotropy parameter A used in the model.","marker":"[38]"}],"fun_headline_variants":["Magnon interactions erase predicted van Hove singularities","CrBr3 magnons: full self-energy gives T^3 and T^2 laws","No spurious peaks in CrBr3: theory matches neutron data","Optical magnons heat as T^3, acoustic as T^2 in CrBr3","Dirac magnons in CrBr3: singularities absent, interactions matter"],"cache_read_input_tokens":3200,"weakest_assumption_plain":"The whole negative result and the extracted exponents rest on the claim that the numerical four-dimensional integrals are converged and accurate, including the handling of vertex phases where $\\gamma_{\\mathbf{k}}=0$ and the regularization of the delta functions; the paper reports no grid sizes, convergence checks, or broadening scheme.","fun_headline_variants_meta":{"raw":{"variants":["Magnon interactions erase predicted van Hove singularities","CrBr3 magnons: full self-energy gives T^3 and T^2 laws","No spurious peaks in CrBr3: theory matches neutron data","Optical magnons heat as T^3, acoustic as T^2 in CrBr3","Dirac magnons in CrBr3: singularities absent, interactions matter"]},"model":"deepseek-v4-flash","effort":"low","cost_usd":0.0003,"raw_usage":{"total_tokens":1804,"prompt_tokens":1088,"completion_tokens":716,"prompt_tokens_details":{"cached_tokens":384},"prompt_cache_hit_tokens":384,"prompt_cache_miss_tokens":704,"completion_tokens_details":{"reasoning_tokens":629}},"tokens_in":704,"tokens_out":716,"duration_ms":7555,"temperature":1.0,"reasoning_tokens":629,"cache_read_input_tokens":384,"cache_creation_input_tokens":0},"cache_creation_input_tokens":0},"created_at":"2026-08-07T05:33:00.455852+00:00","model_set":{"reader":"deepseek-v4-flash"},"falsifier":"Recompute the kinematic factors and decay rates of Eqs. (11)-(24) with a documented grid-refinement study and explicit delta-function regularization: if van Hove-like peaks reappear or the fitted exponents $\\beta_u=3$ and $\\beta_d=2$ shift with grid size, the central claim fails. Alternatively, a neutron experiment with enough resolution along the optical band near the $M$ point could check directly whether the renormalization scales as $T^3$ rather than $T^2$.","supporting_citations":[{"cited_title":null,"cited_arxiv_id":null,"evidence_quote":"Supplies the prior thermal-magnon-approximation calculation whose van Hove singularities this paper revisits."},{"cited_title":null,"cited_arxiv_id":null,"evidence_quote":"Provides the inelastic neutron scattering data showing no van Hove features and the scaled-energy data used for comparison."},{"cited_title":null,"cited_arxiv_id":null,"evidence_quote":"Predicts log corrections and negative renormalization in spin-wave perturbation theory, used to interpret the triangular-lattice behavior and high-temperature breakdown."},{"cited_title":null,"cited_arxiv_id":null,"evidence_quote":"Gives the earlier thermal-magnon-approximation prediction for monolayer MnBi2Te4 that the full calculation here supersedes."},{"cited_title":null,"cited_arxiv_id":null,"evidence_quote":"Recent calculation reporting T^3 renormalization in CrI3, compared in the temperature-exponent discussion."},{"cited_title":null,"cited_arxiv_id":null,"evidence_quote":"Furnishes the single-ion anisotropy parameter A used in the model."}],"review_version":1}