{"id":"6053d0f9-a008-43b6-a203-f00e13805515","arxiv_id":"2505.09884","paper_version":1,"verdict":"CONDITIONAL","confidence":"MODERATE","novelty_score":6.0,"correctness_risk":"medium","formal_verification":"none","parameter_count":3,"one_line_summary":"NaTmSe2 hosts a dipolar spin-disordered ground state with gapless spinon-like excitations, interpreted as a triangular-lattice transverse-field Ising magnet with a multipolar transverse field (Δ = 1.34 meV) larger than the Ising couplings (J1 ≈ 0.198 meV).","lead":"NaTmSe2 is a layered magnet whose atomic moments stay disordered down to 50 millikelvin, yet it keeps showing gapless magnetic waves at low energy. The study interprets this as a clean realization of the transverse-field Ising model, a basic quantum magnet, and argues the waves are fractionalized spinon excitations.","discovery_kind":"new_application","skeptic_critique":{"model":"deepseek-v4-flash","headline":"The effective spin-1/2 exchange mapping is internally inconsistent: Eq. (2) gives J1≈0.29 meV, not 0.198 meV, so the DMRG/ED confirmation and quoted Δ/J1 rest on the wrong parameter set.","rationale":"The reader's verdict is CONDITIONAL with medium risk; my read supports this. The conversion factor is the single most load-bearing assumption because it connects the experimental J=6 fit to every claimed quantitative statement in the abstract and to the numerical ED/DMRG confirmation. The paper provides Eq. (2) wave functions and its own geff formula, so the correct projection factor can be computed without new experiments, and it disagrees with the quoted factor. This is an internal inconsistency, not a disagreement with external consensus. The DMRG gaplessness claim is also fragile (finite Ly=6, linear 1/Lx extrapolation, and a parameter regime in which a transverse-field Ising paramagnet should be gapped), but that concern is harder to evaluate without the data in the Supplementary Materials; the conversion-factor error is concrete and verifiable now. The experimental observations (no magnetic order, gapless continuum, C_p~T^2) are strong and mutually consistent, so the paper should not be rejected; it needs a corrected derivation and recomputed numerics. I therefore leave the reader's CONDITIONAL verdict unchanged.","tokens_in":13752,"tokens_out":25028,"duration_ms":252839,"concrete_test":"Re-derive the reduction from Eq. (1) to Eq. (3) by projecting Ĵz onto the doublet of Eq. (2); compute J1=4|⟨ψ0|Ĵz|ψ1⟩|²Θ1 and check whether the resulting TFIM reproduces the J=6 spin-wave dispersion in Fig. 2(h) for Θ1=0.00354 meV. Then rerun the DMRG gap calculation of Fig. 4(h) with the corrected J1≈0.291 meV (and the same J2≈0.026 meV, Δ=1.34 meV). If the linearly extrapolated gap remains zero, the gapless claim survives the parameter correction; if it becomes finite, the numerical evidence for gapless spinons was an artifact of the incorrect 56-factor mapping.","verdict_should_be":"UNCHANGED","load_bearing_attack":"The section 'J1-J2 TFIM' asserts that Θ1 and Θ2 convert to J1 and J2 by the factor J(J+1)/S(S+1)=56, yielding J1=0.198 meV. This is not the factor that follows from the paper's own CEF wave functions. From Eq. (2), ⟨ψ0|Ĵz|ψ1⟩=−4.53, and the paper's own formula geff=2gJ⟨ψ0|Ĵz|ψ1⟩≈10.55 implies the projected operator is Ĵz=2λS^z with λ=4.53. Projecting Θ1ΣĴz_iĴz_j onto the doublet then gives J1=(2λ)^2Θ1=4×(4.53)^2×0.00354≈0.291 meV, not 56×0.00354=0.198 meV. The factor 56 uses the ratio of ⟨J²⟩ to ⟨S²⟩, which is appropriate for a high-temperature Curie-Weiss scale, not for the transition matrix element that controls low-energy exchange and the CEF-excitation dispersion. The discrepancy (0.198 vs 0.291 meV, Δ/J1=6.8 vs 4.6) is much larger than the reported fitting uncertainty in Θ1. Because the equivalence claimed in Fig. 2(i) cannot hold for both parameter sets, the effective model used for ED (Fig. 4(d)-(f)) and DMRG (Fig. 4(h)-(i)) is not the one implied by the J=6 fit of Fig. 2(h). The quantitative parameter determination and the numerical gaplessness confirmation therefore inherit an unresolved inconsistency, even though the qualitative conclusion Δ>J1 may survive.","agreement_with_reader":"agree"},"referee_report":{"model":"deepseek-v4-flash","summary":"This manuscript reports a combined experimental and theoretical study of the triangular-lattice magnet NaTmSe2, arguing that it realizes a J1-J2 transverse-field Ising model (TFIM) with dominant transverse field Δ=1.34 meV, nearest-neighbor Ising coupling J1≈0.198 meV, and next-nearest-neighbor coupling J2≈0.026 meV. The evidence includes CEF level determination by inelastic neutron scattering, magnetization and specific heat, absence of magnetic Bragg peaks at 50 mK, absence of muon precession at 0.28 K, a low-energy INS continuum with a spectral cutoff, specific heat C_p ~ T^α with α≈2, and ED/DMRG calculations that extrapolate to a gapless spectrum. On this basis the authors conclude that NaTmSe2 hosts a dipolar spin-disordered state with gapless spinon excitations mediated by a multipolar transverse field.","tokens_in":13928,"tokens_out":14176,"duration_ms":135800,"significance":"If the central claim holds, NaTmSe2 is a notable realization of a frustrated transverse-field Ising magnet on a clean triangular lattice, complementing TmMgGaO4 and extending the family of rare-earth multipolar magnets. The experimental package is internally consistent: no order down to millikelvin temperatures, a gapless continuum, and power-law specific heat together form a coherent case for a quantum-disordered ground state, and the material's disorder-free structure is a genuine advantage. The manuscript would be strengthened by making the quantitative connection between the J=6 CEF model and the effective spin-1/2 model rigorous; as written, this step contains an unresolved conversion-factor inconsistency that affects the quoted exchange parameters and the numerical checks.","major_comments":[{"comment":"The conversion factor J(J+1)/S(S+1)=56 used to obtain J1=0.198 meV and J2=0.026 meV is not the factor that follows from the authors' own CEF wave functions. From Eq. (2), ⟨ψ0|Ĵz|ψ1⟩ ≈ -4.53. Projecting Ĵz onto the CEF doublet gives Ĵz = -2⟨ψ0|Ĵz|ψ1⟩ S^z (up to a unitary choice of pseudo-spin basis), so the exchange term Θ1 Σ Ĵz_i Ĵz_j becomes J1 Σ S^z_i S^z_j with J1 = 4⟨ψ0|Ĵz|ψ1⟩² Θ1 ≈ 82.1 Θ1 ≈ 0.291 meV, and similarly J2 ≈ 0.038 meV. The factor 56, which compares ⟨J²⟩=J(J+1) with ⟨S²⟩=3/4, is the appropriate scale for a different quantity (e.g., a Curie-Weiss or total-moment normalization), not for the transition matrix element that controls the CEF-excitation dispersion fitted in Fig. 2(h). With the corrected matrix element, Δ/J1 is about 4.6 rather than 6.8; although the qualitative Δ>J1 regime survives, the quoted quantitative parameters, the claimed equivalence in Fig. 2(i), and the ED/DMRG results in Fig. 4(d)-(i) inherit the inconsistency unless the numerical work is repeated with the correctly projected couplings. The authors should present the explicit projection of Eq. (1) onto the doublet and reconcile all reported values.","section":"J1-J2 TFIM, Eq. (2)-(3)"},{"comment":"The confirmation of model equivalence is partly circular. Θ1 and Θ2 are obtained by fitting the J=6 model to the dispersion of the first CEF excitation (Fig. 2(h)), and the effective spin-1/2 model with converted J1 and J2 is then said to 'confirm the equivalence of the two models' by reproducing the same spectrum (Fig. 2(i)). This is a consistency check on the fitting procedure, not an independent validation of the reduction. The equivalence should be established by a first-principles projection of the J=6 Hamiltonian onto the CEF doublet, which would also resolve the conversion-factor problem above, and, ideally, by predicting a quantity not used in the fit (for example the field dependence of the excitation dispersion or of the specific heat).","section":"J1-J2 TFIM and Fig. 2(h)-(i)"},{"comment":"The numerical support for gaplessness should be documented more thoroughly. The extrapolation in Fig. 4(h) uses Ly=6 cylinders and a linear fit in 1/Lx; for a gapped two-dimensional system, cylindrical finite-size gaps can scale to zero in a linear-in-1/Lx fit over a short range, so the extrapolation alone is not conclusive. Please report the raw gap values and fit range, show results for at least one additional Ly value, and compare the gap scaling against the expected exponential behavior of a gapped phase. This is especially important because the calculation uses the disputed J1/J2 values from the conversion discussed above.","section":"Spin excitations, Fig. 4(h)"}],"minor_comments":[{"comment":"The fourth CEF excitation energy is quoted as 34.34 meV in the text but as 35.34 meV in the Fig. 2 caption; please correct the inconsistency.","section":"CEF excitations and Fig. 2 caption"},{"comment":"The compound name appears as NaTa7O19 in the introduction and as PrZnAl11O9 in the spin ground-state section; both appear to be typographical errors for the neodymium heptatantalate and PrZnAl11O19 mentioned in the cited references.","section":"Introduction and Spin ground state"},{"comment":"The comparison between the field dependence of the specific-heat exponent α and the DMRG gap is qualitative; please state explicitly whether the linear increase of the gap is expected to produce a linear increase of α near the gapless point, or whether the agreement is only in monotonic behavior.","section":"Spin excitations, Fig. 4(i)"}],"recommendation":"major_revision","confidential_remarks":"The experimental data set is strong and the qualitative scenario (no static order, gapless continuum, T^2 specific heat) is likely to be of broad interest to the frustrated-magnetism and quantum-spin-liquid communities. The main risk is the undocumented and, as written, incorrect conversion from the J=6 exchange parameters to the effective spin-1/2 TFIM couplings; because the ED and DMRG sections rely on those couplings, the quantitative confirmation of gaplessness is not yet established for the material's actual parameters. I would encourage the editor to request a corrected projection and rerun or reanalyzed numerics rather than rejecting, since the issue appears fixable within the manuscript's scope."},"author_rebuttal":null,"desk_editor":{"model":"deepseek-v4-flash","letter":"Read the NaTmSe2 paper. The experimental package is genuinely good: neutron diffraction, muSR, INS, and specific heat all point the same way—no static order down to 50 mK, a gapless continuum below 0.5 meV, and Cp ~ T^2. The CEF scheme is cross-checked against the dilute compound NaTm0.1Lu0.9Se2, which gives it real footing. The material is a clean triangular-lattice Ising system without the Mg/Ga disorder of TmMgGaO4, and that alone makes it worth attention.\n\nThe main new result is material-specific: the first CEF level scheme, exchange parameters, and disordered ground state for NaTmSe2. The conceptual framework is borrowed from the TmMgGaO4 literature, which the paper acknowledges.\n\nNow the soft spots. The stress-test note is correct: the conversion from the J=6 Ising parameters Θ1, Θ2 to the effective spin-1/2 J1, J2 uses a factor J(J+1)/S(S+1)=56, but the CEF wave functions in Eq. (2) give ⟨ψ0|Ĵz|ψ1⟩ ≈ 4.53, so the correct conversion factor is (2λ)^2 ≈ 82. That puts J1 ≈ 0.29 meV, not 0.198 meV. The ratio Δ/J1 drops from about 6.8 to 4.6. The qualitative statement Δ > J1 survives, but the claimed equivalence of the two models in Fig. 2(i) cannot hold for both parameter sets. This is not a rounding issue; it affects the DMRG and ED calculations that support the gaplessness claim. The authors need to reconcile this.\n\nThe spinon label is an interpretation. The data show a gapless continuum, which is consistent with spinons but also with other explanations. The ED comparison is made at Q = [0,0] while the data are at finite L; the figure labels are sloppy. The multipolar polarized component is inferred from the model, not directly observed; the abstract overstates it as a revealed result.\n\nNo code or data repositories are linked, so the numerical results are not independently checkable. That would be worth fixing.\n\nBottom line: the experimental work is solid and the material is potentially important. But the quantitative parameter extraction has a real internal inconsistency, and the spinon attribution needs to be framed more carefully. I'd send it to a serious referee, but with the expectation of a substantial revision. If I worked in this area, I'd wait for the revision before citing it.","headline":"Strong experimental package for NaTmSe2, but the effective-model exchange conversion is internally inconsistent—fix the factor before trusting the spinon claim.","tokens_in":14789,"tokens_out":4594,"would_cite":false,"duration_ms":40733,"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":"NaTmSe2 realizes the transverse-field Ising model with a multipolar transverse field, yielding a spin-disordered ground state and gapless spinon excitations.","keywords":["NaTmSe2","triangular lattice","transverse-field Ising model","quantum spin liquid","spinon excitations","multipolar moments","crystal electric field","muon spin relaxation"],"falsifier":"A high-resolution inelastic neutron scattering measurement at 20 mK with energy resolution better than 0.05 meV could settle the claim: if the scattering intensity vanishes below a finite energy rather than rising continuously from zero, the gapless-spinon interpretation fails.","tokens_in":13310,"feed_emoji":"🧲","tokens_out":13885,"duration_ms":119949,"temperature":0.7,"pith_summary":"NaTmSe2, a layered rare-earth chalcogenide with Tm3+ ions on a triangular lattice, is presented as a clean realization of the transverse-field Ising model, with exchange couplings $J_1 \\approx 0.198$ meV and $J_2 \\approx 0.026$ meV and a transverse field $\\Delta = 1.34$ meV set by the crystal-electric-field gap. Because $\\Delta$ exceeds $J_1$, the model sits in a regime where the dipolar Ising component should be quantum-disordered while the multipolar component is polarized. Combining neutron scattering, muon spin relaxation, specific heat, and exact-diagonalization/DMRG calculations, the paper argues that NaTmSe2 shows no static magnetic order down to 50 mK and hosts continuous, gapless spinon excitations below about 0.5 meV. If correct, NaTmSe2 becomes a triangular-lattice Ising material that realizes a quantum spin liquid through a multipolar transverse field rather than an applied magnetic field, and a single magnet that carries two different magnetic states in separate dipolar and multipolar channels.","feed_headline":"Gapless spinons emerge in triangular Ising magnet NaTmSe2","feed_subtitle":"A multipolar transverse field, not an applied magnet, keeps dipoles disordered and drives the low-energy excitations.","key_machinery":"The load-bearing object is the effective spin-1/2 transverse-field Ising model on the triangular lattice, $\\hat H = J_1 \\sum_{\\langle ij\\rangle} S_i^z S_j^z + J_2 \\sum_{\\langle\\langle ik\\rangle\\rangle} S_i^z S_k^z - \\Delta \\sum_i S_i^y$, obtained by projecting the full $J=6$ crystal-field Hamiltonian onto the non-Kramers ground doublet of Tm$^{3+}$. The transverse field $\\Delta = 1.34$ meV acts on the multipolar component $S^y$, and its non-commutation with the dipolar Ising term $S^z$ is what generates the quantum fluctuations that disorder the dipoles. The mapping between the two Hamiltonians uses a fixed rescaling factor $J(J+1)/S(S+1) = 56$ to convert the fitted exchange constants $\\Theta_1, \\Theta_2$ into $J_1, J_2$; the effective $g$-factor along $c$, $g_{\\rm eff} \\approx 10.55$, fixes the dipolar coupling strength. The argument is carried by the combination of a crystal-electric-field refinement, the effective spin model, and numerical spectroscopies (exact diagonalization for the dynamic structure factor, DMRG for gap scaling) that together tie the measured continuum and $T^2$ specific heat to fractionalized spinon excitations.","core_discovery":"According to the paper, NaTmSe2 realizes the $J_1$-$J_2$ transverse-field Ising model with $J_1 \\approx 0.198$ meV, $J_2 \\approx 0.026$ meV, and $\\Delta = 1.34$ meV, placing it in the $\\Delta > J_1$ regime. The transverse field is not a magnetic field acting on dipoles; it is the energy gap between the two lowest crystal-electric-field states of Tm$^{3+}$, and it enters the effective Hamiltonian as a multipolar operator $S^y$. The non-commutativity between $S^z$ and $S^y$ generates quantum fluctuations that destroy dipolar Ising order, leaving a state that is multipolar-polarized but dipolar-disordered. The experimental evidence is that neutron diffraction finds no magnetic Bragg peaks at 50 mK, zero-field muon relaxation shows a homogeneous dynamic environment with a plateau in relaxation rate, inelastic neutron scattering reveals a continuum below 0.5 meV, and the zero-field specific heat follows $C_p \\sim T^2$ with exponent $\\alpha \\approx 1.99$. DMRG gap extrapolation to the thermodynamic limit gives zero gap, and both exact diagonalization and DMRG capture the observed continuum and the field-induced gap. The authors conclude that the low-energy excitations are gapless spinons emerging from the dipolar-disordered ground state and mediated by the multipolar transverse field.","pith_inferences":["If the effective $J_1$ were as large as about 0.29 meV (using the actual crystal-electric-field matrix element rather than the fixed factor 56), the ratio $\\Delta/J_1$ would drop from about 6.8 to about 4.6; the paper's qualitative conclusions would survive, but the margin for gaplessness would be narrower than claimed.","The tolerance-factor flexibility of the chalcogenide family suggests a testable extension: substituting the selenium ligand or the sodium site should tune $\\Delta/J_1$ continuously, and the specific-heat exponent and inelastic neutron continuum could be mapped across a predicted gapless-to-gapped transition.","The multipolar transverse field could be probed more directly by resonant x-ray scattering or nonlinear magnetic susceptibility, which are sensitive to multipolar fluctuations that conventional neutron diffraction does not see; such an experiment would independently test the channel separation."],"forward_implications":["NaTmSe2 becomes a concrete triangular-lattice material in which the transverse-field Ising model is realized with independently determined parameters, allowing quantitative tests of spin-liquid theories on frustrated Ising lattices.","The coexistence of a polarized multipolar channel and a disordered dipolar channel shows that a single magnet can carry two qualitatively different magnetic states in different operator channels, a feature that could guide searches in other rare-earth chalcogenides.","Because the transverse field is intrinsic (a crystal-electric-field gap) rather than an applied magnetic field, the spin-disordered regime persists to zero applied field; applying a $c$-axis field instead suppresses spinon excitations and opens a gap, as seen in the specific-heat exponent rising with field.","The reported gapless continuum and $T^2$ specific heat provide clear experimental signatures that can be looked for in sister compounds such as KTmSe$_2$ or in substituted variants."],"supporting_citations":[{"why":"Defines the intrinsic quantum Ising model on a triangular-lattice non-Kramers doublet and the multipolar-transverse-field construction that the paper adapts to NaTmSe$_2$.","marker":"[31]"},{"why":"Supplies the TmMgGaO$_4$ case with intertwined dipolar and multipolar order, the comparison system against which NaTmSe$_2$'s disordered ground state is defined.","marker":"[35]"},{"why":"Provides the TmMgGaO$_4$ transverse-field Ising parameters used to argue that NaTmSe$_2$ lies in the $\\Delta > J_1$ regime.","marker":"[34]"},{"why":"The supplementary material contains the crystal-electric-field refinement, DMRG gap extrapolation, and field-dependence calculations that underpin the gapless-spinon conclusion.","marker":"[43]"},{"why":"Gives the crystal-electric-field level scheme of the sister compound KTmSe$_2$, used to contextualize the 1.34 meV gap and the low-energy reduction.","marker":"[46]"},{"why":"Reports a similar gapless triangular-lattice Ising antiferromagnet whose specific heat supports the spinon interpretation used here.","marker":"[40]"},{"why":"Provides the exact-diagonalization dynamic structure factor that the paper compares against the measured inelastic neutron continuum.","marker":"[58]"}],"fun_headline_variants":["Multipolar field births gapless spinons in NaTmSe2","No magnet needed: NaTmSe2's multipolar field frees spinons","Gapless spinons arise from internal multipolar field in NaTmSe2","Dipolar disorder from multipolar field drives NaTmSe2 spinons","NaTmSe2: multipolar transverse field yields gapless spinon continuum"],"cache_read_input_tokens":3200,"weakest_assumption_plain":"The entire conclusion depends on the claim that the real magnetic interactions in NaTmSe2 are equivalent to a simpler model with one fixed conversion factor (56) between the measured exchange constants and the model's couplings; the paper states this equivalence without deriving it from the measured atomic wave functions, and a direct calculation from those wave functions gives a different factor, which would put the system closer to magnetic ordering.","fun_headline_variants_meta":{"raw":{"variants":["Multipolar field births gapless spinons in NaTmSe2","No magnet needed: NaTmSe2's multipolar field frees spinons","Gapless spinons arise from internal multipolar field in NaTmSe2","Dipolar disorder from multipolar field drives NaTmSe2 spinons","NaTmSe2: multipolar transverse field yields gapless spinon continuum"]},"model":"deepseek-v4-flash","effort":"low","cost_usd":0.000186,"raw_usage":{"total_tokens":1359,"prompt_tokens":1014,"completion_tokens":345,"prompt_tokens_details":{"cached_tokens":384},"prompt_cache_hit_tokens":384,"prompt_cache_miss_tokens":630,"completion_tokens_details":{"reasoning_tokens":246}},"tokens_in":630,"tokens_out":345,"duration_ms":3620,"temperature":1.0,"reasoning_tokens":246,"cache_read_input_tokens":384,"cache_creation_input_tokens":0},"cache_creation_input_tokens":0},"created_at":"2026-08-15T21:27:01.837604+00:00","model_set":{"reader":"deepseek-v4-flash"},"falsifier":"A high-resolution inelastic neutron scattering measurement at 20 mK with energy resolution better than 0.05 meV could settle the claim: if the scattering intensity vanishes below a finite energy rather than rising continuously from zero, the gapless-spinon interpretation fails.","supporting_citations":[{"cited_title":"In- trinsic quantum ising model on a triangular lattice magnet 7 TmMgGaO4,","cited_arxiv_id":null,"evidence_quote":"Defines the intrinsic quantum Ising model on a triangular-lattice non-Kramers doublet and the multipolar-transverse-field construction that the paper adapts to NaTmSe$_2$."},{"cited_title":"Partial Up-Up-Down Order with the Continuously Distributed Order Parameter in the Triangular Antiferromagnet TmMgGaO4,","cited_arxiv_id":null,"evidence_quote":"Provides the TmMgGaO$_4$ transverse-field Ising parameters used to argue that NaTmSe$_2$ lies in the $\\Delta > J_1$ regime."},{"cited_title":"Supplementary Materials: Gapless spinon excitations emerg- ing from a multipolar transverse field in the triangle-lattice Ising antiferromagnet NaTmSe2,","cited_arxiv_id":null,"evidence_quote":"The supplementary material contains the crystal-electric-field refinement, DMRG gap extrapolation, and field-dependence calculations that underpin the gapless-spinon conclusion."},{"cited_title":"Exchange-renormalized crystal field excitations in the quantum Ising magnet KTmSe2,","cited_arxiv_id":null,"evidence_quote":"Gives the crystal-electric-field level scheme of the sister compound KTmSe$_2$, used to contextualize the 1.34 meV gap and the low-energy reduction."},{"cited_title":"Possible gapless quantum spin liquid behavior in the triangular-lattice Ising antiferromagnet PrMgAl11O19,","cited_arxiv_id":null,"evidence_quote":"Reports a similar gapless triangular-lattice Ising antiferromagnet whose specific heat supports the spinon interpretation used here."},{"cited_title":"Excitation spectrum and spin Hamiltonian of the 8 frustrated quantum Ising magnet Pr3BWO9,","cited_arxiv_id":null,"evidence_quote":"Provides the exact-diagonalization dynamic structure factor that the paper compares against the measured inelastic neutron continuum."}],"review_version":1}