{"id":"399bcaaf-7571-4f7b-a017-bdd79a6bcb41","arxiv_id":"2608.05988","paper_version":1,"verdict":"CONDITIONAL","confidence":"MODERATE","novelty_score":7.0,"correctness_risk":"medium","formal_verification":"none","parameter_count":3,"one_line_summary":"In the 2D Hubbard model at its spin-density-wave quantum critical point, resistivity is linear in temperature even though the self-energy is not.","lead":"Using a numerical method for the two-dimensional Hubbard model, the authors find that at the quantum critical point the electrical resistivity grows linearly with temperature down to very low temperatures, while the electron self-energy is not linear in temperature. The result challenges the common assumption that strange-metal transport requires a linear-in-temperature self-energy.","discovery_kind":"extension","skeptic_critique":{"model":"deepseek-v4-flash","headline":"The QCP itself may be first-order; footnote [38] admits this possibility and no free-energy or hysteresis check is provided, so the central claim of a continuous unconventional quantum critical point is not yet established.","rationale":"The reader's weakest_assumption focused on the Ornstein-Zernike form for the spin susceptibility, Eq. (5), and whether pseudo-nesting cusps or a q-dependent Gamma0 intrude into the fitting window. That concern affects the extracted exponents but not the direct computation of resistivity, which is obtained from TPSC+ self-energies and the Kubo formula with a gauge-invariant prescription; the OZ ansatz is used only to interpret scaling, not to generate the linear-T resistivity. The first-order transition possibility, by contrast, undermines the very existence of the quantum critical point, which is the foundation of the title, the interpretation of the exponents, and the attribution of the strange-metal behavior to a QCP. The paper explicitly flags this unresolved issue in footnote [38] with the reference to the possibility being 'first-order' and the admission that extensive work would be required to rule it out. No free-energy calculation, hysteresis check, or independent unbiased determination of the order of the transition is presented, so the continuous nature of the transition is an assumption rather than a demonstrated result. A power-law chi_sp(T) over a finite temperature window is also consistent with a system above a weakly first-order transition, where crossover-like behavior can masquerade as critical scaling. Therefore, the most load-bearing concern is not the OZ form but the unverified continuity of the transition. The recommended verdict remains CONDITIONAL, as the paper's other strengths (non-perturbative methodology, sum-rule checks, and direct transport computation) justify consideration, but acceptance should require a definitive check of the order of the transition or a clear statement that the central claim is conditional on a continuous transition.","tokens_in":15334,"tokens_out":8981,"duration_ms":88346,"concrete_test":"Use an unbiased method (e.g., determinant quantum Monte Carlo or DCA) for the 2D Hubbard model at U=6t, t'=0, on a grid of fillings around n=1.1827, computing the low-temperature SDW order parameter and the doping dependence of the spin susceptibility. If the order parameter shows a discontinuous jump or hysteresis as a function of doping, the transition is first-order and the QCP identification fails. Alternatively, within TPSC+, compute the free energy F(n) via coupling-constant integration; a non-convex F(n) requiring a Maxwell construction would indicate a first-order transition.","verdict_should_be":"CONDITIONAL","load_bearing_attack":"The central claim is that the filling n=1.1827 is a quantum critical point with continuous SDW order. The paper's own footnote [38] states: 'There has been a claim that instead of being continuous, the transition could be first-order. Our approach allows this possibility, but would require extensive work.' If the transition is first-order, the 1/T^0.92 power law for chi_sp (Fig. 1a) is a finite-temperature crossover, the extracted exponents γ=0.92, ν=0.98, z=1.28 from Eqs. (5)-(8) are not true critical exponents, and the title claim of an 'unconventional quantum critical point' is unsupported. TPSC+ is not variational and does not compute the free energy, so it cannot distinguish a continuous transition from a weak first-order one; the observed power-law fits alone do not rule out a first-order scenario. This is more fundamental than the Ornstein-Zernike ansatz of Eq. (5), because even an exact OZ form would not establish that the underlying T=0 transition is continuous.","agreement_with_reader":"disagree"},"referee_report":{"model":"deepseek-v4-flash","summary":"The manuscript studies the two-dimensional Hubbard model on the square lattice with nearest-neighbor hopping only, at U=6t, using the TPSC+ approximation. The authors identify the filling n=1.1827 as a quantum critical point separating a Fermi liquid from an incommensurate spin-density-wave phase, based on the temperature dependence of the spin susceptibility and related quantities. They extract critical exponents gamma=0.92, nu=0.98, z=1.28 (modulo logarithmic corrections), which they attribute to Kohn anomalies and near-nesting of hot spots. They find that the zero-frequency self-energy along the Fermi surface has no uniform power-law temperature dependence and that the quasiparticle weight Z_k is strongly T- and k-dependent, yet the dc resistivity computed from a gauge-invariant Kubo formula is linear in T from T=0.003t to T=0.3t. The central conceptual claim is that T-linear resistivity can arise without a T-linear self-energy along the Fermi surface.","tokens_in":15466,"tokens_out":20534,"duration_ms":185557,"significance":"If the results hold, the paper makes a falsifiable prediction: at the specific doping n=1.1827, cold-atom and diagrammatic quantum Monte Carlo experiments should find T-linear resistivity together with an unconventional exponent set (gamma=0.92, nu=0.98, z=1.28). The claim that linear-in-T transport need not imply a linear-in-T zero-frequency self-energy is conceptually important and directly testable. Strengths of the manuscript include that the central quantities are computed outputs rather than fitted targets, the gauge-invariant conductivity prescription in Eqs. (9)-(13) with the f-sum-rule check in Fig. 4, the explicit admission that the Ornstein-Zernike form fails at large wave vectors, and consistency with earlier TPSC+ benchmarking. The main risks are that TPSC+ is an approximate method without controlled error estimates, that the continuous nature of the QCP is not established against the first-order scenario admitted in footnote [38], and that the quoted exponent errors appear to be statistical only, with at least one internal consistency check failing at roughly three times the quoted error.","major_comments":[{"comment":"The continuous nature of the QCP is load-bearing for the title claim, yet the text concedes that \"there has been a claim that instead of being continuous, the transition could be first-order\" and that checking this \"would require extensive work.\" TPSC+ does not produce a free energy and the paper provides no hysteresis or order-parameter diagnostic, so the power-law chi_sp(Q_i,0) ~ 1/T^{0.92} in Fig. 1(a) is also consistent with a finite-temperature crossover above a weak first-order transition; in that case gamma=0.92, nu=0.98, z=1.28 are not true critical exponents and the central claim is unsupported. The reference for the first-order claim is a bare \"[?]\" and cannot be checked. Please either provide a concrete diagnostic that distinguishes the two scenarios (for example, a free-energy comparison, a scaling-collapse test, or an explicit discussion of QMC results at these dopings) or qualify the central claim as a putative QCP.","section":"Spin fluctuations at the QCP; footnote [38]"},{"comment":"The Ornstein-Zernike amplitude relation chi_sp(Q_i,0) = (2/U_sp) xi_sp^2/xi_0^2 is not satisfied by the paper's own exponents: combining Fig. 1(a) (gamma=0.92 +/- 0.003) with Fig. 1(c) (xi_0^2 ~ T^{-0.98 +/- 0.02}) predicts a chi_sp exponent of 1.96 - 0.98 = 0.98, not 0.92; equivalently, the text's deduction xi_sp^2 ~ 1/T^{1.90} differs from the direct fit 2nu = 1.96 +/- 0.02 in Fig. 1(b). The discrepancy of 0.06 is about three times the quoted errors and is not explained by the \"modulo logarithmic corrections\" caveat, and the near-constancy of U_sp in Fig. 1(e) rules that out as a resolution. Because nu and, through omega_SF ~ T^{z nu}, z are headline results, the inconsistency must be resolved or quantified, for example by reporting the fit windows used in each panel and the effect of including logarithmic corrections.","section":"Spin fluctuations at the QCP; Eqs. (5)-(8), Fig. 1"},{"comment":"The exponents of xi_0^2 and Gamma_0 are derived from the q-curvature of chi^(2)(Q_i,0) and from the omega -> 0 slope of Im chi^(2)(Q_i,omega), where the lowest bosonic Matsubara frequency available is 2 pi T. The omega -> 0 extrapolation at each temperature and the choice of q-fitting points introduce systematic errors that are not contained in the quoted +/- 0.02, and z = 1.28 inherits these errors directly from the Gamma_0 exponent 0.70. Please state the extrapolation procedure explicitly and show the sensitivity of the extracted exponents to the number of Matsubara frequencies and to the fitting window.","section":"Spin fluctuations at the QCP; Eqs. (6)-(7), Fig. 1(c),(d)"},{"comment":"The headline transport result, rho linear in T from T=0.003t to T~0.3t, is presented without error bars and without a stability analysis of the maximum-entropy continuation (default model, number of retained spectral moments, and the omega -> 0 extrapolation underlying Re sigma_xx(0)). In addition, the inset of Fig. 4 appears to show the f-sum-rule relative difference growing to the 10% level at the lowest temperatures; the impact of this violation on the low-T continuation should be quantified. Because the \"resilient strange metal\" claim rests entirely on Fig. 3, a sensitivity analysis is needed before the linear-in-T behavior can be considered established.","section":"Resistivity; Fig. 3, Fig. 4"}],"minor_comments":[{"comment":"Footnote [38] and the SM description in reference [88] contain unresolved citations (\"[?]\"), and the Data availability section contains \"[REFERENCE]\" placeholders; the manuscript should be compiled with these resolved before it can be properly evaluated.","section":"Footnotes and Data availability"},{"comment":"The spelling \"Ornstein-Zernicke\" appears several times (for example, in and immediately after Eq. (5)); the standard spelling is \"Ornstein-Zernike\".","section":"Throughout"},{"comment":"The sentence \"These exponents do not correspond to any known universality class\" is very strong given that the exponents are extracted modulo logarithmic corrections from an approximate method; it would be safer to state that the exponent set differs from the known classes surveyed, or to provide an explicit survey of candidate classes.","section":"Discussion and conclusion"},{"comment":"The text states that deviations at n=1.1800 and n=1.1900 confirm the critical filling, but the two deviations are not described (saturation versus a different exponent); please specify the expected behavior on the ordered and disordered sides and how the curves in Fig. 1(a) display it.","section":"Fig. 1(a)"},{"comment":"The inset of Fig. 4 has unclear axis presentation, with the tick \"10\" lacking context; please label both axes explicitly and give the numerical value of the relative difference at the lowest temperature.","section":"End Matter, Fig. 4"},{"comment":"The statement that QCPs \"might explain why T-linear resistivity not only begins near T=0, but also extends to large T\" is speculative and is not addressed by the calculation; consider removing it or clearly marking it as an open question.","section":"Introduction"}],"recommendation":"major_revision","confidential_remarks":"The manuscript appears not to be fully compiled: footnote [38] and the SM description contain unresolved \"[?]\" citations, and the Data availability statement contains placeholder text. I would ask the authors for a complete version early in the revision process. The scientific risk concentrates on the continuous-versus-first-order issue, which the authors themselves flag; the revision should address it with a concrete diagnostic or an explicit qualification rather than a purely cosmetic softening. The paper is squarely within the journal's scope and I have no concerns about novelty disclosure or citation fairness beyond the broken references."},"author_rebuttal":null,"desk_editor":{"model":"deepseek-v4-flash","letter":"First thing to know: this is a genuinely new result, not a repackaged one. For the t'=0 2D Hubbard model at the incommensurate SDW QCP, they report exponents gamma=0.92, nu=0.98, z=1.28, and T-linear dc resistivity down to T=0.003t even though -Im Sigma(k_F,0) has no uniform T power law along the Fermi surface. If the calculation holds up, that is a clean counterexample to the common assumption that strange-metal transport requires a T-linear scattering rate. The resistivity is computed from Kubo with a gauge-invariant prescription, they check the f-sum rule, and the exponents are extracted from calculated susceptibilities, not fitted to force a story. Credit that they flag the limitations: the OZ single-peak form, pseudo-nesting cusps, and the possible first-order transition in footnote [38].\n\nSoft spots, in order of importance. First, the first-order concern is real. The paper's own footnote admits the transition could be first-order and says checking it would require extensive work. TPSC+ does not give a free energy or hysteresis, so nothing in the paper rules out a weak first-order transition. If the T=0 transition is first-order, the power laws in Fig. 1 are crossovers, the exponents are not true critical exponents, and \"unconventional QCP\" overstates the case. This is the load-bearing uncertainty, and it is bigger than the OZ question: even an exact susceptibility would not tell you the order of the transition. Second, the OZ ansatz with a single correlation length and temperature-independent Gamma0 is suspect in exactly the regime used for the fits; the text itself says the form fails at large wave vectors due to square-root cusps. A sensitivity analysis is needed. Third, the resistivity curve has no error bars, and the max-ent analytic continuation is a known source of systematic uncertainty. Fourth, data are promised but placeholders; software not released.\n\nNone of this is fatal. The central claim is internally consistent and presented honestly. The paper is exactly the kind that should go to a serious referee, because the physics is important and the prediction is concrete. I would send it out, but I would push hard for public data, error bars on rho, and a serious sensitivity check on the OZ window and on first-order alternatives.","headline":"A new set of exponents and a clean counterexample to the T-linear self-energy assumption, but the first-order possibility and OZ ansatz mean the 'unconventional QCP' label is not yet nailed down.","tokens_in":16071,"tokens_out":1827,"would_cite":true,"duration_ms":18211,"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":"T-linear resistivity can appear at a 2D Hubbard quantum critical point without a T-linear self-energy along the Fermi surface.","keywords":["Hubbard model","strange metal","T-linear resistivity","quantum critical point","spin-density wave order","Kohn anomaly","non-Fermi liquid","TPSC+"],"falsifier":"Compute the same quantum critical point with a method that resolves the full momentum dependence of the spin susceptibility at large wavevectors (for example diagrammatic quantum Monte Carlo or a theory including the pseudo-nesting cusps) and check whether $\\chi_{\\mathrm{sp}}(Q_i, 0)$ still follows $1/T^{0.92}$ and $\\xi_{\\mathrm{sp}}^2$ still follows $1/T^{1.96}$ below $T \\approx 0.02t$; if the exponents revert to Hertz-Millis values or the resistivity deviates from linearity, the central claim fails.","tokens_in":15074,"feed_emoji":"⚡","tokens_out":6465,"duration_ms":59901,"temperature":0.7,"pith_summary":"The paper predicts strange-metal behavior in the two-dimensional Hubbard model with only nearest-neighbor hopping, at the quantum critical point where incommensurate spin-density-wave order gives way to a Fermi liquid. Using the improved two-particle self-consistent approach, the authors find that the dc resistivity is linear in temperature from $T = 0.003t$ up to roughly $T = 0.3t$, even though the imaginary part of the single-particle self-energy does not follow a single power law anywhere on the Fermi surface and quasiparticle weight is strongly temperature- and momentum-dependent. The central claim is that this separates T-linear transport from the usual assumption that a T-linear self-energy is required. A sympathetic reader should care because it identifies a concrete microscopic route to strange-metal behavior in a model that cold-atom experiments can realize.","feed_headline":"T-linear resistivity survives without T-linear self-energy","feed_subtitle":"At the Hubbard model's spin-density-wave quantum critical point, resistivity stays linear to T=0.003t while quasiparticles vanish.","key_machinery":"The load-bearing object is the Ornstein-Zernike form for the retarded spin susceptibility, Eq. (5), centered on the incommensurate wavevectors $Q_i$, together with the microscopic scales $\\xi_0^2$ and $\\Gamma_0$ extracted from the irreducible particle-hole susceptibility. Kohn anomalies arise because $Q_i$ connects Fermi-surface points with nearly antiparallel velocities ($\\cos\\theta \\approx -0.99$ for the bare dispersion and $-0.999$ for the renormalized dispersion), which causes $\\xi_0^2 \\sim 1/T^{0.98}$ and $\\Gamma_0 \\sim 1/T^{0.70}$ instead of being temperature-independent as in Hertz-Millis theory. These temperature-dependent scales combine to produce the exotic exponents and, through the current-current response evaluated in the Kubo formula, the T-linear resistivity. The calculation is carried out with the improved two-particle self-consistent approach, a non-perturbative method that enforces spin and charge sum rules and the Mermin-Wagner theorem.","core_discovery":"At filling $n = 1.1827$ with $U = 6t$ and $t' = 0$, the zero-frequency spin susceptibility at the incommensurate wavevector scales as $\\chi_{\\mathrm{sp}} \\sim 1/T^{0.92}$, the squared correlation length as $\\xi_{\\mathrm{sp}}^2 \\sim 1/T^{1.96}$, and the characteristic spin-fluctuation frequency as $\\omega_{\\mathrm{SF}} \\sim T^{1.26}$, giving exponents $\\gamma = 0.92$, $\\nu = 0.98$, $z = 1.28$ modulo logarithmic corrections. The authors attribute these unconventional exponents to Kohn anomalies, that is, Fermi-surface points separated by the spin-density-wave wavevector whose renormalized velocities are almost exactly antiparallel, combined with near-nesting, which makes microscopic parameters such as the Landau damping constant temperature-dependent. At the same point, the single-particle self-energy has no uniform temperature power law along the Fermi surface and $Z_k$ is strongly temperature- and momentum-dependent, so Landau quasiparticles are absent. Nevertheless, the Kubo-formula dc resistivity is linear in temperature over two decades, which the paper states is evidence that a linear-in-temperature self-energy along the Fermi surface is not a necessary condition for strange-metal resistivity.","pith_inferences":["If the claim holds, T-linear resistivity should no longer be read as a direct probe of T-linear single-particle scattering; transport and single-particle lifetime are decoupled at this quantum critical point.","The same mechanism, Kohn anomalies producing temperature-dependent microscopic scales, may occur in other two-dimensional itinerant systems with near-nested Fermi surfaces, so the unconventional exponents could be more generic than the specific nearest-neighbor Hubbard model.","A cold-atom measurement of the dc resistivity or spectral function at $n \\approx 1.183$, $U = 6t$, $t' = 0$ would be a clean test: seeing $\\rho \\propto T$ with $Z_k$ collapsing near the anti-node would confirm the scenario.","The paper leaves open the possibility that quasiparticles reappear at asymptotically low temperature; if instead the T-linear resistivity persists to arbitrarily low $T$, the strange-metal behavior would be a genuine zero-temperature phase rather than a crossover."],"forward_implications":["The T-linear resistivity at the quantum critical point remains intact even though Landau quasiparticles are absent, and its slope is slightly larger than Planckian dissipation with $\\alpha \\approx 2$.","The set $(\\gamma, \\nu, z) \\approx (0.92, 0.98, 1.28)$ does not match any known universality class, so the critical point is a new, model-specific one driven by Kohn anomalies and near-nesting.","At $t' = 0$, the same critical behavior holds for both hole and electron doping by particle-hole symmetry, making the prediction directly testable in cold-atom and diagrammatic quantum Monte Carlo setups.","Vertex corrections do not destroy the linearity of the resistivity; earlier work with vertex corrections changes only the slope of the T-linear term.","The linear-in-temperature resistivity does not require the characteristic spin-fluctuation frequency to saturate, as phonon mechanisms would; $\\omega_{\\mathrm{SF}}$ vanishes as $T \\to 0$ and yet the linear law survives."],"supporting_citations":[{"why":"Supplies the improved two-particle self-consistent approach (TPSC+) used for all the calculations.","marker":"[61]"},{"why":"Defines the Hertz-Millis quantum critical theory whose exponents and temperature-independent microscopic parameters the paper contrasts with its own results.","marker":"[72, 73]"},{"why":"Identifies the incommensurate 2kF density-wave onset and the hot-spot geometry that underlies the Kohn anomalies invoked here.","marker":"[75]"},{"why":"Provides the prior discussion of the robustness of Kohn points in three dimensions that the paper extends to two dimensions.","marker":"[78]"},{"why":"Gives the Ornstein-Zernike form for nearly antiferromagnetic itinerant electrons that is adopted as Eq. (5).","marker":"[79]"},{"why":"Documents the non-analytic square-root cusps from pseudo-nesting at large wavevectors, the known limitation of the Ornstein-Zernike form that the paper acknowledges.","marker":"[82]"},{"why":"Provides prior TPSC transport calculations with vertex corrections, supporting the claim that vertex corrections change the slope but not the linearity of the resistivity.","marker":"[93]"}],"fun_headline_variants":["T-linear resistivity without quasiparticles","Strange metal survives vanishing quasiparticles","Resilient strange metal from Kohn anomalies","No Landau quasiparticles, still T-linear resistivity"],"cache_read_input_tokens":3200,"weakest_assumption_plain":"The argument rests on the susceptibility keeping a single-peak Lorentzian (Ornstein-Zernike) form with a constant damping constant all the way down to $T = 0.003t$, even though the paper notes that non-analytic square-root cusps from pseudo-nesting make that form fail at large wavevectors; if those cusps intrude into the fitting window, or if the transition is actually first-order as a claim the paper cites suggests, the extracted exponents and the T-linear resistivity would change.","fun_headline_variants_meta":{"raw":{"variants":["T-linear resistivity without quasiparticles","Strange metal survives vanishing quasiparticles","Resilient strange metal from Kohn anomalies","No Landau quasiparticles, still T-linear resistivity"]},"model":"deepseek-v4-flash","effort":"low","cost_usd":0.000234,"raw_usage":{"total_tokens":1527,"prompt_tokens":1009,"completion_tokens":518,"prompt_tokens_details":{"cached_tokens":384},"prompt_cache_hit_tokens":384,"prompt_cache_miss_tokens":625,"completion_tokens_details":{"reasoning_tokens":460}},"tokens_in":625,"tokens_out":518,"duration_ms":5847,"temperature":1.0,"reasoning_tokens":460,"cache_read_input_tokens":384,"cache_creation_input_tokens":0},"cache_creation_input_tokens":0},"created_at":"2026-08-07T19:45:55.129228+00:00","model_set":{"reader":"deepseek-v4-flash"},"falsifier":"Compute the same quantum critical point with a method that resolves the full momentum dependence of the spin susceptibility at large wavevectors (for example diagrammatic quantum Monte Carlo or a theory including the pseudo-nesting cusps) and check whether $\\chi_{\\mathrm{sp}}(Q_i, 0)$ still follows $1/T^{0.92}$ and $\\xi_{\\mathrm{sp}}^2$ still follows $1/T^{1.96}$ below $T \\approx 0.02t$; if the exponents revert to Hertz-Millis values or the resistivity deviates from linearity, the central claim fails.","supporting_citations":[{"cited_title":"Gauvin-Ndiaye, C","cited_arxiv_id":null,"evidence_quote":"Supplies the improved two-particle self-consistent approach (TPSC+) used for all the calculations."},{"cited_title":"Holder and W","cited_arxiv_id":null,"evidence_quote":"Identifies the incommensurate 2kF density-wave onset and the hot-spot geometry that underlies the Kohn anomalies invoked here."},{"cited_title":"Sch ¨afer, A","cited_arxiv_id":null,"evidence_quote":"Provides the prior discussion of the robustness of Kohn points in three dimensions that the paper extends to two dimensions."},{"cited_title":"Dar ´e, Y","cited_arxiv_id":null,"evidence_quote":"Gives the Ornstein-Zernike form for nearly antiferromagnetic itinerant electrons that is adopted as Eq. (5)."},{"cited_title":"S ´ykora, T","cited_arxiv_id":null,"evidence_quote":"Documents the non-analytic square-root cusps from pseudo-nesting at large wavevectors, the known limitation of the Ornstein-Zernike form that the paper acknowledges."},{"cited_title":"Bergeron, V","cited_arxiv_id":null,"evidence_quote":"Provides prior TPSC transport calculations with vertex corrections, supporting the claim that vertex corrections change the slope but not the linearity of the resistivity."}],"review_version":1}