{"id":"78692ec2-abc2-4cd2-a14f-ad69aebfbfde","arxiv_id":"2608.03013","paper_version":1,"verdict":"CONDITIONAL","confidence":"MODERATE","novelty_score":6.0,"correctness_risk":"medium","formal_verification":"none","parameter_count":4,"one_line_summary":"Long-range repulsive interactions V(r) ~ 1/r^alpha give a scale-covariant self-energy with exponent gamma = 2 - 1/alpha, explaining the doping-dependent ARPES exponents in cuprate strange metals.","lead":"A theory paper proposes that the strange metal state in high-temperature superconductors comes from long-range, poorly screened electrical interactions between charges, not from quantum criticality. It derives a formula connecting the measured energy and temperature exponent of electron scattering to the spatial range of these interactions, and says the exponent changes with doping because screening improves as more charge carriers are added.","discovery_kind":"new_application","skeptic_critique":{"model":"deepseek-v4-flash","headline":"Model caps the predicted exponent at gamma = 1.5, but the cited ARPES data include gamma ~ 1.68; the central relation gamma = 2 - 1/alpha cannot cover the overdoped tail without an unmodeled additional channel.","rationale":"The reader's weakest_assumption focused on the assumed power-law interaction and the superdiffusive hydrodynamic pole. My concern is complementary: even if that derivation is accepted, the model's predicted exponent is bounded above by 1.5, while the same experimental data set that motivates the paper contains values up to gamma ~ 1.68. This is a concrete, internally acknowledged mismatch. Because the paper responds by adding an unspecified Fermi-liquid-like scattering channel, the clean interpretation of gamma as a direct measure of alpha no longer holds in the overdoped regime. This does not invalidate the mechanism for gamma < 1.5, but it does mean the central claim is only conditionally supported. The reader already assigned CONDITIONAL, and my concern reinforces that verdict rather than changing it, so UNCHANGED is appropriate. The proposed test is a straightforward statistical comparison against the empirical form; it would settle whether the gamma > 1.5 discrepancy is a genuine failure of the model in its claimed regime of applicability.","tokens_in":11346,"tokens_out":14283,"duration_ms":147797,"concrete_test":"Re-fit the p ~ 0.29 nodal ARPES self-energy data (or published gamma(p) values) using the model's Gamma_inel = A_gamma T^gamma Phi_gamma(omega/T) restricted to gamma <= 1.5, with A_gamma and the overall normalization as free parameters, and compare against the empirical power-law form Gamma = Gamma_0 + lambda [omega^2 + (C k_B T)^2]^beta / (omega_N)^(2 beta - 1) with beta = 0.84. If the best restricted fit is rejected at a statistically significant level (e.g. delta chi^2 > 4 per point), the overdoped tail lies outside the theory. A complementary check would be to measure alpha(p) independently from a non-ARPES observable (e.g. plasmon dispersion or nonlocal conductivity) and test whether the relation gamma = 2 - 1/alpha holds in the region gamma > 1.5.","verdict_should_be":"UNCHANGED","load_bearing_attack":"The central quantitative claim, Eqn 6, predicts gamma = 2 - 1/alpha for 1 < alpha < 2, so gamma lies in (1, 1.5). For alpha > 2, the text states that diffusive hydrodynamics is restored and gamma is fixed at 1.5. No admissible alpha in the model produces gamma > 1.5. Nevertheless, the ARPES data the paper claims to capture (Smit et al., ref. [17]) include beta ~ 0.84 at p ~ 0.29, i.e. gamma = 2 beta ~ 1.68. The paper's response in item (vi) is to invoke an additional Fermi-liquid-like inelastic channel with undetermined coefficients and to note that the two forms are 'hard to distinguish'. This means the claimed one-to-one relation between the measured self-energy exponent and the nonlocality parameter alpha breaks down in exactly the overdoped regime where quasiparticles are most coherent and ARPES is most reliable. The abstract's assertion that the model 'naturally captures the optimally doped to overdoped regimes' and that spectroscopy-fitted exponents 'directly probe the charged fluid's effective spatial nonlocality' is therefore not supported across the full stated doping range; the continuous rise of gamma beyond 1.5 is not a prediction of the model but an externally added correction.","agreement_with_reader":"partial"},"referee_report":{"model":"deepseek-v4-flash","summary":"This paper proposes that the continuously doping-dependent scale-covariant self-energy observed in nodal ARPES measurements of high-Tc cuprates can be explained by poorly screened, long-ranged effective repulsions V_alpha(r)=g_alpha/|r|^alpha. The author constructs a hydrodynamic screening model in which a diffusive irreducible polarization is combined with the nonlocal interaction via RPA, obtaining a superdiffusive pole omega=-i D_alpha |q|^alpha for alpha<2. Within G0W and after small-angle and tangential-momentum approximations, the inelastic quasiparticle decay rate takes the scale-covariant form Gamma_inel ~ A_gamma T^gamma Phi_gamma(omega/T) with gamma=2-1/alpha for 1<alpha<2, recovering a Marginal Fermi liquid as alpha->1 and diffusive gamma=1.5 for alpha>2. The paper interprets ARPES exponents as direct measures of the effective spatial nonlocality and argues that quantum criticality is not necessary. The underdoped regime is explicitly left beyond the calculation.","tokens_in":11620,"tokens_out":10775,"duration_ms":108779,"significance":"If the central mapping holds, the paper would provide a simple, quantum-criticality-free route to strange-metal scale covariance and would turn ARPES self-energy exponents into a measure of the spatial range of effective interactions. The derivation from Eq. (5) to Eq. (6) is internally coherent, and the End Matter supplies a complete Fermi golden rule account of the four emission/absorption processes and an exact evaluation of the tangential momentum integral. The marginal-Fermi-liquid limit is a useful check. However, the model's predictive content is weakened by the fact that alpha(p) is a free parameter inferred from the same ARPES data, and by the need for an additional, undetermined inelastic channel to reach the experimentally observed gamma~1.68. These issues limit the strength of the claims as currently stated.","major_comments":[{"comment":"For 1<alpha<2, Eq. (6) predicts gamma in (1,1.5); for alpha>2 the text fixes gamma=1.5. No admissible alpha produces gamma>1.5. The ARPES data of Ref. [17] that the paper claims to capture include gamma=2 beta ~1.68 at p~0.29. The response in item (vi) introduces an extra Fermi-liquid-like inelastic channel with undetermined coefficients and notes that the two forms are hard to distinguish. This is an external correction, not a prediction of the model, and it breaks the claimed one-to-one relation between the measured self-energy exponent and the nonlocality parameter alpha exactly in the overdoped regime emphasized in the abstract. The abstract's statement that the model 'naturally captures the optimally doped to overdoped regimes' is therefore not supported for the full stated doping range.","section":"Main Text, Eq. (6) and item (vi)"},{"comment":"The paper explicitly states that it will not deduce from microscopics how alpha varies with doping, but will constrain alpha(p) from ARPES data. Since Eq. (6) is then inverted to read alpha from the same exponents that the model is said to 'capture', the comparison is partly a restatement of the input rather than an independent test. The mapping gamma=2-1/alpha is derived, not fitted, but the predictive content of the paper would be substantially strengthened by an independent constraint on alpha(p), for example from transport or from a microscopic calculation of the screened interaction.","section":"Setup"},{"comment":"The abstract presents 1<=alpha<=3 as a continuous interpolation between Mott insulating and Fermi liquid limits, but the calculated observable does not realize this interpolation: the formula gamma=2-1/alpha is derived only for 1<alpha<2, alpha>2 gives a fixed gamma=1.5, and alpha<1 is explicitly left untreated. The paper should state precisely which observable interpolates with alpha and should reconcile the abstract and Fig. 1 (whose caption restricts the captured regime to 1<=alpha<=2) with the body.","section":"Abstract and Fig. 1"},{"comment":"The entire scaling result rests on the postulate that the effective interaction is an exact power law V_alpha(r)=g_alpha/|r|^alpha over the mesoscopic range relevant to hydrodynamics. This is acknowledged as a postulate, but no microscopic estimate or experimental diagnostic for the power-law form is provided. Because the superdiffusive pole and therefore Eq. (6) fail if the interaction is not a clean 1/r^alpha over the relevant range, this assumption is load-bearing; the manuscript should either justify it from a microscopic model or identify an observable that can falsify it independently of the self-energy exponent.","section":"Screening, nonlocality and hydrodynamics"}],"minor_comments":[{"comment":"Reference [23] contains a malformed DOI and reference [24] is a private communication; please update or replace them with published sources.","section":"References"},{"comment":"Figure 1 caption states 'locality exponent 1≤alpha≤2' while the abstract and text allow 1≤alpha≤3; please reconcile the ranges.","section":"Fig. 1"},{"comment":"After Eq. (6), the phrase 'for γ, α > 1' should read 'for α > 1' because gamma=2-1/alpha is determined by alpha.","section":"Eq. (6)"},{"comment":"In Eq. (1), the parameter C comparing the relative strengths of omega and T is not related to the scaling function Phi_gamma in Eq. (6); please define the connection.","section":"Eq. (1)"},{"comment":"In item (vi), the proposed form 'Γ∼µ(ω^{3/4}+T^{3/4})^2 + λ(ω^2+T^2)' uses ambiguous notation (µ vs. μ, and the exponent structure of the first term); please clarify.","section":"Item (vi)"},{"comment":"The End Matter would benefit from a short derivation of F_alpha(0)=π/(alpha sin(π/2alpha)) rather than quoting it.","section":"End Matter"}],"recommendation":"major_revision","confidential_remarks":"The manuscript is a single-author phenomenological proposal. The central derivation is sound and the paper is honest about several limitations, but the abstract overstates empirical coverage and the free parameter alpha makes the central claim hard to falsify. I would ask for a revision that tempers the abstract, makes the status of the overdoped correction explicit, and adds at least one independent constraint on alpha(p). The malformed DOI and the private-communication reference should be cleaned up."},"author_rebuttal":null,"desk_editor":{"model":"deepseek-v4-flash","letter":"Read this one. It has a clean formal core: for an effective repulsion V(r) ~ 1/r^alpha and a hydrodynamically screened interaction, the G0W self-energy gives a scale-covariant decay rate with gamma = 2 - 1/alpha for 1 < alpha < 2. That formula is new to me, and it gives a concrete physical meaning to the continuously varying ARPES exponent: it becomes a direct measure of spatial nonlocality. The derivation from the integral to the scaling form is coherent, and the End Matter correctly fills in the Fermi golden rule processes and the exact q_parallel integral. The author is also honest about what is not done: alpha(p) is not derived from microscopics, and the underdoped regime is explicitly beyond the calculation. That honesty is real and should be credited.\n\nThe soft spots are mostly where the paper admits them. The model produces gamma in (1, 1.5) for nonlocal screening, and gamma = 1.5 once diffusive hydrodynamics is restored for alpha > 2. But the highest-overdoped ARPES point is fitted with gamma ~ 1.68. The paper's response is to add a separate Fermi-liquid-like inelastic channel with undetermined coefficients, saying the two forms are hard to distinguish. That means the claimed one-to-one relation between the measured exponent and alpha does not hold in exactly the overdoped regime where ARPES is most reliable. The abstract's statement that the model 'naturally captures' the overdoped regime overstates this; the continuous rise of gamma beyond 1.5 is an add-on, not a prediction. The other soft spot is the circularity: alpha(p) is constrained from the same ARPES data whose exponents the theory explains. The relation is derived, not fitted, so this is partly a consistency check rather than a prediction. An independent measurement of alpha, or a quantitative fit of the scaling function Phi(omega/T), would strengthen it a lot.\n\nThese are real but not fatal. The central derivation is internally coherent given the assumptions, and the heuristics (diffusive irreducible polarization, superdiffusive pole) are flagged as such in the text. The paper is a serious phenomenological proposal, not a fitting exercise.\n\nWho should read it: condensed matter theorists working on strange metals and high-Tc phenomenology. I would bring it to reading group. I'd send it to a serious referee; the referee should push hard on the overdoped tail and on the status of alpha(p), but the paper deserves referee time.","headline":"Genuinely new relation gamma = 2 - 1/alpha with an honest limitations section, but the model cannot reach the observed gamma > 1.5 without an extra fitted channel, and alpha(p) is read off from the same data it explains.","tokens_in":12170,"tokens_out":4800,"would_cite":true,"duration_ms":43833,"reading_group":"yes","serious_thinker":"yes","would_accept_peer_review":true},"rs_alignment":null,"lean_confirmation":null,"pith_extraction":{"msc":[],"pacs":[],"model":"deepseek-v4-flash","headline":"Strange-metal scaling laws can come from nonlocal repulsions, not from a quantum critical point.","keywords":["strange metal","high-Tc superconductivity","nonlocal interactions","hydrodynamic screening","scale covariance","self-energy exponent","ARPES","marginal Fermi liquid"],"falsifier":"Measure the frequency- and momentum-resolved charge response in the strange-metal regime and look for the predicted superdiffusive pole $\\omega=-iD_\\alpha|q|^\\alpha$ at intermediate $q$ and $\\omega$; if the dissipative spectrum does not peak along such a pole, the mechanism fails. Alternatively, independently determine $\\alpha(p)$ from the real-space interaction (e.g. via the momentum dependence of the static susceptibility) and check whether the ARPES exponent satisfies $\\gamma=2-1/\\alpha$ across doping.","tokens_in":11058,"feed_emoji":"⚛️","tokens_out":10930,"duration_ms":100305,"temperature":0.7,"pith_summary":"High-temperature superconducting cuprates show a nodal ARPES self-energy that obeys a power law in frequency and temperature with an exponent that drifts continuously with doping. This paper proposes that the exponent is a direct measure of spatial nonlocality: poorly screened repulsive interactions of the form $V_\\alpha(r) = g_\\alpha/|r|^\\alpha$, with a doping-dependent $\\alpha$ between 1 and 3, interpolate between Mott-insulating and Fermi-liquid limits. Combining that interaction with hydrodynamic screening of charge fluctuations yields a scale-covariant inelastic decay rate $\\Gamma(\\omega,T)\\propto T^\\gamma\\,\\Phi(\\omega/T)$ with $\\gamma = 2 - 1/\\alpha$ for $1<\\alpha<2$. If the proposal is right, the exponents fitted by spectroscopy are measurements of the effective interaction range, and scale-covariant strange-metal behavior does not require a quantum critical point. The same mechanism also distinguishes the underdoped regime as qualitatively different, outside the derivation.","feed_headline":"Nonlocal forces explain the strange metal's doping-dependent scaling","feed_subtitle":"It ties ARPES exponents to how far the repulsive interaction reaches, with no quantum critical point required.","key_machinery":"The load-bearing object is the dynamically screened interaction $W^R(q,\\omega)$ (Eqn. 2), obtained by combining the bare power-law interaction $V_\\alpha(q)\\sim 1/|q|^{2-\\alpha}$ with a diffusive irreducible polarization $\\Pi_{\\mathrm{irr}}(q,\\omega)=\\chi D q^2/(D q^2-i\\omega)$. For $\\alpha<2$ its dissipative part peaks at the superdiffusive hydrodynamic pole $\\omega=-iD_\\alpha|q|^\\alpha$, and the self-energy is evaluated in a $G_0W$ approximation with two simplifying approximations: small-angle scattering ($q\\ll k_F$, linearized fermion dispersion) and tangential-momentum dominance ($|q|\\approx q_\\parallel$). This machinery converts the interaction's spatial power law into the scaling exponent $\\gamma=2-1/\\alpha$ of the decay rate.","core_discovery":"The paper's central claim is that the continuously doping-dependent power-law self-energy observed at the node of high-$T_c$ cuprates is not a quantum-critical signature but a hydrodynamic consequence of poorly screened, spatially nonlocal repulsions. Its central result, Eqn. 6, gives $\\Gamma_{\\mathrm{inel}}(k_F,\\omega,T)\\approx A_\\gamma T^\\gamma \\Phi_\\gamma(\\omega/T)$ with $\\gamma=2-1/\\alpha$, obtained from the dynamically screened interaction $W(q,\\omega)$ whose superdiffusive pole follows from the $1/r^\\alpha$ interaction. The derivation uses a diffusive irreducible polarization in the RPA combination $W^{-1}=V^{-1}+\\Pi_{\\mathrm{irr}}$; for $\\alpha<2$ the characteristic momentum at energy transfer $\\Omega$ scales as $q_\\Omega\\sim(\\Omega/D_\\alpha)^{1/\\alpha}$, making tangential scattering dominate and producing scale covariance. The paper identifies the optimal-doping marginal Fermi liquid with $\\alpha\\to 1^+$ ($\\gamma\\to 1^+$), and increasing doping with larger $\\alpha$ and larger fitted $\\gamma$, up to the diffusive value $\\gamma=1.5$ for $\\alpha>2$.","pith_inferences":["A natural next step the paper leaves implicit is to extract $\\alpha(p)$ from independent measurements, such as momentum-resolved electron energy loss or tunneling spectra, and test the predicted $\\gamma(p)$ relation.","The predicted superdiffusive pole $\\omega=-iD_\\alpha|q|^\\alpha$ could be tested directly in quantum simulators with tunable long-range interactions, where the spatial exponent can be varied continuously.","The sharp prediction of a fixed $\\gamma=1.5$ for $\\alpha>2$ gives a threshold: if overdoped samples show fitted exponents passing through 1.5 in a way that tracks screening, that would cleanly distinguish nonlocal hydrodynamic scattering from competing Fermi-liquid-like contributions."],"forward_implications":["Fitted nodal self-energy exponents become direct measurements of the effective interaction exponent $\\alpha$ via $\\gamma=2-1/\\alpha$, turning ARPES into a probe of spatial nonlocality.","Scale-covariant strange-metal behavior can arise without a quantum critical point; spatial nonlocality is a sufficient organizing principle.","Around optimal doping the theory reduces to a marginal Fermi liquid ($\\gamma=1$), and the quasiparticle residue vanishes logarithmically as $\\alpha\\to 1^+$.","If transport lifetime is proportional to inelastic lifetime, in-plane resistivity scales as $T^\\gamma$ with doping-dependent $\\gamma$, matching the reported resistivity exponents within the superconducting dome.","The superconducting state restores local screening, so the abrupt nonlocal-to-local transition in the normal state has no counterpart deep in the superconducting phase."],"supporting_citations":[{"why":"Supplies the newer ARPES fits with a drifting exponent extending to the very overdoped regime; the paper compares its predicted $\\gamma$ to these fits.","marker":"[17]"},{"why":"Supplies the empirical nodal power-law self-energy form with continuously doping-dependent exponent; the paper identifies $\\gamma=2\\beta$ and matches its scale-covariant decay rate to it.","marker":"[18]"},{"why":"Supplies antinodal ARPES data showing abrupt re-emergence of quasiparticles above a critical doping and no abrupt transition in the superconducting state; the paper interprets these as screening and nonlocality dichotomies.","marker":"[15]"},{"why":"Defines the marginal Fermi liquid self-energy that the theory recovers at $\\alpha=1$, $\\gamma=1$, providing the reference phenomenology for the optimal-doping limit.","marker":"[26]"},{"why":"Provide in-plane resistivity scaling measurements across doping inside the superconducting dome, used under the assumption that $\\rho\\propto\\Gamma_{\\mathrm{inel}}$ to identify corresponding $\\alpha$ values.","marker":"[16, 20]"},{"why":"Provides analytical evidence that two-dimensional charged fluids show superdiffusive (non-diffusive) hydrodynamics for $\\alpha<2$, supporting the pole $\\omega=-iD_\\alpha|q|^\\alpha$ assumed for the screened interaction.","marker":"[25]"}],"fun_headline_variants":["Scale covariance from nonlocal repulsion, no quantum criticality","Hydrodynamic screening yields scale-covariant decay in cuprates","Nonlocal repulsion sets strange metal exponent gamma=2-1/alpha","Strange metal scaling without quantum critical point","Cuprate strange metal: doping-tuned exponent from 1/r^alpha forces"],"cache_read_input_tokens":3200,"weakest_assumption_plain":"The argument collapses if, over the relevant mesoscopic range, the true effective interaction between charge carriers is not a clean power law $V(r)\\sim 1/r^\\alpha$ (or if the irreducible polarization is not diffusive), because then the screened interaction lacks the superdiffusive pole from which $\\gamma=2-1/\\alpha$ is derived.","fun_headline_variants_meta":{"raw":{"variants":["Scale covariance from nonlocal repulsion, no quantum criticality","Hydrodynamic screening yields scale-covariant decay in cuprates","Nonlocal repulsion sets strange metal exponent gamma=2-1/alpha","Strange metal scaling without quantum critical point","Cuprate strange metal: doping-tuned exponent from 1/r^alpha forces"]},"model":"deepseek-v4-flash","effort":"low","cost_usd":0.000983,"raw_usage":{"total_tokens":4194,"prompt_tokens":993,"completion_tokens":3201,"prompt_tokens_details":{"cached_tokens":384},"prompt_cache_hit_tokens":384,"prompt_cache_miss_tokens":609,"completion_tokens_details":{"reasoning_tokens":3110}},"tokens_in":609,"tokens_out":3201,"duration_ms":22083,"temperature":1.0,"reasoning_tokens":3110,"cache_read_input_tokens":384,"cache_creation_input_tokens":0},"cache_creation_input_tokens":0},"created_at":"2026-08-08T04:16:06.527002+00:00","model_set":{"reader":"deepseek-v4-flash"},"falsifier":"Measure the frequency- and momentum-resolved charge response in the strange-metal regime and look for the predicted superdiffusive pole $\\omega=-iD_\\alpha|q|^\\alpha$ at intermediate $q$ and $\\omega$; if the dissipative spectrum does not peak along such a pole, the mechanism fails. Alternatively, independently determine $\\alpha(p)$ from the real-space interaction (e.g. via the momentum dependence of the static susceptibility) and check whether the ARPES exponent satisfies $\\gamma=2-1/\\alpha$ across doping.","supporting_citations":[{"cited_title":null,"cited_arxiv_id":null,"evidence_quote":"Supplies the newer ARPES fits with a drifting exponent extending to the very overdoped regime; the paper compares its predicted $\\gamma$ to these fits."},{"cited_title":"Power Law Liquid - A Unified Form of Low-Energy Nodal Electronic Interactions in Hole Doped Cuprate Superconductors","cited_arxiv_id":"1509.01611","evidence_quote":"Supplies the empirical nodal power-law self-energy form with continuously doping-dependent exponent; the paper identifies $\\gamma=2\\beta$ and matches its scale-covariant decay rate to it."},{"cited_title":null,"cited_arxiv_id":null,"evidence_quote":"Supplies antinodal ARPES data showing abrupt re-emergence of quasiparticles above a critical doping and no abrupt transition in the superconducting state; the paper interprets these as screening and nonlocality dichotomies."},{"cited_title":null,"cited_arxiv_id":null,"evidence_quote":"Defines the marginal Fermi liquid self-energy that the theory recovers at $\\alpha=1$, $\\gamma=1$, providing the reference phenomenology for the optimal-doping limit."}],"review_version":1}