{"id":"68c27644-1a44-478b-b291-8253e899554a","arxiv_id":"2505.03958","paper_version":2,"verdict":"CONDITIONAL","confidence":"MODERATE","novelty_score":7.0,"correctness_risk":"medium","formal_verification":"none","parameter_count":6,"one_line_summary":"A first DFT+DMFT calculation of electron-phonon coupling finds that correlations strongly enhance a Jahn-Teller mode coupling in SrVO3, slightly suppress a breathing mode, and introduce strong electron-frequency dependence in both materials.","lead":"This paper calculates how strong electron correlations change electron-phonon coupling in two real metals, SrVO3 and CaCuO2, using a new DFT+DMFT finite-difference approach. The results show mode-specific effects and a strong dependence on electron energy, which matters for transport and phonon lifetimes in correlated materials.","discovery_kind":"new_method","skeptic_critique":{"model":"deepseek-v4-flash","headline":"The headline frequency dependence rests on Padé continuation of a small, noisy Matsubara self-energy difference; no independent continuation or alpha-convergence check is shown.","rationale":"I read the paper in good faith: the working formula from the Dyson equation, the finite-difference DFT+DMFT workflow, and the comparison to DFPT+U are all plausibly correct, and the mode-specific trends in SVO and CCO are physically sensible. The algebra from Eq. 1 through Eq. 6 is sound, and the paper is candid about its approximations, including the neglect of phonon-induced changes to U and J and the lack of charge self-consistency. However, the quantitative claim that correlations induce a strong, U- and doping-dependent frequency dependence in the EPC is the main novel result and the basis for the conclusion that static methods miss important physics. That result is produced by Padé continuation of a small difference between two independently noisy CT-HYB self-energies. This is precisely the reader's weakest assumption, and it is load-bearing because the frequency dependence is not a side detail but the headline. The lack of error bars and the absence of any cross-check with a second continuation method mean that the reported g(ω) curves could in principle reflect numerical noise or Padé artifacts. The α = 1/2 finite-difference scale is a related concern, but the Padé issue is the sharper one because it directly affects the frequency-dependent shape that the paper emphasizes. Since the reader already flagged this issue and assigned a conditional verdict, the appropriate outcome is unchanged: the paper should be accepted only after the continuation and finite-difference convergence are demonstrated.","tokens_in":23148,"tokens_out":5066,"duration_ms":56193,"concrete_test":"Recompute one headline case, e.g., CCO at U = 4.7 eV and 0.15 hole doping for the X-point mode, using the raw Matsubara-axis data: form g(iω_n) by applying Eq. 6 to the finite-difference δΣ(iω_n) before any continuation, then compare it with the Padé-continued g(ω) evaluated at the same Matsubara points, and also with a second continuation method such as maximum entropy or Nevanlinna. If the Padé-based g(ω) fails to reproduce the direct Matsubara g(iω_n) within Monte Carlo error, or if the alternative continuation differs from the Padé curve by more than roughly 20% in the ±0.2 eV window, the reported frequency dependence is not established.","verdict_should_be":"UNCHANGED","load_bearing_attack":"The central new claim is the strong, U- and doping-dependent frequency dependence of the EPC (Figs. 2 and 5). This quantity is computed from Eq. 6 as a finite difference of two DMFT self-energies on the Matsubara axis and then continued to real frequencies with Padé (Sec. II.D). The signal entering the continuation, δΣ(iω_n) = Σ_ph − Σ_cn, is a small difference between two independent CT-HYB runs, and Padé continuation of noisy Matsubara data is known to generate spurious low-frequency structure. The paper reports no Monte Carlo error bars, no comparison with an independent continuation method, and only cites preliminary data from real frequency solvers to be published elsewhere (Sec. V) as confirmation of a model, not of the actual g(ω). Because the frequency dependence is used to conclude that static +U and hybrid methods are inadequate, this is the load-bearing step. A secondary issue in the same numerical machinery is that α = 1/2 is used without a linear-response convergence check; if the O(α) response is nonlinear, the derivative itself is biased in addition to any continuation error.","agreement_with_reader":"agree"},"referee_report":{"model":"deepseek-v4-flash","summary":"The paper defines a many-body electron-phonon coupling as the phonon-induced change of V_KS + Σ(ω), evaluates it with finite-difference DFT+DMFT calculations on supercells, and applies the method to two phonon modes in SrVO3 (M-point Jahn-Teller and R-point breathing) and two breathing modes in CaCuO2 (X-point half-breathing and M-point full-breathing). The central results are mode-specific correlation renormalizations at ω=0 (in SrVO3, 44→87 meV for the M mode and 58→50 meV for the R mode) and, most prominently, a strong frequency dependence of the coupling that grows with U in CaCuO2 and changes sign with doping, together with corresponding modifications to electron scattering rates and phonon linewidths.","tokens_in":23402,"tokens_out":5634,"duration_ms":53640,"significance":"If validated, this work would provide the first direct DFT+DMFT calculation of electron-phonon coupling in realistic materials, with a clean conceptual definition that reduces to standard DFPT when the self-energy vanishes. The mode-specific comparison between orbital-splitting and charge-coupling phonons, and the prediction of a strong dynamical frequency dependence with consequences for transport and phonon lifetimes, are of genuine interest and are stated in a falsifiable way. The paper also gives explicit formulae for electron and phonon self-energies, and it openly identifies several approximations. However, the numerical machinery that produces the central frequency-dependent results is not validated to the standard needed for the paper's main conclusion, so the significance is currently conditional on additional convergence and continuation checks.","major_comments":[{"comment":"The real-frequency EPC g(ω) is obtained by Padé analytic continuation of a small difference between two independent CTHYB self-energies, δΣ(iω_n) = Σ_ph − Σ_cn, and the manuscript reports no Monte Carlo error bars, no consistency check against an independent continuation method, and no direct comparison with a real-frequency solver for the actual g(ω). Because the paper's central claim—a strong, U- and doping-dependent frequency dependence of the coupling—rests entirely on this continuation, this issue is load-bearing. Please quantify the noise on δΣ, show that the Padé result is stable with respect to the number of Matsubara frequencies and to alternative continuation schemes, or clearly restrict the quantitative claims to ω=0 and label the frequency dependence as provisional.","section":"Sec. II.D and Figs. 2, 5"},{"comment":"The finite-difference derivative in Eq. (6) is evaluated with a single perturbation scale α=1/2 for all modes, and the manuscript does not provide a linear-response convergence check. If δΣ(α) is not linear at α=1/2, then the derivative itself is biased in addition to any continuation error. Please show results for at least two additional values of α, or provide a quantitative argument (e.g., from the size of the phonon displacement and the smoothness of the self-energy) that α=1/2 lies in the linear regime.","section":"Sec. II.B and Eq. (6)"},{"comment":"The interpretive model with parameters A, ω0, and dA is fitted to Matsubara-axis data and is said to be \"conceptually confirmed by preliminary data from real frequency solvers to be published elsewhere.\" An unpublished, inaccessible result cannot serve as validation of the actual g(ω) used in the paper, and the model fit does not by itself establish the reliability of the Padé-continued difference δΣ. Please either include the real-frequency solver data, cite a published source, or explicitly label the model as an illustrative interpretation rather than a numerical validation.","section":"Sec. V, Eq. (11)"}],"minor_comments":[{"comment":"The caption contains a duplicated phrase: \"studied are indicated are indicated\" should be \"studied are indicated.\"","section":"Fig. 1 caption"},{"comment":"The Introduction contains the typo \"DFMT calculations\" where \"DFT+DMFT calculations\" is intended.","section":"Sec. I"},{"comment":"The Conclusion contains a duplicated word: \"which competes with with correlation\" should be \"which competes with correlation.\"","section":"Sec. VII"},{"comment":"Reference [38] misspells \"Jahn-Teller\" as \"Janh-Teller.\"","section":"Reference [38]"},{"comment":"The symbol α is described as the ratio of effective atomic displacements to phonon eigen-displacements in Sec. II.B but as a \"scale factor\" in Sec. II.D; please use consistent terminology.","section":"Secs. II.B and II.D"},{"comment":"The manuscript would benefit from a data availability statement specifying input files and analysis scripts, since no repository or code release is mentioned.","section":"General"}],"recommendation":"major_revision","confidential_remarks":"For the editor: I see no evidence of circularity in the main calculation—U and J are taken from prior literature and the EPC is computed from the response of the DMFT self-energy, not fitted to the claimed results. The decisive issue is numerical validation of the frequency-dependent g(ω). If the authors can supply α-convergence tests and error-controlled continuation checks, the paper would be suitable for publication; without those, the central frequency-dependence claim is not yet supported. I also note that the manuscript relies on an unpublished real-frequency solver result; this should be replaced with published or included data before acceptance."},"author_rebuttal":null,"desk_editor":{"model":"deepseek-v4-flash","letter":"Dear colleague,\n\nThis is the first paper I've seen that computes direct electron-phonon matrix elements from DFT+DMFT rather than proxies like spectral shifts or total energies. The working definition — g = <phi|∂(V_KS + Σ(ω))|phi> — is the right generalization, and the derivation from the Dyson equation is sound; you get DFPT back when Σ = 0. The finite-difference workflow, using DFPT displacements and Wannier-projected perturbed/unperturbed DMFT self-energies, is a natural way to do it. They are also candid about double counting, the fixed Wannier basis, and neglect of U(J) changes under distortion, and they compare sensibly against DFPT+U.\n\nThe results are physically plausible: in SrVO3, the Jahn-Teller M-point coupling nearly doubles (44 to 87 meV) while the R-point breathing mode decreases slightly (58 to 50 meV); in CaCuO2, the omega = 0 couplings change modestly but the frequency dependence is strong and grows with U. The scattering rates and phonon linewidths follow from the couplings.\n\nWhere I'd pump the brakes is the frequency dependence — the paper's headline. It is obtained by Padé continuation of δΣ(iω_n) = Σ_ph − Σ_cn, a small difference between two independent CT-HYB runs. That is exactly the situation where Padé is known to produce spurious low-frequency structure. There are no Monte Carlo error bars, no independent continuation (e.g., maximum entropy), and no check that the result is stable to the number of Matsubara points. The finite-difference step uses a single alpha = 1/2 with no linearity check, so the derivative itself could be biased. The omega = 0 numbers are less vulnerable because they sit at the Matsubara low-frequency end, but the \"inadequacy of static theories\" claim leans on the omega-dependent curves, and those curves are not yet demonstrated to be numerical fact. The mention of preliminary real-frequency solver data, to be published elsewhere, confirms a model rather than their actual g(ω).\n\nThis is an addressable problem: run a second continuation method, show the noise floor on δΣ, and test alpha = 0.25/0.5/1.0. Until then, I'd treat the quantitative frequency dependence as provisional while crediting the method and the zero-frequency trends.\n\nWho is this for? People working on e-ph in correlated materials, and method developers in DFT+DMFT. It deserves refereeing — the method is important enough that the community needs to see it scrutinized, and the authors are honest about their approximations. My recommendation: send it to review, with the numerical machinery as the central point to check. I'd also put it on the reading group list for the method alone.","headline":"First direct DFT+DMFT electron-phonon matrix elements, with a clean definition — but the headline frequency dependence rests on Padé continuation of noisy self-energy differences, so treat the omega-dependent curves as provisional.","tokens_in":23980,"tokens_out":2072,"would_cite":true,"duration_ms":19812,"reading_group":"yes","serious_thinker":"yes","would_accept_peer_review":true},"rs_alignment":null,"lean_confirmation":null,"pith_extraction":{"msc":[],"pacs":["71.38.-k","71.27.+a"],"model":"deepseek-v4-flash","headline":"The paper defines electron-phonon coupling beyond DFT as the phonon derivative of the Kohn-Sham potential plus the DMFT self-energy, and shows that in SrVO3 correlation nearly doubles a Jahn-Teller coupling while in CaCuO2 it creates a…","keywords":["electron-phonon coupling","dynamical mean-field theory","DFT+DMFT","frequency-dependent coupling","SrVO3","CaCuO2","Jahn-Teller phonon","phonon linewidth"],"falsifier":"Repeat the finite-difference DFT+DMFT calculation for the CaCuO2 M-mode with $\\alpha$ reduced to 1/4 and 1/8, and substitute a real-frequency impurity solver (or a second analytic-continuation scheme) for the Padé step; if $g(\\omega=0)$ or the sign and slope of the frequency dependence near the Fermi level change substantially, the claimed dynamical renormalization is an artifact of the numerical continuation.","tokens_in":22911,"feed_emoji":"⚛️","tokens_out":7457,"duration_ms":69391,"temperature":0.7,"pith_summary":"This paper establishes a practical definition of electron-phonon coupling for strongly correlated metals, going beyond density functional theory by treating the coupling as the phonon derivative of the Kohn-Sham potential plus the dynamical mean-field self-energy. It claims that this quantity can be computed by finite-difference DFT+DMFT, and applies the method to two materials. In SrVO3, local correlation nearly doubles the Wannier-local coupling of an M-point Jahn-Teller mode (44 meV in DFT to 87 meV at $\\omega=0$ in DFT+DMFT) while slightly reducing the R-point breathing mode (58 to 50 meV). In CaCuO2 the zero-frequency couplings change only moderately, but the frequency dependence is strong, grows with $U$, and changes sign with doping. The paper's conclusion is that static correlation corrections such as DFT+U and hybrid functionals miss a genuinely dynamical piece of electron-phonon physics.","feed_headline":"Correlations nearly double a phonon coupling in SrVO3","feed_subtitle":"Frequency-dependent DFT+DMFT shows static corrections miss electron-phonon physics in correlated metals.","key_machinery":"The central object is the frequency-dependent many-body coupling $g(\\omega)$, defined as the phonon derivative of $\\hat V_{\\mathrm{KS}}+\\hat\\Sigma(\\omega)$ projected onto Kohn-Sham states. The machinery that carries the argument is a finite-difference DFT+DMFT workflow: a supercell is distorted along a DFPT phonon eigenvector by a scale $\\alpha=1/2$, the impurity self-energies on the inequivalent sites are recomputed, and the difference $\\hat\\Sigma_{\\mathrm{ph}}-\\hat\\Sigma_{\\mathrm{cn}}$ is upfolded to the band basis and added to the DFPT Kohn-Sham derivative. The frequency dependence of the self-energy difference, converted to real frequencies by analytic continuation, is what produces the claimed dynamical renormalization of the coupling.","core_discovery":"The central claim is that the many-body electron-phonon coupling defined as $g_{mn\\nu}^{\\mathbf{k}\\mathbf{q}}(\\omega)=\\langle\\phi_{m\\mathbf{k}+\\mathbf{q}}|\\partial_{\\nu\\mathbf{q}}[\\hat V_{\\mathrm{KS}}+\\hat\\Sigma(\\omega)]|\\phi_{n\\mathbf{k}}\\rangle$ can be evaluated from first principles by subtracting DFT+DMFT self-energies on phonon-perturbed and unperturbed supercells and upfolding the difference into the band basis. In SrVO3 the local coupling of the M-point Jahn-Teller mode rises from 44 meV in DFT to 87 meV at $\\omega=0$ in DFT+DMFT, while the R-point breathing coupling drops from 58 to 50 meV. In CaCuO2 the zero-frequency couplings of the X half-breathing and M full-breathing modes are moderately changed, but the frequency dependence becomes very strong, with the coupling at $U=4.7$ eV varying from near zero to roughly twice the zero-frequency value within about one phonon energy. The paper additionally computes electron scattering rates and phonon linewidths from these couplings and finds both correspondingly modified.","pith_inferences":["Inference: If the frequency dependence survives more detailed checks, a systematic comparison of these finite-difference DFT+DMFT couplings with Hubbard-Holstein model results at matched parameters could separate the local vertex contribution from the nonlocal hybridization response.","Inference: The particle-hole asymmetric scattering implied by the frequency-dependent coupling in hole-doped CaCuO2 offers a phonon-based explanation of the measured positive Seebeck coefficient in hole-doped cuprates, a connection the paper raises but does not establish.","Inference: Phonon linewidth measurements across a series of cuprates with varying correlation strength could directly test the predicted opposite $U$ trends of the half-breathing and full-breathing modes, since the two should respond oppositely as the Mott transition is approached."],"forward_implications":["In SrVO3, the mode-specific renormalization means that orbital-splitting Jahn-Teller phonons scatter electrons more strongly than DFT predicts, while charge-coupled breathing phonons scatter them slightly less.","The frequency-dependent couplings make electron scattering rates particle-hole asymmetric near the Fermi energy, a feature that can show up in thermoelectric transport of correlated metals.","In CaCuO2, the strong variation of $g(\\omega)$ on the scale of the phonon energy at larger $U$ indicates that static-phonon approximations may be insufficient for phonon lifetimes and for estimates of phonon-mediated superconductivity.","The computed linewidths respond oppositely to correlation for the two CCO modes: stronger $U$ suppresses the M full-breathing linewidth and enhances the X half-breathing linewidth."],"supporting_citations":[{"why":"It supplies the baseline DFT/DFPT treatment of SrVO3 and the Fermi-surface EPC reference that the DFT+DMFT comparison extends.","marker":"[12]"},{"why":"It provides the density-functional perturbation theory that yields bare phonon frequencies and Kohn-Sham potential derivatives.","marker":"[47]"},{"why":"It supplies the Wannier-function interpolation and Fourier conventions used to convert DFPT displacements into supercell perturbations.","marker":"[50]"},{"why":"It gives the model-system quantum Monte Carlo result that repulsion suppresses Holstein-type coupling, the comparison used for the CCO breathing modes.","marker":"[32]"},{"why":"It provides the companion Hubbard-Holstein DMFT study used to interpret the correlation dependence of the EPC.","marker":"[42]"},{"why":"It establishes the DFT+DMFT supercell lattice-dynamics procedure that the finite-difference workflow builds on.","marker":"[48]"},{"why":"It motivates direct EPC calculation by showing that DFT+DMFT spectral shifts respond strongly to atomic displacements in FeSe.","marker":"[17]"}],"fun_headline_variants":["DFT+DMFT rewrites electron-phonon coupling in correlated metals","SrVO3 phonon coupling nearly doubles with correlations","Frequency-dependent coupling reshapes electron-phonon theory","Static corrections fail for electron-phonon in correlated metals","Jahn-Teller coupling rises from 44 to 87 meV in SrVO3"],"cache_read_input_tokens":3200,"weakest_assumption_plain":"The real-frequency couplings and their frequency dependence are obtained by analytic continuation of Matsubara self-energy differences, and the finite difference uses a fixed perturbation scale $\\alpha=1/2$; if the continuation distorts the low-frequency structure or the response is not linear in $\\alpha$, the central numbers change.","fun_headline_variants_meta":{"raw":{"variants":["DFT+DMFT rewrites electron-phonon coupling in correlated metals","SrVO3 phonon coupling nearly doubles with correlations","Frequency-dependent coupling reshapes electron-phonon theory","Static corrections fail for electron-phonon in correlated metals","Jahn-Teller coupling rises from 44 to 87 meV in SrVO3"]},"model":"deepseek-v4-flash","effort":"low","cost_usd":0.000596,"raw_usage":{"total_tokens":2868,"prompt_tokens":1103,"completion_tokens":1765,"prompt_tokens_details":{"cached_tokens":384},"prompt_cache_hit_tokens":384,"prompt_cache_miss_tokens":719,"completion_tokens_details":{"reasoning_tokens":1675}},"tokens_in":719,"tokens_out":1765,"duration_ms":13576,"temperature":1.0,"reasoning_tokens":1675,"cache_read_input_tokens":384,"cache_creation_input_tokens":0},"cache_creation_input_tokens":0},"created_at":"2026-08-15T23:41:15.791149+00:00","model_set":{"reader":"deepseek-v4-flash"},"falsifier":"Repeat the finite-difference DFT+DMFT calculation for the CaCuO2 M-mode with $\\alpha$ reduced to 1/4 and 1/8, and substitute a real-frequency impurity solver (or a second analytic-continuation scheme) for the Padé step; if $g(\\omega=0)$ or the sign and slope of the frequency dependence near the Fermi level change substantially, the claimed dynamical renormalization is an artifact of the numerical continuation.","supporting_citations":[{"cited_title":null,"cited_arxiv_id":null,"evidence_quote":"It gives the model-system quantum Monte Carlo result that repulsion suppresses Holstein-type coupling, the comparison used for the CCO breathing modes."},{"cited_title":null,"cited_arxiv_id":null,"evidence_quote":"It establishes the DFT+DMFT supercell lattice-dynamics procedure that the finite-difference workflow builds on."}],"review_version":1}