{"id":"a61e9972-5e68-4043-bd90-1b12209e37ff","arxiv_id":"2511.14614","paper_version":2,"verdict":"CONDITIONAL","confidence":"MODERATE","novelty_score":6.0,"correctness_risk":"medium","formal_verification":"none","parameter_count":0,"one_line_summary":"In the 2D Hubbard model near a van Hove singularity, self-consistent ferromagnetic fluctuations split the spectrum and expand the Fermi surface while preserving its topology, producing non-Fermi-liquid damping.","lead":"Using a computational approach that includes non-local electron correlations, this paper shows that magnetic fluctuations near a van Hove singularity can split the electronic spectrum and enlarge the Fermi surface in a model of correlated electrons. The result offers a mechanism for non-Fermi-liquid behavior in materials like Sr2RuO4 and CrTe2.","discovery_kind":"new_application","skeptic_critique":{"model":"deepseek-v4-flash","headline":"The central spectral splitting and Fermi-surface expansion rest solely on MaxEnt continuation of Matsubara data; without an independent continuation method or uncertainty analysis, the two-band structure could be an artifact.","rationale":"The reader's weakest assumption—that the central spectral splitting and Fermi-surface maps depend on MaxEnt continuation—matches my own assessment. The paper presents an internally coherent comparison between DMFT, D-TRILEX, and DΓA variants, and the qualitative split-band scenario is consistent with earlier weak-coupling analyses. However, the quantitative claims of a band fully above the Fermi level and of Fermi-surface expansion are new and rest entirely on the ill-conditioned inversion of Matsubara data. Without error bars, a second continuation method, or a sensitivity analysis, the central claim is not demonstrated to the standard required for a strong acceptance. The paper's lack of a reproducible code/data artifact compounds this, but the scientific crux is the continuation. The reader's CONDITIONAL verdict is appropriate; no further adjustment is needed, but the conditions should explicitly require a real-frequency validation or uncertainty quantification of the splitting.","tokens_in":13333,"tokens_out":4068,"duration_ms":47374,"concrete_test":"Take the converged D-TRILEX Matsubara Green's functions G(k,iν) for n=0.43, T=0.05 at the X, nodal, and antinodal points and continue them with a second independent method—e.g., stochastic analytic continuation (SAC) or Padé approximants—using the same input noise. Also rerun ana_cont with different default models (flat, Gaussian, two-peak) and with artificially increased QMC noise. If the two-peak structure is not reproduced by SAC/Padé, or if the upper peak drops below the Fermi level under a plausible default model, then the splitting and FS expansion are not numerically robust.","verdict_should_be":"UNCHANGED","load_bearing_attack":"The paper's central observable—the splitting of the spectral function into a lower dispersive band and an upper weakly-dispersive band, with only the lower one crossing the Fermi level—is obtained exclusively by analytically continuing the Matsubara Green's function G(k,iν) with the maximum entropy method (ana_cont package), as stated in Sec. II. All momentum-resolved spectra in Figs. 4–6, including the Fermi-surface maps A(k,0) that yield the claimed expansion, are products of this continuation. MaxEnt is a Bayesian inversion whose output depends on the chosen default model and on the noise statistics of the QMC input; it has no built-in error bars and is known to both over-smooth and, in the presence of noise, produce spurious peak splittings. The paper provides no alternative real-frequency solver (e.g., NRG, ED, or stochastic analytic continuation), no default-model sensitivity analysis, and no synthetic-data tests. The claimed 'Fermi surface expansion' and Luttinger-theorem violation are therefore inferred from a possibly ill-posed inversion rather than from a directly computed quantity. A secondary but related unvalidated step is the polynomial extrapolation of ImΣ(k,iν) to ν=0 used for the quasiparticle damping γ in Figs. 2–3. Since the two-band structure and the Fermi-level crossing of the lower band are the basis of the non-Fermi-liquid and Fermi-surface-expansion claims, the absence of any cross-check of the continuation is the load-bearing weakness.","agreement_with_reader":"agree"},"referee_report":{"model":"deepseek-v4-flash","summary":"This paper studies the single-band Hubbard model on a square lattice with t'/t=-0.45 near a van Hove singularity, at densities n=0.43–0.52 and temperatures T=0.05–0.1, using DMFT and the D-TRILEX method. The central claim is that self-consistent inclusion of non-local ferromagnetic fluctuations splits the electronic spectral function into a lower dispersive band that crosses the Fermi level and an upper weakly dispersive band that remains above it, so the Fermi surface remains unsplit but expands, with an associated violation of Luttinger's theorem. The authors also report quasiparticle damping γ≈const(T) at the X point, a nodal–antinodal dichotomy opposite to the antiferromagnetic case, and a comparison with DΓA variants that is used to argue that the flat upper band in λ-corrected DΓA is an artifact. A phase diagram for ferromagnetic and incommensurate ordering is presented. The main evidence for the non-Fermi-liquid behavior and Fermi-surface expansion is obtained from MaxEnt analytic continuation of Matsubara Green's functions and from polynomial extrapolation of the imaginary part of the self-energy to zero frequency.","tokens_in":13660,"tokens_out":5151,"duration_ms":54513,"significance":"If the spectral splitting and Fermi-surface expansion are genuine, this is a clear and interesting demonstration that van Hove-driven ferromagnetic fluctuations alone can produce non-Fermi-liquid behavior in a symmetry-unbroken paramagnet, with potential implications for Sr2RuO4 and CrTe2. The paper has several strengths: no parameter is fitted to produce the splitting or the Fermi-surface expansion; the internal comparisons between DMFT, single-shot and self-consistent D-TRILEX, and DΓA variants are coherent and useful; and the phase diagram contextualizes the temperature range. The central quantitative claims, however, rest on two numerical inversions — maximum-entropy analytic continuation for spectra and polynomial extrapolation for γ — neither of which is cross-checked or supplied with error bars. These are load-bearing gaps because the two-band structure and the Fermi-surface maps are read directly from the MaxEnt output.","major_comments":[{"comment":"All momentum-resolved spectral functions A(k,ω) and Fermi-surface maps A(k,0), including the split two-band structure and the Fermi-surface expansion, are obtained from Matsubara data by maximum-entropy continuation using the ana_cont package. MaxEnt is a regularized inversion whose output depends on the default model and on the noise estimate; it is known to be able to produce spurious peak splitting as well as over-smoothing. The manuscript provides no independent real-frequency solver, no default-model sensitivity scan, and no synthetic-data tests. Because the central claim (only the lower band crosses E_F, the upper band stays above E_F, and the Fermi-surface area increases) is read directly from these MaxEnt spectra, this is a load-bearing gap rather than a presentational issue. Please validate the continuation, for example with a second method (Padé, stochastic analytic continuatio","section":"§II; Figs. 4–6"},{"comment":"The quasiparticle damping γ = -ImΣ_{k,ν=0} is obtained by polynomial extrapolation of ImΣ(iν_n) to zero frequency. The manuscript does not state the polynomial order, the number of low-frequency Matsubara points included, the fit range, or the statistical error. The non-Fermi-liquid conclusion — γ≈const(T) at the X point and the opposite temperature trends between the X point and the nodal/antinodal points — is based on these extrapolated values. Please show the raw Matsubara data with the fitted curve, provide error bars, and give an alternative extrapolation (e.g., Padé or a linear fit excluding the first Matsubara point) to demonstrate that the γ(T) trends are not fit artifacts.","section":"§III.B.1; Fig. 2 caption; Fig. 3"},{"comment":"The Fermi-surface expansion and the claimed Luttinger-theorem violation are inferred from the positions and weights of maxima of MaxEnt A(k,0), together with the statement that the upper band lies above E_F. At T=0.05 the spectra are broad, so the 'Fermi surface' is not sharply defined; an apparent expansion can result from the contour or peak-height criterion rather than from a true change in the Luttinger volume. Furthermore, Luttinger's theorem is a zero-temperature statement about the volume enclosed by the zeros of the single-particle Green's function; in a finite-temperature, symmetry-unbroken paramagnet one needs a precise definition (e.g., the Re G=0 locus or the momentum distribution). I ask for a direct quantitative check: compute the occupied density from the interacting Green's function and compare it with the area enclosed by the apparent Fermi surface, and locate any zeros","section":"§III.B.2; Figs. 4, 6; Conclusion"}],"minor_comments":[{"comment":"The caption says n=0.43, 0.46 and 0.53, while the text and Fig. 2 use n=0.43 and 0.52. Please make the notation consistent.","section":"Fig. 3 caption"},{"comment":"The caption says 'n=0.52 (e-f)', but panels (e)–(h) are shown. Correct to (e–h).","section":"Fig. A1 caption"},{"comment":"The Brillouin-zone axes are not clearly labeled. Please add k_x/k_y axes or an explicit Γ–X–M path to make the Fermi-surface maps self-contained.","section":"Fig. 6"},{"comment":"The DΓA labels appear as 'D□A' in the figure. Fix the typography so that Γ is rendered correctly.","section":"Fig. 4"}],"recommendation":"major_revision","confidential_remarks":"The manuscript is likely publishable after the analytic-continuation and extrapolation issues are addressed. The MaxEnt concern is the main risk: a second continuation method or a systematic uncertainty analysis is essential before the non-Fermi-liquid and Fermi-surface-expansion claims can be accepted. The self-citations to D-TRILEX are methodological and appropriate. The paper fits the scope of cond-mat.str-el."},"author_rebuttal":null,"desk_editor":{"model":"deepseek-v4-flash","letter":"Quick take: this is a careful D-TRILEX study of the Hubbard model at van Hove filling with ferromagnetic fluctuations. The new result is concrete: self-consistent non-local self-energy produces a weakly momentum-dependent splitting of the spectral function, only one band crosses the Fermi level, and the Fermi surface expands, with a nodal–antinodal dichotomy opposite to the AFM case. That is worth knowing.\n\nWhat the paper does well: it compares DMFT, D-TRILEX, and DΓA (including λ-corrected and self-consistent variants) coherently, and the internal comparisons support the qualitative claim that non-local correlations, not the local DMFT self-energy, drive the splitting. The phase diagram and self-energy damping analysis are done carefully, with explicit discussion of Mermin–Wagner and crossover temperatures. The authors are also appropriately skeptical of the λ-corrected DΓA flat band, using single-shot comparisons to attribute that feature to the λ-correction. That is honest method comparison.\n\nThe soft spot is exactly where the stress-test points: the central observable—the two-band splitting and the A(k,0) Fermi-surface maps—is entirely produced by maximum-entropy analytic continuation of Matsubara Green's functions. MaxEnt can create spurious splittings and has no built-in error bars, and the paper offers no cross-check from a different continuation scheme, no default-model sensitivity analysis, and no synthetic-data tests. Since the claim that only one band crosses the Fermi level is the whole basis of the Fermi-surface expansion and the Luttinger-violation statement, this is a load-bearing assumption, not a demonstrated fact. The quasiparticle damping γ also comes from polynomial extrapolation of ImΣ to zero frequency, with no error estimate. The method comparison remains informative because all approaches use the same continuation pipeline, so relative differences are likely meaningful, but the absolute statement 'Fermi surface expands and Luttinger is violated' is stronger than the evidence supports.\n\nAlso, no code or data is provided, so the numerics can't be independently checked. That is a practical problem for a result this strong.\n\nWho this is for: people working on D-TRILEX, van Hove physics, and fluctuation-induced non-Fermi-liquid behavior. The qualitative mechanism is plausible and the method comparison is valuable, but the central quantitative claim—especially the Luttinger violation—needs more than one continuation method. Send it to peer review with a request for independent real-frequency validation or at least a synthetic-data test of the MaxEnt peak splitting, plus error bars on γ.","headline":"Plausible D-TRILEX prediction of fluctuation-induced Fermi-surface expansion and spectral splitting in the van Hove Hubbard model, but the two-band structure is only as solid as the MaxEnt continuation that produced it.","tokens_in":14155,"tokens_out":2655,"would_cite":true,"duration_ms":27728,"reading_group":"yes","serious_thinker":"yes","would_accept_peer_review":true},"rs_alignment":null,"lean_confirmation":null,"pith_extraction":{"msc":[],"pacs":["71.10.Hf","71.27.+a","71.10.Fd"],"model":"deepseek-v4-flash","headline":"Self-consistent ferromagnetic fluctuations near a van Hove singularity split the electronic spectrum and expand the Fermi surface without symmetry breaking.","keywords":["Hubbard model","van Hove singularity","ferromagnetic fluctuations","non-Fermi liquid","D-TRILEX","Fermi surface expansion","spectral function splitting","dynamical mean field theory"],"falsifier":"Apply an alternative analytic continuation (e.g., stochastic optimization or Padé) to the D-TRILEX Matsubara self-energy and Green's function at T = 0.05, n = 0.43, k = X = (π,0), and check whether the two-peak structure persists and whether the upper band remains above the Fermi level. A negative answer – or a result from exact diagonalization on a 4×4 cluster at the same parameters showing a single peak – would falsify the claimed splitting and Fermi-surface expansion.","tokens_in":13236,"feed_emoji":"🧲","tokens_out":8459,"duration_ms":76739,"temperature":0.7,"pith_summary":"The paper argues that in the two-dimensional Hubbard model with the Fermi level set near a van Hove singularity and hopping parameters that favour ferromagnetism, self-consistently treated magnetic fluctuations are by themselves sufficient to destroy Fermi-liquid behaviour even though the system never orders. Using the D-TRILEX method, the authors find that the electronic spectral function splits into two bands at low temperature, with only the lower band crossing the Fermi level. The Fermi surface therefore remains a single surface but expands in area, which they read as a compensation for spectral weight displaced into the upper band. They also report a nodal–antinodal dichotomy with the opposite sign to the antiferromagnetic case, and show that self-consistency and the proper vertex treatment are both required to obtain these features. A sympathetic reader would see this as a minimal, symmetry-preserving mechanism for non-Fermi-liquid physics that connects to materials like Sr2RuO4 and CrTe2.","feed_headline":"Van Hove spin fluctuations split bands and expand the Fermi surface","feed_subtitle":"Self-consistent D-TRILEX shows the Fermi surface gaining area without magnetic order, a non-Fermi-liquid sign.","key_machinery":"the D-TRILEX (dual triply irreducible local expansion) method, a diagrammatic extension of dynamical mean field theory. It generates the nonlocal self-energy and the polarization operator from three-leg (triangular) vertex functions of the DMFT impurity problem, and dresses them self-consistently with dual Green's functions and bosonic propagators in the charge and spin channels. The essential role of this machinery is to capture momentum-dependent ferromagnetic fluctuations near the van Hove singularity and to let their feedback into the electronic propagators build up self-consistently; the split bands and expanded Fermi surface emerge only when this feedback is fully iterated.","core_discovery":"Within D-TRILEX – an approach that adds self-consistent nonlocal self-energy and vertex corrections on top of the local dynamical mean field theory – the authors compute the spectral function of the Hubbard model at t'/t = −0.45, U = 4t, fillings n = 0.43 and 0.52, and temperatures T = 0.05–0.1t above the ferromagnetic crossover. They find that the quasiparticle band splits with a weak momentum dependence: a lower, dispersive band crosses the Fermi level, while an upper, weakly dispersive band stays entirely above it. As a result, the Fermi surface is not split but its area is larger than the non-interacting value for the given density, a violation of the Luttinger theorem that the authors i","pith_inferences":["If the split and expanded Fermi surface survive a real-frequency benchmark, the mechanism could explain the band-splitting observations in materials such as CrTe2 and doped Sr2RuO4 without invoking magnetic order.","The weakly momentum-dependent splitting suggests a minimal effective model of two coupled bands at low energy; deriving such a model from the D-TRILEX self-energy could yield transport and optical predictions, e.g., a low-frequency optical conductivity deficit.","Because the claim rests on MaxEnt continuation, the cleanest confirmation would come from a method with controlled error on the real axis, or from cluster exact diagonalization at the same parameters.","The finding that vertex corrections are essential suggests that simpler self-energy approximations (e.g., bosonization without three-leg vertices) may misjudge the size of the non-Fermi-liquid region in the phase diagram."],"forward_implications":["A non-Fermi-liquid regime with roughly constant (or even increasing) quasiparticle damping at the van Hove point appears above the magnetic crossover temperature, over a wide temperature window.","The spectral splitting and the Fermi-surface expansion occur in the paramagnetic state, so they are pure fluctuation effects requiring no symmetry breaking.","The nodal–antinodal dichotomy is reversed relative to the antiferromagnetic case: more spectral weight sits near the nodal direction and excitations are more coherent at the antinode – a potential fingerprint for ferromagnetic-fluctuation physics.","Among the theories considered, only the self-consistent D-TRILEX gives a dispersive upper band with small spectral weight; the flat upper band seen in some DΓA variants is likely an artifact of the λ-correction.","The expanded Fermi surface implies a Luttinger violation that must be compensated by partial occupancy of the upper band, tying the phenomenon to the emergence of a 'hidden' band in the paramagnetic phase."],"fun_headline_variants":["D-TRILEX: van Hove spin fluctuations expand Fermi surface","Van Hove fluctuations inflate Fermi surface in Hubbard model","Non-Fermi-liquid: band splits, Fermi surface grows","Fermi-surface expansion without magnetic order","Van Hove ferromagnetic fluctuations break Luttinger theorem"],"cache_read_input_tokens":2304,"weakest_assumption_plain":"The split-band and Fermi-surface maps are produced by maximum-entropy analytic continuation of Matsubara Green's functions, which has no built-in error bars; if that continuation artificially splits single-peaked spectra, the central claim collapses.","fun_headline_variants_meta":{"raw":{"variants":["D-TRILEX: van Hove spin fluctuations expand Fermi surface","Van Hove fluctuations inflate Fermi surface in Hubbard model","Non-Fermi-liquid: band splits, Fermi surface grows","Fermi-surface expansion without magnetic order","Van Hove ferromagnetic fluctuations break Luttinger theorem"]},"model":"deepseek-v4-flash","effort":"low","cost_usd":0.000304,"raw_usage":{"total_tokens":1572,"prompt_tokens":721,"completion_tokens":851,"prompt_tokens_details":{"cached_tokens":256},"prompt_cache_hit_tokens":256,"prompt_cache_miss_tokens":465,"completion_tokens_details":{"reasoning_tokens":770}},"tokens_in":465,"tokens_out":851,"duration_ms":6519,"temperature":1.0,"reasoning_tokens":770,"cache_read_input_tokens":256,"cache_creation_input_tokens":0},"cache_creation_input_tokens":0},"created_at":"2026-08-03T21:33:12.505291+00:00","model_set":{"reader":"deepseek-v4-flash"},"falsifier":"Apply an alternative analytic continuation (e.g., stochastic optimization or Padé) to the D-TRILEX Matsubara self-energy and Green's function at T = 0.05, n = 0.43, k = X = (π,0), and check whether the two-peak structure persists and whether the upper band remains above the Fermi level. A negative answer – or a result from exact diagonalization on a 4×4 cluster at the same parameters showing a single peak – would falsify the claimed splitting and Fermi-surface expansion.","supporting_citations":[],"review_version":1}