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Self-consistent ferromagnetic fluctuations near a van Hove singularity split the electronic spectrum and expand the Fermi surface without symmetry breaking.

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2026-08-03 21:33 UTC pith:RTOMYOEZ

load-bearing objection 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. the 3 major comments →

arxiv 2511.14614 v2 pith:RTOMYOEZ submitted 2025-11-18 cond-mat.str-el

Non-Fermi-liquid behaviour and Fermi-surface expansion induced by van Hove-driven ferromagnetic fluctuations: the D-TRILEX analysis

Ilia S. Dedov , Andrey A. Katanin , Evgeny A. Stepanov This is my paper
classification cond-mat.str-el PACS 71.10.Hf71.27.+a71.10.Fd
keywords Hubbard modelvan Hove singularityferromagnetic fluctuationsnon-Fermi liquidD-TRILEXFermi surface expansionspectral function splittingdynamical mean field theory
verification ladder T0 review T1 audit T2 compute T3 formal T4 reserved

The pith

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

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.

Core claim

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

What carries the argument

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.

Load-bearing premise

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.

What would settle it

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.

Watch this falsifier. Get emailed when new claim-graph text bears on it.

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If this is right

  • 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.

Where Pith is reading between the lines

These are editorial extensions of the paper, not claims the author makes directly.

  • 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.

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, simulated authors' rebuttal, and a circularity audit.

Referee Report

3 major / 4 minor

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.

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 (3)
  1. [§II; Figs. 4–6] 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
  2. [§III.B.1; Fig. 2 caption; Fig. 3] 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.
  3. [§III.B.2; Figs. 4, 6; Conclusion] 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
minor comments (4)
  1. [Fig. 3 caption] 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.
  2. [Fig. A1 caption] The caption says 'n=0.52 (e-f)', but panels (e)–(h) are shown. Correct to (e–h).
  3. [Fig. 6] 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.
  4. [Fig. 4] The DΓA labels appear as 'D□A' in the figure. Fix the typography so that Γ is rendered correctly.

Circularity Check

0 steps flagged

No circularity found: the spectral splitting and Fermi-surface expansion are emergent outputs of the self-consistent D-TRILEX calculation, not fits or self-cited inputs.

full rationale

The paper's central results—the splitting of the spectral function, the weak momentum dependence of that splitting, and the Fermi-surface expansion—are obtained by solving the D-TRILEX self-consistency equations (Eqs. 2–5) with DMFT-impurity vertex inputs and then analytically continuing the resulting Matsubara Green's functions. No parameter is tuned to reproduce the claimed splitting or Fermi-surface area, and the comparison with DMFT and DΓA is a genuine computational contrast, not a reduction of the output to an input. The D-TRILEX method itself is cited from prior work of the authors, but that is a normal methodological dependence: the method is an independent computational framework and the cited papers do not contain the specific prediction of Fermi-surface expansion for this model. The only load-bearing numerical step that could be questioned is the maximum-entropy analytic continuation (Sec. II, 'obtained from the Matsubara Green's function G(k, iν) via analytic continuation using the maximum entropy method'), but MaxEnt is a standard inversion technique, not an input that by construction produces the two-band structure; any concern about its reliability is a correctness/robustness issue, not circularity. The paper itself even flags method-dependence of the splitting ('we find that the features of this splitting and the dichotomy are method-dependent'), which further indicates the result is not definitionally tied to a single fitted input. Thus no circular step can be exhibited, and the appropriate score is 0.

Axiom & Free-Parameter Ledger

0 free parameters · 3 axioms · 0 invented entities

No parameter is fitted to the target result. The model parameters U, t', n, and T are explicit inputs. The 'α' subtracted in the Fermi-liquid diagnostic is a convention (real-part contribution) rather than a fitted parameter, and the polynomial extrapolation used to read γ is a post-processing procedure, not a fit to the conclusion. No new particles, forces, or conserved quantities are introduced.

axioms (3)
  • domain assumption D-TRILEX partially bosonized vertex approximation (three-point vertices connected by bosonic propagators) is quantitatively reliable for the Hubbard model near the van Hove singularity.
    This is the method used for all non-local results; if the vertex/bosonization approximation is inaccurate, the reported spectral splitting and Fermi-surface expansion are artifacts. Introduced in Sec. II, Eqs. (2)–(5), citing Refs. [27–29].
  • domain assumption Maximum-entropy analytic continuation of finite Matsubara data resolves the two bands and the ν=0 Fermi-surface maps without uncontrolled bias.
    All A(k,ω) and Fermi-surface plots come from MaxEnt via the ana_cont package (Sec. II); no error bars or alternative continuation checks are given, so the split-band observation is contingent on MaxEnt being faithful.
  • domain assumption The chosen model parameters (U=4t, t'/t=-0.45, n≈0.43–0.52) place the system in a regime where ferromagnetic van Hove fluctuations dominate, and conclusions are representative of that regime.
    Model parameters are inputs; they are not derived or varied to show universality. The density and hopping ratio are chosen specifically to enhance ferromagnetic fluctuations.

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Cite this review

Pith. "Pith review of Non-Fermi-liquid behaviour and Fermi-surface expansion induced by van Hove-driven ferromagnetic fluctuations: the D-TRILEX analysis." pith.science (2026). https://pith.science/paper/RTOMYOEZ

@misc{pith2026251114614,
  author       = {Pith},
  title        = {Pith review of: Non-Fermi-liquid behaviour and Fermi-surface expansion induced by van Hove-driven ferromagnetic fluctuations: the D-TRILEX analysis},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/RTOMYOEZ}},
  note         = {Machine review of arXiv:2511.14614}
}
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read the original abstract

We consider the electronic and magnetic properties of the Hubbard model on a square lattice with the Fermi level near van Hove singularity and the ratio of the next-nearest-neighbor and nearest-neighbor hoppings $t'/t=-0.45$, which favours the ferromagnetic instability. We find, that a self-consistent consideration of the ferromagnetic fluctuations within the D-TRILEX approach results in the splitting of the electronic spectral function at low temperatures. This splitting exhibits only a weak momentum dependence, and only one of the split bands crosses the Fermi level. As a result, the Fermi surface itself remains unsplit, but its area increases, reflecting the presence of non-Fermi-liquid electronic excitations. We show that both the self-consistent account of the non-local contributions to the electronic self-energy and the proper treatment of electron interaction vertices in D-TRILEX are important to obtain this behaviour.

Figures

Figures reproduced from arXiv: 2511.14614 by Andrey A. Katanin, Evgeny A. Stepanov, Ilia S. Dedov.

Figure 2
Figure 2. Figure 2: FIG. 2. Self-Energies on Matsubara frequencies at [PITH_FULL_IMAGE:figures/full_fig_p003_2.png] view at source ↗
Figure 3
Figure 3. Figure 3: ), showing only a slight increase upon lowering T, opposite to the DMFT trend. In addition, the ab￾solute values of quasiparticle damping are almost twice as large as in DMFT. These findings demonstrate that non-local corrections to the self-energy associated with the van Hove singularity drastically enhance non-Fermi￾liquid behavior and prevent the system from approaching the Fermi-liquid regime as the te… view at source ↗
Figure 4
Figure 4. Figure 4: FIG. 4. Momentum-resolved spectral functions for [PITH_FULL_IMAGE:figures/full_fig_p004_4.png] view at source ↗
Figure 5
Figure 5. Figure 5: FIG. 5. Spectral functions in D-TRILEX at [PITH_FULL_IMAGE:figures/full_fig_p005_5.png] view at source ↗
Figure 6
Figure 6. Figure 6: FIG. 6. Spectral functions at [PITH_FULL_IMAGE:figures/full_fig_p005_6.png] view at source ↗

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    Self-energies We next consider the local self-energies obtained within DMFT and D-TRILEX for 0.05t < T <0.1t, i.e., above the transition temperature, and for fillings n= 0.43 andn= 0.52 close to the van Hove singularity. The corresponding result is shown in Fig. 2. In DMFT we find that the quasiparticle dampingγ k =−ImΣ k,ν=0, shown in Fig. 3, decreases w...

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