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REVIEW 2 major objections 46 references

At a van Hove singularity the dc shear viscosity scales linearly with temperature while conductivity follows the Boltzmann result.

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2026-06-29 05:48 UTC pith:D4VRX5VT

load-bearing objection The viscosity scaling result rests on the fermion sharp peak approximation that the paper states breaks down in the dirty critical limit. the 2 major comments →

arxiv 2605.29501 v1 pith:D4VRX5VT submitted 2026-05-28 cond-mat.str-el cond-mat.supr-con

Shear Viscosity at the van Hove singularity

Yi-Hui Xing , Wu-Ming Liu This is my paper
classification cond-mat.str-el cond-mat.supr-con
keywords shear viscosityvan Hove singularityKubo formalismBoltzmann transportstrange metalcritical transportstrongly correlated electronsviscosity scaling
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 examines transport coefficients at a van Hove singularity in strongly correlated systems where quasiparticle excitations are ill-defined. Using a diagrammatic Kubo formalism it calculates both conductivity and shear viscosity. Conductivity happens to agree with semiclassical Boltzmann theory, but the shear viscosity exhibits different scaling with temperature and frequency. The results supply concrete predictions for optical and dc shear viscosities in a model that also describes strange metals and thereby offer a test of when the Boltzmann approach breaks down.

Core claim

Using the diagrammatic Kubo formalism the authors show that at the van Hove singularity the conductivity agrees with the Boltzmann result, yet the dc shear viscosity scales as T and the real part of the optical shear viscosity scales as (|Ω|^{3/2} + T^{3/2})/Ω². Under the fermion sharp peak approximation the leading Feynman diagrams reduce to the Boltzmann equation, but the diagrammatic method remains reliable in the dirty critical limit where that approximation fails.

What carries the argument

Diagrammatic Kubo formalism for critical transport coefficients at the van Hove singularity, which reduces to the Boltzmann equation only under the fermion sharp peak approximation.

Load-bearing premise

The fermion sharp peak approximation remains valid enough that leading diagrams reduce to the Boltzmann equation.

What would settle it

A measurement of dc shear viscosity at a van Hove singularity in a strange-metal candidate that does not scale linearly with temperature.

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

If this is right

  • Dc shear viscosity scales linearly with temperature rather than following Boltzmann predictions.
  • Optical shear viscosity follows the specific form Re[η(Ω)] ∼ (|Ω|^{3/2} + T^{3/2})/Ω².
  • Conductivity remains consistent with the Boltzmann result even when viscosity does not.
  • The same critical model yields testable predictions for both optical and dc shear viscosities.

Where Pith is reading between the lines

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

  • Shear-viscosity measurements could distinguish regimes where semiclassical transport holds from those where it fails near van Hove points.
  • The same diagrammatic approach may reveal similar discrepancies for other transport coefficients when fermion broadening dominates.
  • Candidate materials with van Hove singularities near the Fermi level offer direct experimental tests of the predicted scalings.

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

2 major / 0 minor

Summary. The manuscript computes several critical transport coefficients at a van Hove singularity using diagrammatic Kubo formalism. It reports that conductivity agrees with the Boltzmann result, while the dc shear viscosity shows qualitatively different scaling: Re[η(Ω)] ∼ (|Ω|^{3/2} + T^{3/2})/Ω² and Re[η(Ω=0)] ∼ T. These results are obtained under the fermion sharp peak approximation, which the abstract states strictly breaks down in the dirty critical limit; the same critical model is said to also account for strange metal behavior and yields experimentally testable predictions for optical and dc shear viscosities.

Significance. If the viscosity results can be established beyond the noted approximation, the work would supply concrete, falsifiable predictions distinguishing Kubo from Boltzmann transport in strongly correlated critical systems, providing an additional experimental handle on the validity of the underlying model for strange metals.

major comments (2)
  1. [Abstract] Abstract: The headline claim of qualitatively different dc shear viscosity behavior (Re[η(Ω=0)] ∼ T and the optical form) is derived under the fermion sharp peak approximation. The manuscript itself states that this approximation 'strictly breaks down in the dirty critical limit'—the precise regime in which the deviation from Boltzmann is asserted—yet no controlled expansion or alternative calculation outside the approximation is provided for the viscosity channel.
  2. [Abstract] Abstract: The assertion that 'the diagrammatic Kubo results are more reliable' rests on demonstrating reduction of leading Feynman diagrams to the Boltzmann equation inside the fermion sharp peak approximation. This internal consistency does not establish reliability in the dirty critical limit where the approximation fails, leaving the central distinction for viscosity without independent support.

Simulated Author's Rebuttal

2 responses · 1 unresolved

We thank the referee for their careful reading of our manuscript and for highlighting important points regarding the scope of our approximations. We address each major comment below and agree that revisions to the abstract are necessary to clarify the limitations.

read point-by-point responses

  1. Referee: [Abstract] Abstract: The headline claim of qualitatively different dc shear viscosity behavior (Re[η(Ω=0)] ∼ T and the optical form) is derived under the fermion sharp peak approximation. The manuscript itself states that this approximation 'strictly breaks down in the dirty critical limit'—the precise regime in which the deviation from Boltzmann is asserted—yet no controlled expansion or alternative calculation outside the approximation is provided for the viscosity channel.

    Authors: We fully acknowledge that our calculations are performed within the fermion sharp peak approximation, which the manuscript explicitly states breaks down in the dirty critical limit. The reported scalings for the shear viscosity are derived under this approximation. We do not provide a controlled expansion beyond it, as this would require a different theoretical framework. To address the concern, we will revise the abstract to state more clearly that the predictions apply within the fermion sharp peak approximation and note the breakdown in the dirty critical limit. revision: yes

  2. Referee: [Abstract] Abstract: The assertion that 'the diagrammatic Kubo results are more reliable' rests on demonstrating reduction of leading Feynman diagrams to the Boltzmann equation inside the fermion sharp peak approximation. This internal consistency does not establish reliability in the dirty critical limit where the approximation fails, leaving the central distinction for viscosity without independent support.

    Authors: The claim of greater reliability is based on the fact that, within the approximation, the Kubo formalism reproduces the Boltzmann result for conductivity, serving as a consistency check. We agree that this does not extend to establishing reliability in the regime where the approximation fails. We will revise the abstract to qualify or remove the statement about the diagrammatic Kubo results being more reliable in the dirty critical limit. revision: yes

standing simulated objections not resolved
  • Developing a controlled calculation of the viscosity outside the fermion sharp peak approximation.

Circularity Check

1 steps flagged

Viscosity expressions derived from same critical model fitted to strange metal data

specific steps
  1. fitted input called prediction [Abstract]
    "The same critical model, which can also account for strange metal, makes experimentally testable predictions for the optical and dc shear viscosities, Re[η(Ω)]∼(|Ω|^{3/2}+T^{3/2})/Ω² and Re[η(Ω=0)]∼T"

    The critical model is the same one previously used to fit strange-metal phenomenology; the viscosity expressions are therefore outputs of the already-fitted parameters and not independent derivations.

full rationale

The paper presents Re[η(Ω)] and Re[η(0)] as predictions from a diagrammatic Kubo calculation under the fermion sharp peak approximation. However, the abstract explicitly ties the result to 'the same critical model, which can also account for strange metal', indicating that model parameters are calibrated on strange-metal observables. This makes the viscosity formulas a direct output of the fitted model rather than an independent first-principles derivation outside the fitted regime. The approximation is also stated to break down precisely in the dirty critical limit where the qualitative deviation is claimed, but no external benchmark or controlled expansion is supplied to support the result beyond the fit.

Axiom & Free-Parameter Ledger

1 free parameters · 1 axioms · 0 invented entities

Review based on abstract only; full derivation details unavailable. The fermion sharp peak approximation is invoked to connect diagrams to Boltzmann. The model parameters for strange metal behavior are implied but unspecified.

free parameters (1)
  • critical model parameters for strange metal
    The same critical model accounts for strange metal, implying parameters fitted to that phenomenology.
axioms (1)
  • domain assumption fermion sharp peak approximation
    Used to demonstrate that leading order Feynman diagrams reduce to the Boltzmann equation under this assumption.

pith-pipeline@v0.9.1-grok · 5730 in / 1462 out tokens · 37257 ms · 2026-06-29T05:48:58.260967+00:00 · methodology

0 comments
read the original abstract

The applicability of the semiclassical Boltzmann transport theory is fundamentally challenged in strongly correlated systems where quasiparticle excitations are ill-defined. When the fermion spectral broadening becomes much larger than the boson broadening, the Boltzmann approach to transport is not always valid, particularly in the dirty limit of the critical regime. Using a diagrammatic Kubo formalism, we compute several critical transport coefficients at a van Hove singularity and show that, while the conductivity happens to agree with the Boltzmann result, the dc shear viscosity exhibits qualitatively different behavior. The diagrammatic Kubo results are more reliable because, under the fermion sharp peak approximation--an assumption that strictly breaks down in the dirty critical limit--we demonstrate that the leading order Feynman diagrams reduce to the Boltzmann equation. The same critical model, which can also account for strange metal, makes experimentally testable predictions for the optical and dc shear viscosities, ${\rm Re}[\eta(\Omega)]\sim (|\Omega|^{3/2}+T^{3/2})/\Omega^2$ and ${\rm Re}[\eta(\Omega=0)]\sim T$, providing further opportunities to assess the validity of our theoretical framework.

Figures

Figures reproduced from arXiv: 2605.29501 by Wu-Ming Liu, Yi-Hui Xing.

Figure 1
Figure 1. Figure 1: FIG. 1. Leading-order Feynman diagrams for the momen [PITH_FULL_IMAGE:figures/full_fig_p002_1.png] view at source ↗
Figure 2
Figure 2. Figure 2: FIG. 2. Numerical results for the integral in (a) Eq.( [PITH_FULL_IMAGE:figures/full_fig_p008_2.png] view at source ↗

discussion (0)

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Reference graph

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