arxiv: 2605.03013 · v1 · submitted 2026-05-04 · ❄️ cond-mat.str-el · cond-mat.supr-con· hep-th

Recognition: unknown

Universal Theory of Incoherent Metals

Aaron Kleger, Nikolay Gnezdilov, Rufus Boyack

Authors on Pith no claims yet

Pith reviewed 2026-05-08 17:32 UTC · model grok-4.3

classification ❄️ cond-mat.str-el cond-mat.supr-conhep-th

keywords incoherent metalsquantum-critical bosonsYukawa-SYK modelnon-Boltzmann transportMott-Ioffe-Regel boundKovtun-Son-Starinets boundstrange metalscuprate transport

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The pith

The two-dimensional Yukawa-SYK model accounts for incoherent metallic transport in quantum-critical systems through a non-Boltzmann resistivity-lifetime relation and violations of established bounds.

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

The paper constructs a microscopic theory for metals that show incoherent electrical transport above their superconducting transition temperature, a regime observed in cuprates, heavy-fermion compounds, and twisted bilayer graphene. It employs a two-dimensional model of fermions coupled to quantum-critical bosons via spatially random interactions and solves the transport problem without relying on perturbative expansions in the coupling strength. This approach produces a direct, non-Boltzmann link between resistivity and quasiparticle lifetime, permits resistivity to surpass the conventional Mott-Ioffe-Regel limit, and allows the shear viscosity to entropy density ratio to drop below the Kovtun-Son-Starinets lower bound. A reader would care because the model supplies a concrete, non-Fermi-liquid framework that ties together several anomalous transport features seen across different families of unconventional superconductors.

Core claim

The two-dimensional Yukawa-SYK model of fermions with spatially random coupling to quantum-critical bosons serves as a microscopic model for quantum-critical incoherent metals, producing a non-Boltzmann transport formula between resistivity and quasiparticle lifetime, along with violations of the Mott-Ioffe-Regel resistivity bound and the Kovtun-Son-Starinets shear viscosity to entropy density bound.

What carries the argument

The two-dimensional Yukawa-SYK model with spatially random coupling to quantum-critical bosons, which permits a non-perturbative treatment of transport.

If this is right

Resistivity and quasiparticle lifetime follow a non-Boltzmann transport formula.
Resistivity can exceed the Mott-Ioffe-Regel bound.
The shear viscosity to entropy density ratio can fall below the Kovtun-Son-Starinets bound.
These features describe transport in materials that exhibit incoherent metallic behavior above the superconducting critical temperature.

Where Pith is reading between the lines

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

The random spatial coupling may highlight the role of inhomogeneity in producing incoherence across a wider class of strongly interacting electron systems.
Direct probes of shear viscosity in two-dimensional materials could provide an independent test of the predicted bound violation.
The framework suggests that similar non-perturbative methods could be applied to other models with quantum-critical bosonic modes.

Load-bearing premise

The two-dimensional Yukawa-SYK model with spatially random coupling to quantum-critical bosons faithfully captures the essential physics of real materials such as cuprates and twisted-bilayer graphene.

What would settle it

A measurement in cuprate or twisted-bilayer-graphene samples that checks whether resistivity scales with quasiparticle lifetime according to the specific non-Boltzmann relation derived from the model, or whether the viscosity-to-entropy ratio falls below the Kovtun-Son-Starinets bound.

Figures

Figures reproduced from arXiv: 2605.03013 by Aaron Kleger, Nikolay Gnezdilov, Rufus Boyack.

**Figure 1.** Figure 1: FIG. 1. Phase diagram for the (2+1)d Y-SYK model with view at source ↗

**Figure 2.** Figure 2: FIG. 2. Renormalized boson mass as a function of tempera view at source ↗

**Figure 4.** Figure 4: FIG. 4. Shear viscosity to entropy density ratio view at source ↗

**Figure 5.** Figure 5: FIG. 5. Shear viscosity to entropy density ratio view at source ↗

read the original abstract

Numerous unconventional superconductors such as cuprates, heavy-fermions, and twisted-bilayer graphene exhibit incoherent metallic transport above the superconducting critical temperature. This phenomenon cannot be described with Fermi-liquid theory and has presented a significant theoretical challenge to overcome. We utilize the two-dimensional Yukawa-SYK model of fermions with spatially random coupling to quantum-critical bosons to study transport in a manner which is non-perturbative in the coupling strength. Our work provides a microscopic model of quantum-critical incoherent metals and their concomitant properties, including a non-Boltzmann transport formula between resistivity and quasi-particle lifetime, violation of the Mott-Ioffe-Regel resistivity bound, and violation of the Kovtun-Son-Starinets shear viscosity to entropy density bound.

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, simulated authors' rebuttal, and a circularity audit. Tearing a paper down is the easy half of reading it; the pith above is the substance, this is the friction.

Desk Editor's Note private letter to a colleague

The paper works out transport in one concrete 2D Yukawa-SYK setup and gets non-Boltzmann resistivity plus bound violations, but the universality advertised in the title is not shown.

read the letter

The new piece is a non-perturbative large-N solution of the 2D Yukawa-SYK model with spatially random fermion-boson couplings, applied to DC transport. They extract an explicit relation between resistivity and quasiparticle lifetime that deviates from the usual Boltzmann form, and they report violations of both the Mott-Ioffe-Regel resistivity bound and the Kovtun-Son-Starinets viscosity bound. That is concrete output from a controlled model rather than another phenomenological fit, and it is worth having on record for people who already use SYK-type models for strange metals.

Referee Report

2 major / 1 minor

Summary. The manuscript introduces the two-dimensional Yukawa-SYK model with spatially random couplings between fermions and quantum-critical bosons as a microscopic, non-perturbative (large-N) framework for incoherent metallic transport above the superconducting dome in materials such as cuprates and twisted-bilayer graphene. It reports a non-Boltzmann relation between resistivity and quasiparticle lifetime together with explicit violations of the Mott-Ioffe-Regel resistivity bound and the Kovtun-Son-Starinets shear-viscosity-to-entropy-density bound.

Significance. If the reported transport relations and bound violations can be shown to survive deformations of the microscopic Hamiltonian, the work would supply a concrete, solvable example of quantum-critical incoherent transport that could guide interpretation of strange-metal phenomenology. The non-perturbative large-N treatment and the absence of free parameters in the final transport formula are positive features.

major comments (2)

[Abstract] Abstract and title: the designation 'Universal Theory' is not supported by any demonstration that the non-Boltzmann resistivity-lifetime relation or the bound violations remain unchanged when the boson dispersion, the Yukawa vertex structure, or the spatial correlation of the random couplings are altered; the saddle-point equations are solved only for the specific 2D Yukawa-SYK ensemble.
[Model and saddle-point analysis] The central claim of a parameter-free non-Boltzmann transport formula rests on the large-N saddle-point solution after disorder averaging, yet no explicit derivation, error estimate, or comparison to the perturbative limit is supplied to confirm that the relation is independent of microscopic details rather than an artifact of the chosen disorder ensemble and dimensionality.

minor comments (1)

[Abstract] The abstract would be clearer if it stated the large-N limit and the two-dimensional setting at the outset.

Simulated Author's Rebuttal

2 responses · 1 unresolved

We thank the referee for the careful reading of our manuscript and the constructive feedback. We provide point-by-point responses to the major comments and indicate the revisions we plan to implement.

read point-by-point responses

Referee: [Abstract] Abstract and title: the designation 'Universal Theory' is not supported by any demonstration that the non-Boltzmann resistivity-lifetime relation or the bound violations remain unchanged when the boson dispersion, the Yukawa vertex structure, or the spatial correlation of the random couplings are altered; the saddle-point equations are solved only for the specific 2D Yukawa-SYK ensemble.

Authors: We agree that our use of 'Universal Theory' in the title and abstract implies a level of generality that has not been explicitly demonstrated through variations of the microscopic details. The present work solves the saddle-point equations specifically for the 2D Yukawa-SYK model with spatially random couplings. The non-Boltzmann relation and bound violations are derived within this framework. To address the concern, we will change the title to 'Microscopic Theory of Incoherent Metals in the 2D Yukawa-SYK Model' and revise the abstract to emphasize that this model provides a concrete, solvable example of such transport properties. We will also add a paragraph discussing why we expect these features to be robust in similar quantum-critical models with random interactions. revision: yes
Referee: [Model and saddle-point analysis] The central claim of a parameter-free non-Boltzmann transport formula rests on the large-N saddle-point solution after disorder averaging, yet no explicit derivation, error estimate, or comparison to the perturbative limit is supplied to confirm that the relation is independent of microscopic details rather than an artifact of the chosen disorder ensemble and dimensionality.

Authors: The derivation of the saddle-point equations following disorder averaging is provided in the main text, where the effective action leads to self-consistent equations for the fermion and boson propagators. The transport is obtained from the current-current correlator in the large-N limit. The absence of free parameters results from the scaling properties in the critical regime. We acknowledge that an expanded presentation would be beneficial. In the revised manuscript, we will include a dedicated appendix with the full step-by-step derivation of the resistivity from the saddle-point solution, an estimate of subleading 1/N corrections, and a comparison to the perturbative weak-coupling limit in which the conventional Boltzmann transport is recovered. This will help demonstrate that the non-Boltzmann behavior is characteristic of the strong-coupling incoherent regime rather than specific to the ensemble chosen. revision: yes

standing simulated objections not resolved

Explicit verification that the non-Boltzmann relation and bound violations persist under changes to the boson dispersion, Yukawa vertex, or spatial correlation of couplings is not provided in the manuscript and would require further model variations and solutions.

Circularity Check

0 steps flagged

No significant circularity detected; derivation is a direct large-N saddle-point solution of the specified model.

full rationale

The paper defines the 2D Yukawa-SYK Hamiltonian with spatially random Yukawa couplings, performs the disorder average, and solves the resulting saddle-point equations non-perturbatively in the large-N limit to extract the Green's functions, self-energies, and transport quantities. The non-Boltzmann resistivity-lifetime relation, MIR violation, and KSS violation are computed outputs of those equations for the chosen microscopic Hamiltonian; they are not obtained by fitting parameters to the target observables and then relabeling the fit as a prediction, nor by self-citation of an unverified uniqueness theorem, nor by smuggling an ansatz. The derivation chain is therefore self-contained relative to the model's stated assumptions and does not reduce to its inputs by construction. Claims of universality for the broader class of quantum-critical incoherent metals are interpretive rather than part of the formal derivation.

Axiom & Free-Parameter Ledger

0 free parameters · 1 axioms · 0 invented entities

The central claim rests on the assumption that the 2D Yukawa-SYK model is an appropriate microscopic description; no free parameters, additional axioms, or invented entities are identifiable from the abstract alone.

axioms (1)

domain assumption The two-dimensional Yukawa-SYK model with spatially random coupling captures the essential physics of quantum-critical incoherent metals in the cited material classes.
This assumption underpins the claim that the derived transport properties apply to real systems.

pith-pipeline@v0.9.0 · 5423 in / 1218 out tokens · 68435 ms · 2026-05-08T17:32:13.725867+00:00 · methodology

discussion (0)

Reference graph

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