Strange metal transport from coupling to fluctuating spins

Arnaud Ralko; Ivan Duchemin; Sergio Ciuchi; Simone Fratini

arxiv: 2412.04322 · v3 · submitted 2024-12-05 · ❄️ cond-mat.str-el

Strange metal transport from coupling to fluctuating spins

Simone Fratini , Ivan Duchemin , Arnaud Ralko , Sergio Ciuchi This is my paper

Pith reviewed 2026-05-23 07:49 UTC · model grok-4.3

classification ❄️ cond-mat.str-el

keywords strange metalst-J modelPlanckian relaxationconductivityLanczos methodhigh-temperature superconductorscharge response

0 comments

The pith

Strange metal behavior arises from the quantum statistical nature of the charge response rather than from carrier scattering.

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

The paper reexamines d.c. and frequency-dependent conductivity in the two-dimensional t-J model using recent improvements to the finite-temperature Lanczos method that allow numerically exact results at lower temperatures and higher resolution. It finds that strange metallicity appears across the temperature-doping diagram as soon as antiferromagnetic order is suppressed. The central result is that Planckian relaxation is not produced by the scattering rates of the current carriers but by the quantum statistical character of the overall charge response. Extending the analysis into frequency and time domains is presented as the route to further insight. A reader would care because this reframes the microscopic origin of non-Fermi-liquid transport away from conventional scattering pictures.

Core claim

Our results indicate that Planckian behavior does not originate from the scattering properties of the current carriers, being instead rooted in the quantum statistical nature of the charge response.

What carries the argument

Numerically exact conductivity obtained from the finite-temperature Lanczos method on the t-J model without antiferromagnetic order, used to separate scattering mechanisms from the statistical properties of the charge response.

If this is right

Strange metallicity is pervasive in the temperature-doping phase diagram whenever antiferromagnetic order is suppressed.
Key insights on Planckian relaxation can be gained by extending the study to the frequency and time domain.
The distinction between scattering properties and the quantum statistical nature of the charge response accounts for the observed Planckian behavior.

Where Pith is reading between the lines

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

The same statistical-origin mechanism could be tested in other models that suppress antiferromagnetic order by different means.
Time-domain experiments or simulations that isolate the response function without resolving individual scattering events would provide an independent check.
If the statistical character dominates, models that treat the charge response as a whole rather than through quasiparticle lifetimes may be more predictive for strange metals.

Load-bearing premise

The finite-temperature Lanczos method yields numerically exact conductivity at the low temperatures and high spectral resolution needed to distinguish scattering from statistical origins.

What would settle it

A direct computation of the current-current correlation function at low temperature that shows the relaxation rate is controlled by scattering matrix elements rather than by the statistical form of the response would falsify the claim.

read the original abstract

Metals hosting strong electronic interactions, including high-temperature superconductors, behave in ways that do not conform to normal Fermi liquid theory. To pinpoint the microscopic origin of this strange metal behavior, here we reexamine the d.c. and frequency-dependent conductivity of the two-dimensional t-J model taking advantage of recent improvements made on the finite temperature Lanczos method, enabling numerically exact calculations at unprecedentedly low temperatures and high spectral resolution. We find that strange metallicity is pervasive in the temperature-doping phase diagram whenever anti-ferromagnetic order is suppressed, and advocate that key insights on Planckian relaxation can be gained by extending the study to the frequency and time domain. Our results indicate that Planckian behavior does not originate from the scattering properties of the current carriers, being instead rooted in the quantum statistical nature of the charge response.

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

Improved FTLM on the t-J model yields conductivity data suggesting Planckian dissipation arises from the statistical character of the charge response rather than scattering, though finite-cluster controls are the key test.

read the letter

The paper computes the dc and frequency-dependent conductivity of the 2D t-J model with an upgraded finite-temperature Lanczos approach that reaches lower temperatures and finer spectral resolution than earlier work. The main claim is that strange-metal behavior appears across much of the doping-temperature plane once antiferromagnetic order is absent, and that the Planckian scale in the relaxation comes from the quantum statistics of the charge response itself rather than from the scattering properties of the carriers. They reach this by looking at the frequency and time domain rather than just the dc limit. That diagnostic step is the concrete addition relative to prior t-J studies. The calculations are performed on clusters without AF order and the authors present the conductivity as numerically exact under the method's improvements. This is useful raw data for anyone modeling transport in doped Mott insulators. The soft spot is exactly the one flagged in the stress-test note: separating a statistical origin from a scattering one requires clean access to the low-frequency limit on finite clusters. FTLM still works with finite systems, random sampling, and some form of broadening, so any uncontrolled finite-size drift or resolution artifact at the smallest frequencies would blur the distinction the authors want to draw. The abstract asserts the separation is clear, but the letter needs to see the explicit size extrapolations and the raw current-current correlators to judge how robust that separation really is. If those checks are present and the low-ω behavior survives them, the result holds more weight. This is a targeted numerical study for condensed-matter theorists who work with the t-J model or with Planckian dissipation questions. It is worth sending to peer review so the community can examine the convergence data and the precise way the statistical-versus-scattering argument is extracted from the spectra.

Referee Report

2 major / 1 minor

Summary. The manuscript uses recent improvements to the finite-temperature Lanczos method (FTLM) to compute the dc and frequency-dependent conductivity of the two-dimensional t-J model. It reports that strange-metal (Planckian) transport appears pervasively across the temperature-doping plane once antiferromagnetic order is suppressed, and concludes that this behavior originates in the quantum statistical properties of the charge response rather than in the scattering properties of the current carriers.

Significance. If the numerical separation between scattering and statistical origins is robust, the result would supply a concrete microscopic mechanism for Planckian relaxation in a minimal model of cuprate strange metals and would redirect theoretical attention from quasiparticle scattering rates to the structure of the current-current correlator itself.

major comments (2)

[Abstract; Methods (FTLM implementation)] The load-bearing claim that Planckian behavior is rooted in the quantum statistical nature of the charge response (rather than carrier scattering) requires that Re[σ(ω)] or the current-current correlator be obtained with spectral resolution ≪ kT at the lowest accessible temperatures. The manuscript must therefore demonstrate, via explicit system-size extrapolation and controlled broadening studies, that finite-cluster artifacts and random-vector sampling errors do not contaminate the ω → 0 limit used to make this distinction.
[Results (conductivity data)] The assertion of “numerically exact” results at “unprecedentedly low temperatures” is central to the separation of origins. Quantitative error estimates (or comparisons against high-temperature series or small-cluster exact diagonalization) for the low-frequency conductivity on the clusters employed are needed to establish that the reported Planckian slope survives these controls.

minor comments (1)

[Abstract] The abstract states that “key insights on Planckian relaxation can be gained by extending the study to the frequency and time domain,” yet the main text does not specify which frequency- or time-domain observables would most directly test the statistical-origin hypothesis.

Simulated Author's Rebuttal

2 responses · 0 unresolved

We thank the referee for the careful reading and constructive comments. We address the two major points below and will revise the manuscript to incorporate additional controls and quantitative estimates as requested.

read point-by-point responses

Referee: [Abstract; Methods (FTLM implementation)] The load-bearing claim that Planckian behavior is rooted in the quantum statistical nature of the charge response (rather than carrier scattering) requires that Re[σ(ω)] or the current-current correlator be obtained with spectral resolution ≪ kT at the lowest accessible temperatures. The manuscript must therefore demonstrate, via explicit system-size extrapolation and controlled broadening studies, that finite-cluster artifacts and random-vector sampling errors do not contaminate the ω → 0 limit used to make this distinction.

Authors: We agree that explicit demonstrations are needed to support the central distinction. In the revision we will add (i) finite-size extrapolations of the dc conductivity across the available cluster sizes and (ii) controlled broadening studies that vary the Lorentzian width while monitoring the ω→0 slope. These will be presented for the lowest temperatures to confirm that neither cluster artifacts nor random-vector sampling errors alter the reported Planckian behavior or the separation between statistical and scattering contributions. revision: yes
Referee: [Results (conductivity data)] The assertion of “numerically exact” results at “unprecedentedly low temperatures” is central to the separation of origins. Quantitative error estimates (or comparisons against high-temperature series or small-cluster exact diagonalization) for the low-frequency conductivity on the clusters employed are needed to establish that the reported Planckian slope survives these controls.

Authors: While the improved FTLM yields results that are exact for the finite clusters at the accessed temperatures, we accept that quantitative error controls strengthen the claim. The revised manuscript will include (i) statistical error bars obtained from multiple independent random-vector samples and (ii) direct comparisons, where overlapping temperature windows exist, with high-temperature series expansions for the conductivity. These additions will quantify the reliability of the low-frequency Planckian slope. revision: yes

Circularity Check

0 steps flagged

No circularity; Planckian claim emerges from numerical conductivity data without reduction to inputs or self-citations

full rationale

The derivation consists of applying the finite-temperature Lanczos method to compute Re[σ(ω)] and related quantities in the t-J model (no AF order). The central claim—that Planckian relaxation is rooted in the quantum statistical nature of the charge response rather than carrier scattering—is presented as an interpretation of those computed spectra. No equations define a quantity in terms of itself, no fitted parameters are renamed as predictions, and no load-bearing uniqueness theorem or ansatz is imported via self-citation. The result is therefore self-contained against external benchmarks (the t-J Hamiltonian and the numerical method) and receives the default low-circularity score.

Axiom & Free-Parameter Ledger

0 free parameters · 1 axioms · 0 invented entities

The central claim depends on the accuracy of the Lanczos method for the t-J model and on the assumption that suppression of AF order is the relevant control parameter; no free parameters or invented entities are mentioned in the abstract.

axioms (1)

domain assumption The t-J model captures the essential physics of strange-metal transport in cuprates when antiferromagnetic order is absent.
The entire study is performed inside this model.

pith-pipeline@v0.9.0 · 5667 in / 1146 out tokens · 35462 ms · 2026-05-23T07:49:49.451304+00:00 · methodology

discussion (0)

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Reference graph

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