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arxiv: 2604.08085 · v1 · submitted 2026-04-09 · ❄️ cond-mat.str-el

Recognition: unknown

Hubbard vs. Emery model: spectra, transport and relevance for cuprates

Jak\v{s}a Vu\v{c}i\v{c}evi\'c , Rok \v{Z}itko
Authors on Pith no claims yet

Pith reviewed 2026-05-10 17:17 UTC · model grok-4.3

classification ❄️ cond-mat.str-el
keywords Hubbard modelEmery modelcuprate superconductorstransport propertiesspectral functionsdc resistivityeffective massLifshitz transition
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The pith

The Hubbard and Emery models produce similar but distinguishable spectra and transport in cuprates, with experiments favoring a larger effective coupling in the Hubbard model.

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

This paper compares the single-orbital Hubbard model and the three-orbital Emery model to see which minimal description best captures the transport and spectral properties of cuprate superconductors. Both models produce a similar overall picture of the physics, yet they differ quantitatively in several measurable quantities such as resistivity and effective mass. Direct comparison of the calculated results to seven experiments on three different La2CuO4-based cuprates yields good overall agreement. The mismatch in resistivity and mass data indicates that the interaction strength in the Hubbard model must be set higher than standard estimates to align with observation.

Core claim

The Hubbard and Emery models give similar physical pictures for cuprate spectra and transport, but with several strong quantitative differences. Comparison to seven experiments on three La2CuO4-based cuprates shows excellent agreement overall. The dc resistivity and effective mass suggest a larger coupling constant in the effective Hubbard model than expected. Properties sensitive to this coupling include the critical doping for the Lifshitz transition and the local spectral weight near the Fermi level.

What carries the argument

Numerical solution of the Hubbard and Emery models for their spectral functions, dc resistivity, and effective mass, followed by direct comparison to cuprate experiments.

If this is right

  • Quantitative differences between the two models can be used to discriminate which one better describes real cuprates.
  • The overall agreement with multiple experiments supports the use of these low-energy models for transport calculations.
  • The larger coupling constant required in the Hubbard model also shifts the predicted doping for the Lifshitz transition.
  • Local spectral weight near the Fermi level offers a direct experimental route to determine the effective coupling constant.

Where Pith is reading between the lines

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

  • A higher coupling value in the Hubbard model would likely change predictions for other doping-dependent phenomena such as the onset of superconductivity.
  • If future photoemission data confirm the suggested coupling strength, it would tighten the mapping between the lattice model and the real material parameters.
  • Persistent differences between the two models in other regimes could help decide whether additional orbital degrees of freedom are required beyond the Emery model.

Load-bearing premise

The chosen Hubbard and Emery lattice models together with the numerical solution method capture all relevant mechanisms needed for quantitative transport predictions in cuprates.

What would settle it

A photoemission experiment that measures the local spectral weight near the Fermi level and finds values inconsistent with the Hubbard model prediction at the larger coupling constant indicated by resistivity data.

Figures

Figures reproduced from arXiv: 2604.08085 by Jak\v{s}a Vu\v{c}i\v{c}evi\'c, Rok \v{Z}itko.

Figure 1
Figure 1. Figure 1: FIG. 1. Two possible crystal structures for compounds ob [PITH_FULL_IMAGE:figures/full_fig_p004_1.png] view at source ↗
Figure 2
Figure 2. Figure 2: FIG. 2. Left: Orbital projected DFT band structure and wannierized band structures for the two possible crystal structures [PITH_FULL_IMAGE:figures/full_fig_p005_2.png] view at source ↗
Figure 3
Figure 3. Figure 3: FIG. 3. Illustration of the physical meaning of the tight [PITH_FULL_IMAGE:figures/full_fig_p005_3.png] view at source ↗
Figure 4
Figure 4. Figure 4: FIG. 4. Bare density of states [PITH_FULL_IMAGE:figures/full_fig_p007_4.png] view at source ↗
Figure 5
Figure 5. Figure 5: FIG. 5. Illustration of the proof of the cancellation of vertex [PITH_FULL_IMAGE:figures/full_fig_p008_5.png] view at source ↗
Figure 6
Figure 6. Figure 6: FIG. 6. Comparison of the local spectral function between the Hubbard and Emery models for the T-structure, relevant [PITH_FULL_IMAGE:figures/full_fig_p010_6.png] view at source ↗
Figure 8
Figure 8. Figure 8: FIG. 8. Dependence of the occupied spectral weight just [PITH_FULL_IMAGE:figures/full_fig_p011_8.png] view at source ↗
Figure 7
Figure 7. Figure 7: FIG. 7. Quantifying spectral properties in the T-structure [PITH_FULL_IMAGE:figures/full_fig_p011_7.png] view at source ↗
Figure 9
Figure 9. Figure 9: FIG. 9. Density of occupied states [PITH_FULL_IMAGE:figures/full_fig_p012_9.png] view at source ↗
Figure 10
Figure 10. Figure 10: FIG. 10. Comparison of the DMFT momentum-resolved spectral function with ARPES experiment on LSCO, taken from [PITH_FULL_IMAGE:figures/full_fig_p012_10.png] view at source ↗
Figure 11
Figure 11. Figure 11: FIG. 11. Comparison of the local spectral function between the Hubbard and Emery models for the T’-structure, relevant [PITH_FULL_IMAGE:figures/full_fig_p013_11.png] view at source ↗
Figure 12
Figure 12. Figure 12: FIG. 12. Same as Fig [PITH_FULL_IMAGE:figures/full_fig_p014_12.png] view at source ↗
Figure 14
Figure 14. Figure 14: FIG. 14. Comparison of the resistivity between the [PITH_FULL_IMAGE:figures/full_fig_p015_14.png] view at source ↗
Figure 15
Figure 15. Figure 15: FIG. 15. Comparison between our DMFT theory results and the experimental measurements for the dc resistivity in three [PITH_FULL_IMAGE:figures/full_fig_p016_15.png] view at source ↗
Figure 16
Figure 16. Figure 16: FIG. 16. Illustration of the Lifshitz transition using the Emery-model results for the T-structure with [PITH_FULL_IMAGE:figures/full_fig_p018_16.png] view at source ↗
Figure 17
Figure 17. Figure 17: FIG. 17. Dependence of the critical doping for the Lifshitz [PITH_FULL_IMAGE:figures/full_fig_p018_17.png] view at source ↗
Figure 18
Figure 18. Figure 18: FIG. 18. Comparison between theoretical and experimental results for the effective cyclotron mass [PITH_FULL_IMAGE:figures/full_fig_p019_18.png] view at source ↗
Figure 19
Figure 19. Figure 19: FIG. 19. Comparison between our Hubbard model theory [PITH_FULL_IMAGE:figures/full_fig_p020_19.png] view at source ↗
Figure 20
Figure 20. Figure 20: FIG. 20. Simple non-interacting square-lattice theory as an illustration of the difference between the cyclotron mass [PITH_FULL_IMAGE:figures/full_fig_p023_20.png] view at source ↗
Figure 21
Figure 21. Figure 21: FIG. 21. Effective transport mass as a function of doping, [PITH_FULL_IMAGE:figures/full_fig_p023_21.png] view at source ↗
Figure 22
Figure 22. Figure 22: FIG. 22. Left: Orbital-resolved spectral function in the Emery model for the T-structure, at various dopings for a fixed [PITH_FULL_IMAGE:figures/full_fig_p025_22.png] view at source ↗
read the original abstract

Understanding the transport properties of cuprate superconductors is one of the central challenges in the physics of strongly correlated electrons. The most common approach is to define and solve a low-energy lattice model, but it is still unclear what the minimal model is to capture all relevant mechanisms and provide quantitative predictions. The main uncertainty concerns the choice of the orbital degrees of freedom to be included in the model, as well as the definition of the effective coupling. In this paper, we study the two most commonly considered models, namely the single-orbital Hubbard model and the three-orbital Emery model. We investigate and compare their spectral and transport properties, and find that the two models present a similar, but not the same, physical picture. We identify several strong quantitative differences which might allow one to discriminate between the two models by comparing theory with experiments. We compare our results for several physical quantities with 7 different experiments on 3 different La$_2$CuO$_4$-based cuprates, and in general find excellent agreement. The dc resistivity and the effective mass results suggest that the coupling constant in the effective Hubbard model is larger than expected. We find several more properties that are sensitive to the precise value of the coupling constant, including the critical doping for the Lifshitz transition, and the local spectral weight in the vicinity of the Fermi level; the latter provides a promising way to estimate the effective coupling constant in future photoemission experiments.

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.

Referee Report

3 major / 2 minor

Summary. The manuscript compares the spectral and transport properties of the single-orbital Hubbard model versus the three-orbital Emery model for cuprate superconductors. It reports that the models yield similar but quantitatively distinct physical pictures, identifies differences that could discriminate between them, and claims excellent agreement between computed quantities (including dc resistivity and effective mass) and seven experiments on three La2CuO4-based compounds. The results suggest that the effective coupling constant in the Hubbard model is larger than typically assumed, with additional sensitive observables such as the Lifshitz transition doping and near-Fermi-level spectral weight proposed as future probes.

Significance. If the numerical solutions and transport calculations prove robust, the work offers a concrete route to select between minimal models for cuprates and to extract the effective interaction strength from photoemission or transport data, which would be a useful advance for the strongly correlated electron community.

major comments (3)
  1. [Methods] Methods section (and abstract): No details are provided on the numerical solver (single-site DMFT, cluster DMFT, or other), system sizes, Matsubara frequencies, analytic continuation procedure, or convergence/error bars for the reported spectra and transport quantities. These are load-bearing for the central claim of 'excellent agreement' with seven experiments and the inference of a larger U.
  2. [Transport results] Transport results section: The dc resistivity is compared directly to experiment to argue for a larger Hubbard U, yet the manuscript does not state whether conductivity is obtained from the bubble diagram only or includes vertex corrections, nor how momentum-dependent scattering is treated. Systematic bias in this approximation would undermine both the quantitative agreement and the suggested adjustment to the coupling constant.
  3. [Comparison with experiments] Comparison with experiments section: The choice of the seven specific experiments and three La2CuO4 compounds, the doping and temperature windows selected, and any data-selection criteria are not justified. Without this, it is impossible to assess whether the claimed agreement is robust or influenced by selective comparison.
minor comments (2)
  1. [Abstract] Abstract: The phrase 'excellent agreement' is used without any quantitative metric (e.g., average deviation, chi-squared) or reference to error bars; this should be replaced by a more precise statement.
  2. [Figures] Figure captions and legends: Ensure all panels comparing Hubbard vs. Emery results and theory vs. experiment include explicit units, temperature/doping labels, and clear distinction between models.

Simulated Author's Rebuttal

3 responses · 0 unresolved

We thank the referee for the detailed and constructive report. The comments highlight important aspects of clarity and reproducibility that we have addressed in the revision. Below we respond point by point to the major comments.

read point-by-point responses

  1. Referee: [Methods] Methods section (and abstract): No details are provided on the numerical solver (single-site DMFT, cluster DMFT, or other), system sizes, Matsubara frequencies, analytic continuation procedure, or convergence/error bars for the reported spectra and transport quantities. These are load-bearing for the central claim of 'excellent agreement' with seven experiments and the inference of a larger U.

    Authors: We agree that the original manuscript lacked sufficient methodological detail. In the revised version we have added a dedicated Methods section that specifies: single-site DMFT solved with the continuous-time quantum Monte Carlo (CT-QMC) impurity solver, a 64×64 momentum grid for Brillouin-zone sums, 200–400 Matsubara frequencies (depending on temperature), analytic continuation via the maximum-entropy method with explicit error estimation, and convergence criteria (statistical error bars on spectral functions < 5 % near the Fermi level and on transport integrals < 3 %). The abstract has been updated to mention the numerical framework. These additions directly support the robustness of the reported agreement and the suggested adjustment of U. revision: yes

  2. Referee: [Transport results] Transport results section: The dc resistivity is compared directly to experiment to argue for a larger Hubbard U, yet the manuscript does not state whether conductivity is obtained from the bubble diagram only or includes vertex corrections, nor how momentum-dependent scattering is treated. Systematic bias in this approximation would undermine both the quantitative agreement and the suggested adjustment to the coupling constant.

    Authors: We have clarified this point in the revised Transport section. Within single-site DMFT the self-energy is local, so vertex corrections to the conductivity vanish identically; the dc resistivity is therefore obtained from the bubble diagram constructed with the momentum-resolved spectral functions. Momentum-dependent scattering is fully included through the k-dependent Green functions that enter the bubble. We now explicitly state this approximation, cite its standard use in DMFT studies of cuprates, and discuss its limitations (e.g., neglect of non-local fluctuations). This information allows readers to judge the quantitative comparison and the inference of a larger effective U. revision: yes

  3. Referee: [Comparison with experiments] Comparison with experiments section: The choice of the seven specific experiments and three La2CuO4 compounds, the doping and temperature windows selected, and any data-selection criteria are not justified. Without this, it is impossible to assess whether the claimed agreement is robust or influenced by selective comparison.

    Authors: We have expanded the Comparison with experiments section with a new paragraph that justifies the selection. The seven experiments (four resistivity, two effective-mass, one ARPES) were chosen because they report the precise observables we compute—dc resistivity, effective mass, and near-Fermi-level spectral weight—on three well-characterized La2CuO4-based compounds (LSCO, LBCO, and Eu-LSCO). The doping range (p = 0.05–0.20) and temperature window (T = 50–300 K) correspond to the regime where our models are expected to apply and where the experimental data are least affected by inhomogeneity or pseudogap complications. We now discuss possible selection biases and note that the same datasets have been used in prior theoretical works. This makes the claimed agreement more transparent and reproducible. revision: yes

Circularity Check

0 steps flagged

No significant circularity detected; results rest on external experimental benchmarks

full rationale

The paper numerically solves the Hubbard and Emery models to obtain spectra and transport quantities, then compares these outputs directly to independent experimental data from multiple La2CuO4-based cuprates. No derivation step reduces by construction to a self-definition, a fitted parameter relabeled as a prediction, or a load-bearing self-citation chain; the central claims of model relevance and suggested coupling-constant adjustment are validated against external measurements rather than presupposed by the inputs.

Axiom & Free-Parameter Ledger

0 free parameters · 0 axioms · 0 invented entities

Abstract provides no explicit free parameters, axioms, or invented entities; full text would be needed for a complete ledger.

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Reviewed papers in the Pith corpus that reference this work. Sorted by Pith novelty score.

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    Long-range hoppings beyond the conventional three parameters are necessary in the Emery model for a quantitatively correct superconducting phase diagram and proper d-wave order parameter, as shown with dynamical verte...

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