V. J. Emery and P. W. Anderson's views and related issues regarding the basics of cuprates: a re-look

Navinder Singh

REVIEW 4 major objections 5 minor 1 cited by

V. J. Emery and P. W. Anderson's views and related issues regarding the basics of cuprates: a re-look

T0 review · 4 major / 5 minor · reviewed 2026-08-07 · deepseek-v4-flash

Challenge this review Re-run · record.json Download PDF Read on arXiv ↗

Pith's one-line read Cuprate one-band models fail key experiments

desk verdict A readable perspective reasserting Emery's critique of the Zhang-Rice reduction, but the toy-model argument is flawed and the central claim is not established. read the letter →

arxiv 2505.23200 v2 pith:YLT76VH6 submitted 2025-05-29 cond-mat.supr-con cond-mat.str-el

Navinder Singh This is my paper

classification cond-mat.supr-concond-mat.str-el

keywords cupratesuperconductivityZhang-Ricesingletthree-bandmodelone-bandreductiontwo-componentJohnston-NakanoscalingNMRKnightshiftt-J

verification ladder T0 review T1 audit T2 compute T3 formal

The pith

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

The reading

The paper argues that the standard reduction of the copper-oxide three-band model to an effective one-band model through the Zhang-Rice singlet fails against the experimental record. It reviews thirty-five years of evidence—magnetic susceptibility scaling, NMR Knight shifts, Hall coefficient phenomenology, and numerical studies of quasiparticles and pairing—and concludes that only a description with two distinct electronic components, localized copper spins plus mobile oxygen holes, can account for the data. A simple toy model of a particle hopping between low- and high-energy sites is used to illustrate why a doped hole would prefer extended delocalized resonances over a local singlet. If correct, the minimal description of cuprate planes must retain oxygen degrees of freedom, and one-band t-J type models cannot be treated as equivalent to the three-band model.

What carries the argument

The central object is the Zhang-Rice singlet, a proposed spin-zero composite of a doped oxygen hole bound to a copper d-hole on one CuO2 plaquette. The paper's counter-machinery is a two-component decomposition: the measured susceptibility is the doping-weighted sum of a spin-liquid susceptibility from localized copper moments and a Pauli-like susceptibility from mobile oxygen holes, with the exchange coupling weakening linearly with doping up to x about 0.2. A second piece is a toy tight-binding model on an alternating O/C lattice whose ground state, for |t| much smaller than U, is an extended resonance whose energy decreases as the number of sites in the resonance grows, illustrating why the doped carrier would not settle into a local bound pair.

What would settle it

Run an exact diagonalization or DMRG calculation of a single doped hole in a three-band CuO2 cluster with realistic charge-transfer energy and copper-oxygen exchange included, and look for a bound state whose dominant weight is a local singlet on one Cu-O plaquette; if such a state lies below the extended delocalized states, the toy-model conclusion is wrong. For the two-component claim, a site-selective NMR experiment on LSCO showing that copper and oxygen Knight shifts track a single common susceptibility would falsify it.

Watch

Extended reading notes

Core claim

The central claim is that the Zhang-Rice reduction of the three-band model to a one-band t-J model is not justified. The evidence the paper assembles: the universal Johnston-Nakano scaling of the static spin susceptibility is naturally produced by a spin-liquid component whose exchange coupling weakens with doping plus a Fermi-liquid component; the NMR Knight shifts in LSCO and other compounds require two distinct susceptibilities at copper and oxygen sites, with the single-fluid hyperfine cancellation accidental and violated in some materials; the temperature-dependent Hall coefficient decomposes into a doping-dependent part and a thermally activated part tied to the pseudogap; and numerical studies show that one-band models can reproduce a quasiparticle dispersion for the wrong reasons, while the three-band model reproduces the dispersion even with copper spins frozen. The paper concludes that single-band models fail essential experimental phenomenology and that the two-component, three-band picture is the necessary minimal description of cuprate planes.

Load-bearing premise

The argument's load-bearing premise is that a spinless toy model—which the paper explicitly says ignores spin physics—can show that a doped hole in a real CuO2 plane will not form a local spin singlet; the existence of the Zhang-Rice singlet is defined by spin exchange, so ignoring spin exchange removes the very mechanism being tested.

Editorial extensions

If this is right

If the central claim is right, the one-band t-J family cannot be used as a stand-in for cuprate physics; results obtained from it must be checked against a description that keeps oxygen orbitals explicit.
Johnston-Nakano scaling would be understood as the signature of two components, not of a single electron fluid.
The contrasting copper and oxygen Knight shifts would be expected features of the cuprate plane, and models that predict a single susceptibility would be ruled out by data.
Numerical searches for superconducting order should target three-band models with the charge-transfer gap as a parameter, where pairing appears on both hole- and electron-doped sides.
The pseudogap energy extracted from the Hall effect would coincide with the ARPES pseudogap, supporting mobile carriers on oxygen-derived Fermi arcs.

Reading between the lines

Editorial extensions of the paper, not claims the author makes directly.

Beyond the paper: a direct numerical test of the toy model with spin included—a hole moving on the alternating lattice against a dynamic antiferromagnetic background with spin-fluctuation frequency comparable to the hopping scale—would show whether the extended-resonance ground state survives when spin exchange is no longer ignored.
Beyond the paper: if the two-component reading is right, site-selective probes of copper versus oxygen response should see the spin-liquid component vanish continuously as doping approaches the quantum critical point near x about 0.2, matching the vanishing of the Hall activation term.
Beyond the paper: single-band numerical results on stripe and pair-density-wave order may be artifacts of the reduction rather than intrinsic properties of CuO2 planes, since oxygen degrees of freedom are absent from the outset.

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Editorial analysis

A structured set of objections, weighed in public.

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

Desk Editor's Note

read the letter

This is a review/perspective, not a new result. Its useful core is a synthesis: Barzykin-Pines two-component phenomenology, Berciu's quasiparticle dynamics results, Gor'kov-Teitel'baum Hall analysis, and recent numerical work, all marshaled to argue that the three-band Emery model beats one-band reductions. That synthesis is genuinely helpful and the paper deserves credit for bringing it together.

The paper's own contribution is a toy model meant to show that a doped hole forms extended resonances rather than a local Zhang-Rice singlet. That argument does not work. The model drops spin entirely, even though the ZR singlet is defined by spin exchange between the doped hole and a copper moment. The author admits this in Section IV, so the conclusion that the hole “will not settle in a local singlet” simply does not follow from the model. There is also a quantitative error: Eq. (10) gives an energy that grows linearly with ring size, but for an alternating C-O ring the exact lowest eigenvalue saturates. So the toy model is both logically inadequate and numerically overstated.

That said, the persuasive weight of the paper was never meant to rest on the toy model alone. The external evidence is real and worth engaging: Johnston-Nakano scaling, the strain on the Mila-Rice-Shastry hyperfine scenario, and Berciu's demonstration that one-band and three-band models with matched dispersions have different quasiparticle dynamics. The paper also honestly flags a serious problem for its own side: the LSCO Knight shift data show the opposite assignment from the Barzykin-Pines picture. That is a major caveat, and the author does not hide it.

The citation pattern is acceptable. The author leans on his own earlier critiques, but the main evidence is external. Some of the language is overheated (“dismal failure”), and the conclusion overreaches what the review establishes.

This is a paper for researchers following the one-band versus three-band debate. A serious referee can separate the flawed toy model from the legitimate synthesis. I would not cite it for the toy model, but I would cite it as a compact reference for the phenomenological case against one-band reductions.

Recommendation: send to peer review but require major revision. Drop the toy model or reframe it as motivation, fix Eq. (10), soften the conclusions, and confront the LSCO contradiction head-on. The underlying debate is important and this perspective is worth publishing in revised form.

Referee Report

4 major / 5 minor

Summary. The manuscript re-examines the historical debate between V. J. Emery and P. W. Anderson over whether cuprate superconductivity requires a three-band (or two-component) description rather than a one-band reduction. The author argues that Emery's criticism of the Zhang-Rice singlet reduction was correct, that Barzykin–Pines two-component phenomenology is naturally realized in the three-band Emery model, and that one-band models fail to reproduce NMR Knight shifts, Johnston–Nakano susceptibility scaling, and other experimental features. A simple toy model of a particle hopping on alternating O/C sites is introduced to argue that a doped hole forms extended resonances rather than a local spin singlet. The manuscript concludes that single-band models face a "dismal failure" and that the Emery three-band/two-component picture is the necessary minimal description.

Significance. If the paper's central claim were established, it would challenge a widely used simplification in cuprate theory and support a return to three-band models. The manuscript does provide a useful service by collecting and juxtaposing arguments from Emery, Barzykin–Pines, Gor'kov–Teitel'baum, and recent numerical studies, and it explicitly highlights unresolved tensions in the literature, such as the LSCO Knight-shift contradiction. However, the paper's significance is severely limited by the fact that its novel toy-model argument omits spin while targeting a spin-singlet object, and by a self-admitted experimental contradiction that the author leaves unresolved. The review is largely qualitative: the central quantitative claim, Eq. (10), is incorrect, and the numerical and phenomenological evidence is presented selectively without quantitative checks. The paper therefore does not currently provide a convincing basis for overturning the one-band reduction, even if Emery's position may ultimately be correct for other reasons.

major comments (4)

[Section IV] The toy model cannot decide whether a Zhang-Rice singlet forms, because the model explicitly drops spin. The manuscript states "we have completely ignored the spin physics" in Section IV and then uses the toy model's extended low-energy states to conclude that the hole "will not settle in a local singlet." But the ZR singlet is defined by spin exchange between a doped oxygen hole and a copper moment: with no spin in the Hilbert space there is no singlet channel to form or to fail to form. The conclusion that the hole remains mobile therefore does not follow from the toy model; it is an unsupported assertion about spin physics absent from the calculation.
[Section IV, Eq. (10)] The quantitative claim that a ring resonance has energy λ_- ≈ -(n-2)t^2/U is incorrect for a periodic alternating O/C ring. The exact one-particle spectrum of such a ring is bounded: for an alternating chain with site energies 0 and U and hopping t, the lowest eigenvalue is (U - sqrt(U^2 + 16t^2))/2 ≈ -4t^2/U for all n ≥ 4, not a value that grows linearly with ring size. The paper's own result for the four-site loop, Eq. (7), gives -4t^2/U, which is inconsistent with -(n-2)t^2/U for n=4. Thus the conclusion that "a resonance over very extended sites leads to lower energy" is an artifact of the approximate formula, and the toy model's argument against local singlet formation is not quantitatively valid.
[Section V.C.3] The manuscript itself admits a direct contradiction of its central phenomenological thesis. It states that in the Barzykin–Pines model the copper-site susceptibility is temperature dependent (spin-liquid component) and the oxygen-hole susceptibility is temperature independent (Fermi-liquid component), but "what is seen in the LSCO is just the opposite," and calls this "an important open problem." This is a load-bearing unresolved issue: the conclusion that NMR Knight shifts provide evidence against the single-component picture and in favor of the Emery/Barzykin–Pines two-component picture is not supported by the LSCO data described in the same section. The paper cannot claim an "overwhelming amount of evidence" when its key example contains an admitted contradiction.
[Section VIII] The treatment of numerical studies is selective and does not support the sweeping conclusion that one-band models are a "dismal failure." The section acknowledges that recent DMRG and AFQMC studies of the one-band Hubbard model (ref. [54]) reproduce a superconducting dome on both hole- and electron-doped sides, and that another DMRG study (ref. [55]) finds robust d-wave superconductivity in the t-J model. The paper dismisses these results on the basis of the t-J model's failure to reproduce the quasiparticle dispersion, but does not quantitatively compare the predictive power of one-band versus three-band models on a common footing. A fair assessment would require either a quantitative benchmark or a more nuanced conclusion, rather than labeling all one-band models a "dismal failure."

minor comments (5)

[Throughout] There are numerous typographical errors, including "witch" for "which," "diagnosable" for "diagonalizable," and "Sold Stae Commun." for "Solid State Communications." The paper would benefit from careful proofreading.
[Section II, Eq. (1)] Equation (1) is written informally as "H + T + U..." with missing operator notation and no explicit sum over sites; the Hubbard interaction term is not fully defined. Please write the Hamiltonian in standard notation.
[Section IV, Fig. 4] The figure captions and labels (especially the distinction between "loop" and "star" resonances) are difficult to follow; a clearer diagram with the site basis states labeled explicitly would help.
[Section VI] The summary of Berciu and collaborators' work is presented without a clear citation of the specific numerical parameters or method, making it hard for a reader to verify the claims about spin fluctuations being "less relevant" in the three-band model.
[Section VII] The claim that the GTTA model provides a "lesson" that the temperature-dependent carrier density comes from localized copper spins is asserted rather than derived; the connection to the oxygen sublattice is not made quantitative.

Circularity Check

1 steps flagged · score 2.0 of 10

No significant circularity in the main argument; the central one-band-vs-three-band claim rests on independent experimental and numerical literature, with only a minor supporting self-citation chain in the GTTA section.

other [Section VII, 'Connection between the Gor'kov-Teitel'baum phenomenological model and the three-band Emery model' (GTTA validation paragraph, refs [25] and [26]).]
"The validity of the GTTA model is checked through the deduction of the doping dependent gap Δ(x) purely from the Hall coefficient data and its doping dependence agrees very well with that of the pseudogap obtained from a completely different experiment (ARPES). Thus Δ_GTTA(x) = Δ_PG(x) (for LSCO, refer to[24]; and for other cuprates, refer to[25]). For a brief review of the GTTA model refer to[26]."

For the 'other cuprates' part of the GTTA validation, the paper refers to the author's own later arXiv preprint [25], and for a summary to the author's own review article [26], rather than to an independent external derivation or dataset. This creates a mild self-citation chain in a supporting phenomenological section: the GTTA compatibility argument is partially justified by the author's previous work. However, this section is not the main load-bearing pillar of the paper. The central conclusion that single-band models fail to account for the experimental phenomenology is carried by independent external references (Barzykin-Pines, NMR studies, Berciu et al., and numerical DMRG/QMC works), so this does not amount to meaningful circularity in the overall argument.

full rationale

The paper is a literature-based perspective rather than a derivation with fitted predictors. The Section IV toy model is self-contained: it diagonalizes finite tight-binding clusters and does not fit parameters to the data it is used to interpret. Its acknowledged omission of spin ('we have completely ignored the spin physics') is a validity limitation, not a circular reduction, because the model does not claim to derive Zhang-Rice singlet formation from within a spinful Hilbert space. The Barzykin-Pines two-component decomposition is imported as external cited phenomenology, and interpreting it as evidence against one-band models is an interpretive claim rather than a fitted parameter being renamed as a prediction. Likewise, the Johnston-Nakano scaling and NMR Knight-shift arguments are presented through external experimental and theoretical references. The only self-referential element is the GTTA discussion, where the author's own prior work [25,26] is used to validate the model for 'other cuprates' and to provide a review; this is a minor self-citation that is not load-bearing for the paper's central claim. Therefore the paper exhibits no significant circularity, and the score of 2 reflects only this minor supporting self-citation chain.

Assumptions & free parameters 4 free parameters · 4 assumptions · 0 invented entities

The central claim relies on the toy model's spinless assumption, on the Barzykin-Pines two-component decomposition of susceptibility, and on the Gor'kov-Teitel'baum Hall-effect model. All three carry parameters that are either chosen by hand or fitted to data. The paper introduces no new physical entities.

free parameters (4)

Barzykin-Pines critical doping x_c = 0.2
The spin-liquid weight f(x)=1-x/0.2 drops to zero at x=0.2; this cutoff is fit to susceptibility and NMR data and is load-bearing for the claim that a distinct spin-liquid component exists.
Effective superexchange J = ~1200 K
Used in Eq. (11) as the spin-liquid exchange scale; the doping dependence f(x) is a fitted linear form, not derived from a microscopic model.
GTTA activation parameters n1 and Δ(x) = not stated
In Section VII, the Gor'kov-Teitel'baum model fits Hall coefficient data; the agreement between Δ(x) and the ARPES pseudogap is cited as evidence, but both quantities are extracted by fitting.
Toy model energy ratio U/t = large (|t|<<U)
The toy model assumes U is much larger than t to produce the -n t^2/U energy ordering; this choice is ad hoc and is not taken from cuprate parameters.

assumptions (4)

ad hoc to paper A spinless alternating O/C lattice with site energies 0 and U captures the relevant physics of a doped hole in the CuO2 plane.
Introduced in Section IV; the model excludes spin, yet is used to argue against local spin-singlet formation.
domain assumption The variational calculations of Ebrahimnejad, Sawatzky, and Berciu accurately describe quasiparticle dynamics and justify the three-band model over the one-band model.
Section VI relies on refs [22,23] without independent verification of the variational accuracy.
domain assumption The Barzykin-Pines decomposition of the magnetic susceptibility into spin-liquid and Fermi-liquid components is the correct interpretation of the data.
Section V adopts this phenomenology and uses it as evidence against one-band models; no competing single-band explanation is quantitatively compared.
domain assumption The p to 1+p transition at p*=0.19 marks the disappearance of the localized spin component.
Section V.B invokes the Proust-Taillefer review [11] to connect the vanishing of the spin-liquid component to the pseudogap endpoint.

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Cite this review

Pith. "Pith review of V. J. Emery and P. W. Anderson's views and related issues regarding the basics of cuprates: a re-look." pith.science (2026). https://pith.science/paper/YLT76VH6

@misc{pith2026250523200,
  author       = {Pith},
  title        = {Pith review of: V. J. Emery and P. W. Anderson's views and related issues regarding the basics of cuprates: a re-look},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/YLT76VH6}},
  note         = {Machine review of arXiv:2505.23200}
}

abstract

In 1991, V. J. Emery in his important review article entitled "Some aspects of the theory of high temperature superconductors"\cite{emery1} argued against the Zhang-Rice reduction of three-band to an effective one-band model. In his words "...therefore it seems that the simple $t-J$ model does not account for the properties of high temperature superconductors". Over approximately 35 years after the initial debates\cite{debates} much has happened in the field pertaining to this topic. Even though it is one of the most discussed issue, a comprehensive account and the required resolution are lacking. Connected to the debate over one-band versus three-band models is another discussion: the one-component versus two-component model for cuprates. The two-component model is most strongly advocated by Barzykin and Pines\cite{bp}. In this article the author attempts a perspective and a re-look on some of these issues. After an analysis of a large body of literature, author finds that V. J. Emery's criticism of the Zhang-Rice reduction was correct. Many central experimental features of cuprates cannot be rationalized within the one-band model, and Johnston-Nakano scaling is one such example. Other examples are also discussed. Author introduces a simple-minded toy model to illustrate the core issues involved.

Figures

Figures reproduced from arXiv: 2505.23200 by the authors.

**Figure 2.** FIG. 2. A schematic energy level diagram. [PITH_FULL_IMAGE:figures/full_fig_p002_2.png] view at source ↗

**Figure 3.** FIG. 3. Schematic of the toy model [PITH_FULL_IMAGE:figures/full_fig_p003_3.png] view at source ↗

Figures from the paper (4 more)

**Figure 4.** Figure 4: FIG. 4. Some of the various possible resonances. [PITH_FULL_IMAGE:figures/full_fig_p004_4.png]

**Figure 5.** Figure 5: FIG. 5. Ammonia molecule [PITH_FULL_IMAGE:figures/full_fig_p004_5.png]

**Figure 6.** Figure 6: FIG. 6. Schematic behaviour of the static magnetic suscepti [PITH_FULL_IMAGE:figures/full_fig_p006_6.png]

**Figure 7.** Figure 7: FIG. 7. Schematic behaviour of the quasiparticle dispersion [PITH_FULL_IMAGE:figures/full_fig_p008_7.png]

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Forward citations

Cited by 1 Pith paper

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

On the T-linear resistivity of cuprates: theory
cond-mat.str-el 2025-07 reject novelty 3.0 of 10

With the critical coupling |M(q)|^2 ~ 1/(q^2+ξ^{-2}) and a correlation length ξ(T)~1/T, paramagnon scattering produces T-linear resistivity in the memory-function formalism.

Reference graph

Works this paper leans on

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Or, will it keep running into the lattice without forming any resonance? Or forming a very ex- tended resonance? To analyze the problem, consider each case one by one. 4 |1⟩ |2⟩|3⟩ |4⟩ |5⟩ |1⟩ |2⟩ |1⟩ |2⟩ |3⟩ |1⟩ |2⟩ |3⟩ |4⟩ A B C D Loop StarTwo sites Three sites FIG. 4. Some of the various possible resonances. Case A: Resonating over |1⟩ and |2⟩. Look at...

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Pith tools

Reviewed August 7, 2026 · model on record in the stance chip above.

[1] [54]

Fluctuating intertwined stripes in the strange metal regime of the Hubbard model

E. W. Huang, T. Liu, W. O. Wang, H.-C. Jiang, P. Mai, T. A. Maier, S. Johnston, B. Moritz, and T. P. Dev- ereaux, “Fluctuating intertwined stripes in the strange metal regime of the Hubbard model”, Phys. Rev. B 107, 085126 (2023)

work page 2023

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Intertwined spin, charge, and pair cor- relations in the two-dimensional Hubbard model in the thermodynamic limit

P. Mai, S. Karakuzu, G. Balduzzi, S. Johnston, and T. A. Maier, “Intertwined spin, charge, and pair cor- relations in the two-dimensional Hubbard model in the thermodynamic limit”, Proc. Natl. Acad. Sci. USA 119, e2112806119 (2022)

work page 2022

[3] [1]

Will the particle stay at the initial O-type site, for- ever? (it is sitting in a local minima of energy!)

work page

[4] [2]

Or, will it hop (flit) to C-type site and come back to the original O-type site, and repeat this motion forever (in Linus Pauling’s words, will it set into a ”resonance”)? Figure 4 A

work page

[5] [3]

Or, will it hop to C-type site and rather than com- ing back to the original O-type, it will hop to di- ametrically opposite O-type site and come back again following its original path and repeat the mo- tion (i.e., set in a resonance over three sites O-C-O ( |1⟩, |2⟩, and |3⟩); Figure 4 B)?

work page

[6] [4]

Or, will it set into ”loop” kind of resonance? Or a ”star” kind of resonance (Figure 4 C and D)

work page

[7] [5]

flip- flops

Or, will it keep running into the lattice without forming any resonance? Or forming a very ex- tended resonance? To analyze the problem, consider each case one by one. 4 |1⟩ |2⟩|3⟩ |4⟩ |5⟩ |1⟩ |2⟩ |1⟩ |2⟩ |3⟩ |1⟩ |2⟩ |3⟩ |4⟩ A B C D Loop StarTwo sites Three sites FIG. 4. Some of the various possible resonances. Case A: Resonating over |1⟩ and |2⟩. Look at...

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[8] [6]

χ(T,x) TTmax(x1) χmax(x1) dopingx1 x2>x1 dopingx2 Tmax(x2) χmax(x2) 0 FIG

Static magnetic susceptibility and the Johnston-Nakano scaling At a given doping p <0.2 the static bulk spin suscep- tibility schematically looks like (figure 6). χ(T,x) TTmax(x1) χmax(x1) dopingx1 x2>x1 dopingx2 Tmax(x2) χmax(x2) 0 FIG. 6. Schematic behaviour of the static magnetic suscepti- bility as a function of temperature in the underdoped regime. C...

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