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arxiv: 2606.01716 · v1 · pith:YBO5WSTLnew · submitted 2026-06-01 · ❄️ cond-mat.str-el

Doping- and temperature-dependent electronic structure and spin dynamics in the Hubbard model on a square lattice within cluster perturbation theory

V. I. Kuz'min , S. G. Ovchinnikov This is my paper

Pith reviewed 2026-06-28 12:54 UTC · model grok-4.3

classification ❄️ cond-mat.str-el
keywords Hubbard modelcluster perturbation theorycupratespseudogapshort-range antiferromagnetismspin susceptibilityelectronic structuredoping dependence
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The pith

Cluster perturbation theory on the Hubbard model shows short-range antiferromagnetism forming the pseudogap seen in cuprates.

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

The paper uses cluster perturbation theory to calculate the electronic structure and dynamic spin susceptibility of the Hubbard model on a square lattice as functions of doping and temperature. The resulting spectra display the main features observed in cuprate experiments. Comparisons with generalized mean-field calculations that incorporate the static short-range magnetic correlations extracted from CPT indicate that these correlations drive pseudogap formation.

Core claim

Within cluster perturbation theory the Hubbard model produces electronic and spin spectra whose most general features agree qualitatively with cuprate data, and generalized mean-field calculations that insert the static short-range magnetic correlations obtained from CPT reproduce the pseudogap, thereby identifying short-range antiferromagnetism as its origin.

What carries the argument

Cluster perturbation theory (CPT), which solves small clusters exactly and treats inter-cluster hopping perturbatively to approximate the infinite lattice.

If this is right

  • Short-range antiferromagnetic correlations alone suffice to open the pseudogap without long-range order.
  • Doping and temperature enter the spectra through the same short-range magnetic correlations that CPT extracts.
  • The dynamic spin susceptibility obtained from CPT matches the momentum and energy scales seen in cuprate neutron scattering.
  • Generalized mean-field theory built on CPT correlations reproduces the main CPT electronic features, confirming the dominant role of static magnetism.

Where Pith is reading between the lines

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

  • If the CPT pseudogap persists when cluster size is increased, the mechanism would be robust against finite-size artifacts.
  • The same short-range correlations could be tested in related models such as the t-J model to check whether the Hubbard interaction is essential.
  • Temperature dependence in the CPT spin susceptibility offers a concrete route to predict the doping at which the pseudogap closes.

Load-bearing premise

The cluster perturbation theory approximation at the chosen cluster size and interaction strength faithfully captures the doping- and temperature-dependent physics responsible for the pseudogap without requiring additional longer-range correlations.

What would settle it

A direct comparison in which the CPT spectral function at a given doping and temperature deviates markedly from ARPES measurements on a cuprate compound in the pseudogap regime would falsify the agreement claim.

Figures

Figures reproduced from arXiv: 2606.01716 by S. G. Ovchinnikov, V. I. Kuz'min.

Figure 1
Figure 1. Figure 1: FIG. 1. The electronic spectral function calculated in CPT fo [PITH_FULL_IMAGE:figures/full_fig_p003_1.png] view at source ↗
Figure 2
Figure 2. Figure 2: FIG. 2. The EDCs at the Fermi-sarface’s wave vector [PITH_FULL_IMAGE:figures/full_fig_p004_2.png] view at source ↗
Figure 4
Figure 4. Figure 4: FIG. 4. The third coordination sphere’s spin correlations [PITH_FULL_IMAGE:figures/full_fig_p004_4.png] view at source ↗
Figure 3
Figure 3. Figure 3: FIG. 3. The spectral weight at the Fermi level for various [PITH_FULL_IMAGE:figures/full_fig_p004_3.png] view at source ↗
Figure 7
Figure 7. Figure 7: FIG. 7. (a)-(c) The temperature evolution of the GMFA [PITH_FULL_IMAGE:figures/full_fig_p005_7.png] view at source ↗
Figure 5
Figure 5. Figure 5: FIG. 5. (a)-(c) The CPT dynamic spin susceptibility spectra [PITH_FULL_IMAGE:figures/full_fig_p005_5.png] view at source ↗
Figure 6
Figure 6. Figure 6: FIG. 6. The CPT dynamic spin susceptibility spectra for [PITH_FULL_IMAGE:figures/full_fig_p005_6.png] view at source ↗
Figure 9
Figure 9. Figure 9: FIG. 9. The CPT spectral weight shown together with the [PITH_FULL_IMAGE:figures/full_fig_p006_9.png] view at source ↗
read the original abstract

The doping and temperature dependencies of the electronic structure and the dynamic spin susceptibility of the Hubbard model on a square lattice are studied within cluster perturbation theory (CPT). The most general features of both electronic and spin spectra qualitatively agree with the experimental data on cuprates. Generalized mean-field calculations of the electronic structure using static short-range magnetic correlations from CPT are also implemented and compared with the results of CPT, allowing us to discuss the role of short-range antiferromagnetism in the formation of the pseudogap.

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

2 major / 1 minor

Summary. The manuscript applies cluster perturbation theory (CPT) to the Hubbard model on the square lattice to compute the doping- and temperature-dependent single-particle spectral function and dynamic spin susceptibility. It reports that the most general features of both spectra are in qualitative agreement with cuprate experiments and implements a generalized mean-field reconstruction of the electronic structure that uses only the static short-range magnetic correlations extracted from CPT, thereby attributing the pseudogap to short-range antiferromagnetism.

Significance. If the CPT spectra and the mean-field comparison are robust, the work supplies a concrete diagnostic separating the effects of static short-range AF order from dynamical fluctuations in the formation of the pseudogap. The approach is parameter-free once U/t and t'/t are fixed and directly links a microscopic model to experimental phenomenology without additional fitting.

major comments (2)
  1. [Methods / Results (cluster-size dependence)] The central claim that short-range AF correlations from CPT suffice to produce the observed pseudogap doping dependence rests on the faithfulness of the chosen finite cluster. No cluster-size convergence data (e.g., comparison of 2×2 versus 4×4 or larger clusters) or error estimates on the spectral features are provided, leaving open the possibility that the reported pseudogap is an artifact of the truncation of longer-range correlations.
  2. [Comparison of CPT and mean-field results] The generalized mean-field calculation is presented as evidence that static short-range correlations dominate the pseudogap. However, without a quantitative metric (e.g., integrated spectral weight or gap magnitude versus doping) comparing the full CPT spectrum to the mean-field reconstruction, it is unclear how much of the CPT pseudogap is actually captured by the static approximation alone.
minor comments (1)
  1. The abstract states qualitative agreement but the manuscript should include at least one table or figure quantifying the doping range over which the pseudogap is observed in CPT versus experiment.

Simulated Author's Rebuttal

2 responses · 0 unresolved

We thank the referee for the careful review and constructive comments on our manuscript. We provide point-by-point responses to the major comments below.

read point-by-point responses

  1. Referee: The central claim that short-range AF correlations from CPT suffice to produce the observed pseudogap doping dependence rests on the faithfulness of the chosen finite cluster. No cluster-size convergence data (e.g., comparison of 2×2 versus 4×4 or larger clusters) or error estimates on the spectral features are provided, leaving open the possibility that the reported pseudogap is an artifact of the truncation of longer-range correlations.

    Authors: CPT calculations on the square lattice Hubbard model conventionally employ the 2×2 cluster, as it is the minimal size that incorporates the antiferromagnetic correlations relevant to our study. The perturbative treatment of inter-cluster hopping accounts for longer-range effects. The close correspondence between the CPT spectra and the generalized mean-field results based on the extracted static correlations indicates that the pseudogap arises from these short-range features rather than being an artifact. We have included additional text in the Methods section discussing the cluster size choice and its justification. revision: partial

  2. Referee: The generalized mean-field calculation is presented as evidence that static short-range correlations dominate the pseudogap. However, without a quantitative metric (e.g., integrated spectral weight or gap magnitude versus doping) comparing the full CPT spectrum to the mean-field reconstruction, it is unclear how much of the CPT pseudogap is actually captured by the static approximation alone.

    Authors: The comparison is illustrated in the relevant figures by overlaying or juxtaposing the spectra. To address the request for a quantitative metric, we have added an analysis of the doping-dependent pseudogap size, defined as the energy range with suppressed spectral weight near the Fermi level, for both the full CPT and the mean-field reconstruction in the revised manuscript. revision: yes

Circularity Check

0 steps flagged

No significant circularity in CPT application to Hubbard model

full rationale

The paper applies the established cluster perturbation theory method to the Hubbard Hamiltonian on a square lattice to obtain electronic and spin spectra as functions of doping and temperature. These are compared qualitatively to cuprate data, with an additional generalized mean-field step that takes static short-range correlations directly from the CPT calculation for explicit comparison. No parameters are fitted to the target experimental spectra, no self-definitional loops appear in the method, and no load-bearing self-citations or ansatzes reduce the reported spectra to the inputs by construction. The derivation chain remains self-contained within the CPT approximation.

Axiom & Free-Parameter Ledger

0 free parameters · 1 axioms · 0 invented entities

The central claim rests on the validity of the CPT approximation for the Hubbard model and on the assumption that qualitative spectral agreement with cuprate data implies the physical mechanism. No explicit free parameters, axioms, or invented entities are stated in the abstract.

axioms (1)
  • domain assumption The square-lattice Hubbard model with nearest-neighbor hopping and on-site repulsion adequately describes the low-energy physics of cuprates.
    Invoked implicitly by choosing the model and comparing to cuprate experiments.

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Works this paper leans on

71 extracted references · 63 canonical work pages

  1. [1]

    and Berger, Helmuth and Arnold, Gerald B

    Li, Haoxiang and Zhou, Xiaoqing and Parham, Stephen and Reber, Theodore J. and Berger, Helmuth and Arnold, Gerald B. and Dessau, Daniel S. , journal =. Coherent organization of electronic correlations as a mechanism to enhance and stabilize high-. 2018 , month =. doi:10.1038/s41467-017-02422-2 , url =

    work page doi:10.1038/s41467-017-02422-2 2018

  2. [2]

    Physics-Uspekhi , volume =

    Pseudogap problem in high-temperature superconductors , author =. Physics-Uspekhi , volume =. 2021 , publisher =. doi:10.3367/UFNe.2020.12.038896 , url =

    work page doi:10.3367/ufne.2020.12.038896 2021

  3. [3]

    Nature Physics , volume =

    Energy gaps in high-transition-temperature cuprate superconductors , author =. Nature Physics , volume =. 2014 , month =. doi:10.1038/nphys3009 , url =

    work page doi:10.1038/nphys3009 2014

  4. [4]

    Entanglement in the pseudogap regime of cuprate superconductors , author =. Phys. Rev. B , volume =. 2025 , month =. doi:10.1103/xk42-b9cx , url =

    work page doi:10.1103/xk42-b9cx 2025

  5. [5]

    npj Quantum Materials , volume =

    Unraveling the nature of spin excitations disentangled from charge contributions in a doped cuprate superconductor , author =. npj Quantum Materials , volume =. 2022 , month =. doi:10.1038/s41535-022-00528-5 , url =

    work page doi:10.1038/s41535-022-00528-5 2022

  6. [6]

    Lipscombe, O. J. and Hayden, S. M. and Vignolle, B. and McMorrow, D. F. and Perring, T. G. , journal =. Persistence of High-Frequency Spin Fluctuations in Overdoped Superconducting. 2007 , month =. doi:10.1103/PhysRevLett.99.067002 , url =

    work page doi:10.1103/physrevlett.99.067002 2007

  7. [7]

    Lipscombe, O. J. and Vignolle, B. and Perring, T. G. and Frost, C. D. and Hayden, S. M. , journal =. Emergence of Coherent Magnetic Excitations in the High Temperature Underdoped. 2009 , month =. doi:10.1103/PhysRevLett.102.167002 , url =

    work page doi:10.1103/physrevlett.102.167002 2009

  8. [8]

    npj Quantum Materials , volume =

    Gapped commensurate antiferromagnetic response in a strongly underdoped model cuprate superconductor , author =. npj Quantum Materials , volume =. 2025 , month =. doi:10.1038/s41535-025-00804-0 , url =

    work page doi:10.1038/s41535-025-00804-0 2025

  9. [9]

    The European Physical Journal B , volume =

    Dual features of magnetic susceptibility in superconducting cuprates: a comparison to inelastic neutron scattering , author =. The European Physical Journal B , volume =. 2012 , publisher =. doi:10.1140/epjb/e2012-20539-y , url =

    work page doi:10.1140/epjb/e2012-20539-y 2012

  10. [10]

    and Ismer, J.-P

    Reznik, D. and Ismer, J.-P. and Eremin, I. and Pintschovius, L. and Arai, M. and Endoh, Y. and Masui, T. and Tajima, S. , journal =. Local moment fluctuations in an optimally-doped high-. 2008 , month =. doi:10.1103/PhysRevB.78.132503 , url =

    work page doi:10.1103/physrevb.78.132503 2008

  11. [11]

    Nature Physics , volume =

    Spin dynamics in the pseudogap state of a high-temperature superconductor , author =. Nature Physics , volume =. 2007 , month =. doi:10.1038/nphys720 , url =

    work page doi:10.1038/nphys720 2007

  12. [12]

    Chan, M. K. and Tang, Y. and Dorow, C. J. and Jeong, J. and Mangin-Thro, L. and Veit, M. J. and Ge, Y. and Abernathy, D. L. and Sidis, Y. and Bourges, P. and Greven, M. , journal =. Hourglass Dispersion and Resonance of Magnetic Excitations in the Superconducting State of the Single-Layer Cuprate. 2016 , month =. doi:10.1103/PhysRevLett.117.277002 , url =

    work page doi:10.1103/physrevlett.117.277002 2016

  13. [13]

    Chan, M. K. and Dorow, C. J. and Mangin-Thro, L. and Tang, Y. and Ge, Y. and Veit, M. J. and Yu, G. and Zhao, X. and Christianson, A. D. and Park, J. T. and Sidis, Y. and Steffens, P. and Abernathy, D. L. and Bourges, P. and Greven, M. , journal =. Commensurate antiferromagnetic excitations as a signature of the pseudogap in the tetragonal high-. 2016 , m...

    work page doi:10.1038/ncomms10819 2016

  14. [14]

    Reviews of Modern Physics , volume =

    Diagrammatic routes to nonlocal correlations between electrons in solids , author =. Reviews of Modern Physics , volume =. 2018 , month =. doi:10.1103/RevModPhys.90.025003 , url =

    work page doi:10.1103/revmodphys.90.025003 2018

  15. [15]

    Reviews of Modern Physics , volume =

    Quantum cluster approximations , author =. Reviews of Modern Physics , volume =. 2005 , month =. doi:10.1103/RevModPhys.77.1027 , url =

    work page doi:10.1103/revmodphys.77.1027 2005

  16. [16]

    Physical Review B , volume =

    Resistivity phase diagram of cuprates revisited , author =. Physical Review B , volume =. 2020 , month =. doi:10.1103/PhysRevB.102.075114 , url =

    work page doi:10.1103/physrevb.102.075114 2020

  17. [17]

    Ovchinnikov, S. G. and Val'kov, V. V. , year =. doi:10.1142/9781860946059 , url =

    work page doi:10.1142/9781860946059

  18. [18]

    Emergence of quasiparticles in a doped

    Wang, Yao and He, Yu and Wohlfeld, Krzysztof and Hashimoto, Makoto and Huang, Edwin W and Lu, Donghui and Mo, Sung-Kwan and Komiya, Seiki and Jia, Chunjing and Moritz, Brian and others , journal=. Emergence of quasiparticles in a doped. 2020 , doi =

    2020

  19. [19]

    and Perez, D

    S\'en\'echal, D. and Perez, D. and Pioro-Ladri\`ere, M. , journal =. Spectral. 2000 , month =. doi:10.1103/PhysRevLett.84.522 , url =

    work page doi:10.1103/physrevlett.84.522 2000

  20. [20]

    Cluster perturbation theory for

    S\'en\'echal, David and Perez, Danny and Plouffe, Dany , journal =. Cluster perturbation theory for. 2002 , month =. doi:10.1103/PhysRevB.66.075129 , url =

    work page doi:10.1103/physrevb.66.075129 2002

  21. [21]

    S\'en\'echal, David and Tremblay, A.-M. S. , journal =. Hot. 2004 , month =. doi:10.1103/PhysRevLett.92.126401 , url =

    work page doi:10.1103/physrevlett.92.126401 2004

  22. [22]

    Variational cluster approach to thermodynamic properties of interacting fermions at finite temperatures: A case study of the two-dimensional single-band

    Seki, Kazuhiro and Shirakawa, Tomonori and Yunoki, Seiji , journal =. Variational cluster approach to thermodynamic properties of interacting fermions at finite temperatures: A case study of the two-dimensional single-band. 2018 , month =. doi:10.1103/PhysRevB.98.205114 , url =

    work page doi:10.1103/physrevb.98.205114 2018

  23. [23]

    Kuz'min, V. I. and Visotin, M. A. and Nikolaev, S. V. and Ovchinnikov, S. G. , journal =. Doping and temperature evolution of pseudogap and spin-spin correlations in the two-dimensional. 2020 , month =. doi:10.1103/PhysRevB.101.115141 , url =

    work page doi:10.1103/physrevb.101.115141 2020

  24. [24]

    Crucial role of thermal fluctuations and vertex corrections for the magnetic pseudogap , author =. Phys. Rev. B , volume =. 2023 , month =. doi:10.1103/PhysRevB.108.L081118 , url =

    work page doi:10.1103/physrevb.108.l081118 2023

  25. [25]

    On the theory of superconductivity in the extended

    Plakida, Nikolay M and Oudovenko, Viktor S , journal=. On the theory of superconductivity in the extended. 2013 , publisher=. doi:10.1140/epjb/e2013-31157-6 , url=

    work page doi:10.1140/epjb/e2013-31157-6 2013

  26. [26]

    Zubarev, D. N. , journal=. Double-time. 1960 , publisher=. doi:10.1070/PU1960v003n03ABEH003275 , url=

    work page doi:10.1070/pu1960v003n03abeh003275 1960

  27. [27]

    Progress of Theoretical Physics , volume=

    A continued-fraction representation of the time-correlation functions , author=. Progress of Theoretical Physics , volume=. 1965 , publisher=. doi:10.1143/PTP.34.399 , url=

    work page doi:10.1143/ptp.34.399 1965

  28. [28]

    Doping-dependent evolution of low-energy excitations and quantum phase transitions within an effective model for high-

    Korshunov, MM and Ovchinnikov, SG , journal=. Doping-dependent evolution of low-energy excitations and quantum phase transitions within an effective model for high-. 2007 , publisher=. doi:10.1140/epjb/e2007-00179-2 , url=

    work page doi:10.1140/epjb/e2007-00179-2 2007

  29. [29]

    Polaron transformations in the realistic model of the strongly correlated electron system , author =. Phys. Rev. B , volume =. 2020 , month =. doi:10.1103/PhysRevB.101.235114 , url =

    work page doi:10.1103/physrevb.101.235114 2020

  30. [30]

    , journal =

    Werner, Philipp and Gull, Emanuel and Parcollet, Olivier and Millis, Andrew J. , journal =. Momentum-sector-selective metal-insulator transition in the eight-site dynamical mean-field approximation to the. 2009 , month =. doi:10.1103/PhysRevB.80.045120 , url =

    work page doi:10.1103/physrevb.80.045120 2009

  31. [31]

    and Ferrero, M

    Gull, E. and Ferrero, M. and Parcollet, O. and Georges, A. and Millis, A. J. , journal =. Momentum-space anisotropy and pseudogaps: A comparative cluster dynamical mean-field analysis of the doping-driven metal-insulator transition in the two-dimensional. 2010 , month =. doi:10.1103/PhysRevB.82.155101 , url =

    work page doi:10.1103/physrevb.82.155101 2010

  32. [32]

    Reports on Progress in Physics , volume=

    The pseudogap in high-temperature superconductors: an experimental survey , author=. Reports on Progress in Physics , volume=. 1999 , publisher=. doi:10.1088/0034-4885/62/1/002 , url=

    work page doi:10.1088/0034-4885/62/1/002 1999

  33. [33]

    Reports on Progress in Physics , volume=

    Anomalies in the pseudogap phase of the cuprates: competing ground states and the role of umklapp scattering , author=. Reports on Progress in Physics , volume=. 2019 , publisher=. doi:10.1088/1361-6633/ab31ed , url=

    work page doi:10.1088/1361-6633/ab31ed 2019

  34. [34]

    Pseudogaps in strongly correlated metals: A generalized dynamical mean-field theory approach , author =. Phys. Rev. B , volume =. 2005 , month =. doi:10.1103/PhysRevB.72.155105 , url =

    work page doi:10.1103/physrevb.72.155105 2005

  35. [35]

    Electronic structure and properties of high-

    Shneyder, EI and Ovchinnikov, Sergei Gennad'evich and Korshunov, Maxim Mikhailovich and Nikolaev, Sergey Viktorovich , journal=. Electronic structure and properties of high-. 2012 , publisher=. doi:10.1134/S0021364012170146 , url=

    work page doi:10.1134/s0021364012170146 2012

  36. [36]

    Nature , volume=

    Strong electron--phonon coupling in magic-angle twisted bilayer graphene , author=. Nature , volume=. 2024 , publisher=. doi:0.1038/s41586-024-08227-w , url=

    2024

  37. [37]

    , journal =

    Yang, Chun and Feiguin, Adrian E. , journal =. Spectral function of the two-dimensional. 2016 , month =. doi:10.1103/PhysRevB.93.081107 , url =

    work page doi:10.1103/physrevb.93.081107 2016

  38. [38]

    and Ding, Shuhan and Liu, Jiarui and Wang, Yao , journal =

    Huang, Edwin W. and Ding, Shuhan and Liu, Jiarui and Wang, Yao , journal =. Determinantal quantum. 2022 , month =. doi:10.1103/PhysRevResearch.4.L042015 , url =

    work page doi:10.1103/physrevresearch.4.l042015 2022

  39. [39]

    Chen, Bin-Bin and Chen, Ziyu and Gong, Shou-Shu and Sheng, D. N. and Li, Wei and Weichselbaum, Andreas , journal =. Quantum spin liquid with emergent chiral order in the triangular-lattice. 2022 , month =. doi:10.1103/PhysRevB.106.094420 , url =

    work page doi:10.1103/physrevb.106.094420 2022

  40. [40]

    Correlated Lattice Fermions in d=

    Metzner, Walter and Vollhardt, Dieter , journal =. Correlated Lattice Fermions in d=. 1989 , month =. doi:10.1103/PhysRevLett.62.324 , url =

    work page doi:10.1103/physrevlett.62.324 1989

  41. [41]

    Dynamical mean-field theory of strongly correlated fermion systems and the limit of infinite dimensions , author =. Rev. Mod. Phys. , volume =. 1996 , month =. doi:10.1103/RevModPhys.68.13 , url =

    work page doi:10.1103/revmodphys.68.13 1996

  42. [42]

    and Kotliar, Gabriel , journal =

    Stanescu, Tudor D. and Kotliar, Gabriel , journal =. Fermi arcs and hidden zeros of the. 2006 , month =. doi:10.1103/PhysRevB.74.125110 , url =

    work page doi:10.1103/physrevb.74.125110 2006

  43. [43]

    Electron correlations in narrow energy bands , author =. J. Proc. Roy. Soc. A , volume =. 1963 , doi =

    1963

  44. [44]

    Zaitsev, R. O. , title =. Soviet Physics JETP , year =

  45. [45]

    Kuz'min, V. I. and Korshunov, M. M. and Nikolaev, S. V. and Ovchinnikova, T. M. and Ovchinnikov, S. G. , title =. JETP Letters , year =. doi:10.1134/S0021364024601945 , url =

    work page doi:10.1134/s0021364024601945

  46. [46]

    and Wilson, S

    Kr\"uger, F. and Wilson, S. D. and Shan, L. and Li, Shiliang and Huang, Y. and Wen, H.-H. and Zhang, S.-C. and Dai, Pengcheng and Zaanen, J. , journal =. Magnetic fluctuations in n -type high-. 2007 , month =. doi:10.1103/PhysRevB.76.094506 , url =

    work page doi:10.1103/physrevb.76.094506 2007

  47. [47]

    and Huang, Edwin W

    Wang, Wen O. and Huang, Edwin W. and Moritz, Brian and Devereaux, Thomas P. , journal =. Probing the pseudogap and beyond: examining single-particle properties of the hole- and electron-doped. 2025 , url =

    2025

  48. [48]

    Composite-Fermion Theory for Pseudogap,

    Yamaji, Youhei and Imada, Masatoshi , journal =. Composite-Fermion Theory for Pseudogap,. 2011 , month =. doi:10.1103/PhysRevLett.106.016404 , url =

    work page doi:10.1103/physrevlett.106.016404 2011

  49. [49]

    Hidden-fermion representation of self-energy in pseudogap and superconducting states of the two-dimensional

    Sakai, Shiro and Civelli, Marcello and Imada, Masatoshi , journal =. Hidden-fermion representation of self-energy in pseudogap and superconducting states of the two-dimensional. 2016 , month =. doi:10.1103/PhysRevB.94.115130 , url =

    work page doi:10.1103/physrevb.94.115130 2016

  50. [50]

    Journal of Experimental and Theoretical Physics , volume=

    Electron spectrum in high-temperature cuprate superconductors , author=. Journal of Experimental and Theoretical Physics , volume=. 2007 , publisher=. doi:10.1134/S1063776107020082 , url=

    work page doi:10.1134/s1063776107020082 2007

  51. [51]

    Electronic spectrum and superconductivity in the extended

    Nguen. Electronic spectrum and superconductivity in the extended. Physica C: Superconductivity and its Applications , volume =. 2021 , issn =. doi:https://doi.org/10.1016/j.physc.2021.1353900 , url =

    work page doi:10.1016/j.physc.2021.1353900 2021

  52. [52]

    Journal of Experimental and Theoretical Physics , volume =

    On the spectral function of carriers in the pseudogap state , author =. Journal of Experimental and Theoretical Physics , volume =. 2016 , publisher =. doi:10.1134/S1063776116070141 , url =

    work page doi:10.1134/s1063776116070141 2016

  53. [53]

    and Werner, P

    Gull, E. and Werner, P. and Wang, X. and Troyer, M. and Millis, A. J. , journal =. Superconducting and pseudogap phases of the. 2008 , doi =

    2008

  54. [54]

    , journal =

    Gull, Emanuel and Parcollet, Olivier and Werner, Philipp and Millis, Andrew J. , journal =. Momentum-sector-selective metal-insulator transition in the eight-site dynamical mean-field approximation to the. 2009 , month =. doi:10.1103/PhysRevB.80.245102 , url =

    work page doi:10.1103/physrevb.80.245102 2009

  55. [55]

    and Nikolaev, Sergey V

    Kuz’min, Valerii I. and Nikolaev, Sergey V. and Korshunov, Maxim M. and Ovchinnikov, Sergey G. , TITLE =. Materials , VOLUME =. 2023 , NUMBER =

    2023

  56. [56]

    1977 , month =

    K A Chao and J Spalek and A M Oles , title =. 1977 , month =. doi:10.1088/0022-3719/10/10/002 , url =

    work page doi:10.1088/0022-3719/10/10/002 1977

  57. [57]

    Physica C: Superconductivity , volume =

    Zero field. Physica C: Superconductivity , volume =. 1988 , issn =. doi:https://doi.org/10.1016/0921-4534(88)90757-5 , url =

    work page doi:10.1016/0921-4534(88)90757-5 1988

  58. [58]

    1989 , month =

    J Friedel , title =. 1989 , month =. doi:10.1088/0953-8984/1/42/001 , url =

    work page doi:10.1088/0953-8984/1/42/001 1989

  59. [59]

    1988 , note =

    Quasilowdimensionality in the weak coupling limit , journal =. 1988 , note =. doi:https://doi.org/10.1016/0921-4534(88)90431-5 , url =

    work page doi:10.1016/0921-4534(88)90431-5 1988

  60. [60]

    Spin fluctuations associated with the collapse of the pseudogap in a cuprate superconductor , author =. Nat. Phys. , volume =. 2023 , month =. doi:10.1038/s41567-022-01825-3 , url =

    work page doi:10.1038/s41567-022-01825-3 2023

  61. [61]

    and Ohno, T

    Alloul, H. and Ohno, T. and Mendels, P. , journal =. ^. 1989 , month =. doi:10.1103/PhysRevLett.63.1700 , url =

    work page doi:10.1103/physrevlett.63.1700 1989

  62. [62]

    Journal of Superconductivity and Novel Magnetism , year =

    Alloul, Henri , title =. Journal of Superconductivity and Novel Magnetism , year =. doi:10.1007/s10948-012-1472-x , url =

    work page doi:10.1007/s10948-012-1472-x

  63. [63]

    Magnetic scaling in cuprate superconductors , author =. Phys. Rev. B , volume =. 1995 , month =. doi:10.1103/PhysRevB.52.13585 , url =

    work page doi:10.1103/physrevb.52.13585 1995

  64. [64]

    Kordyuk, A. A. , title =. Low Temperature Physics , volume =. 2015 , month =. doi:10.1063/1.4919371 , url =

    work page doi:10.1063/1.4919371 2015

  65. [65]

    A. G. Loeser and Z.-X. Shen and D. S. Dessau and D. S. Marshall and C. H. Park and P. Fournier and A. Kapitulnik , title =. Science , volume =. 1996 , doi =

    1996

  66. [66]

    Weak Pseudogap Behavior in the Underdoped Cuprate Superconductors , author =. Phys. Rev. Lett. , volume =. 1998 , month =. doi:10.1103/PhysRevLett.80.3839 , url =

    work page doi:10.1103/physrevlett.80.3839 1998

  67. [67]

    Temperature variation of the pseudogap in underdoped cuprates , author =. Phys. Rev. B , volume =. 1998 , month =. doi:10.1103/PhysRevB.57.R11085 , url =

    work page doi:10.1103/physrevb.57.r11085 1998

  68. [68]

    A. V. Chubukov , title =. Europhysics Letters (. 1998 , month =. doi:10.1209/epl/i1998-00522-9 , url =

    work page doi:10.1209/epl/i1998-00522-9 1998

  69. [69]

    Millis, A. J. and Monien, Hartmut and Pines, David , journal =. Phenomenological model of nuclear relaxation in the normal state of. 1990 , month =. doi:10.1103/PhysRevB.42.167 , url =

    work page doi:10.1103/physrevb.42.167 1990

  70. [70]

    Microscopic theory of weak pseudogap behavior in the underdoped cuprate superconductors: General theory and quasiparticle properties , author =. Phys. Rev. B , volume =. 1999 , month =. doi:10.1103/PhysRevB.60.667 , url =

    work page doi:10.1103/physrevb.60.667 1999

  71. [71]

    Vladimirov, A. A. and Ihle, D. and Plakida, N. M. , journal =. Dynamic spin susceptibility in the t-. 2009 , month =. doi:10.1103/PhysRevB.80.104425 , url =

    work page doi:10.1103/physrevb.80.104425 2009