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arxiv: 2512.15437 · v2 · submitted 2025-12-17 · ❄️ cond-mat.str-el

Functional renormalization group for extremely correlated electrons

Jonas Arnold , Peter Kopietz , Andreas R\"uckriegel This is my paper

Pith reviewed 2026-05-16 21:40 UTC · model grok-4.3

classification ❄️ cond-mat.str-el
keywords functional renormalization groupHubbard modelinfinite U limitprojected Hilbert spaceLuttinger's theoremNagaoka ferromagnetismstrongly correlated electronsbad metal
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The pith

In the infinite-U Hubbard model, strong renormalization collapses the bandwidth and violates Luttinger's theorem at moderate densities.

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

This work introduces a strong-coupling functional renormalization group technique for the Hubbard model at infinite on-site repulsion, where the Hilbert space is projected to exclude double occupancies and only kinematic interactions survive. Non-canonical operators enforce the projection while the flow equations track the evolution of the single-particle spectrum under nearest-neighbor hopping on the square lattice. The calculation shows that the bandwidth and quasiparticle residue shrink markedly with rising electron density, damping increases, and a polaronic continuum appears below the main band in the hole sector. Fermi-liquid behavior persists only at low densities in the paramagnetic regime; at higher fillings the system enters a bad-metal state with pronounced magnetic correlations that favor Nagaoka ferromagnetism at very high density and stripe antiferromagnetism at intermediate densities. Both paramagnetic and ferromagnetic solutions exhibit clear violations of Luttinger's theorem.

Core claim

The central claim is that a truncated strong-coupling functional renormalization group flow, formulated with non-canonical operators in the projected Hilbert space, produces a density-dependent renormalization of the electronic spectrum in the infinite-U Hubbard model. Bandwidth and quasiparticle weight decrease while damping and particle-hole asymmetry grow, a polaronic hole continuum emerges, and Luttinger's theorem is violated in both paramagnetic and ferromagnetic regimes, with the ground state indicated to be the Nagaoka ferromagnet at high densities and a stripe antiferromagnet at intermediate densities.

What carries the argument

The strong-coupling functional renormalization group flow equations applied to non-canonical fermionic operators that represent electrons in the Hilbert space projected to no double occupancies.

If this is right

  • Quasiparticle residue and bandwidth both decrease steadily with increasing electron density.
  • A polaronic continuum of states appears below the quasiparticle band in the hole-doped sector.
  • Luttinger's theorem is violated in the paramagnetic phase and in the ferromagnetic regime.
  • Magnetic correlations strengthen with density, indicating a crossover to Nagaoka ferromagnetism at high filling and possible stripe antiferromagnetism at intermediate filling.

Where Pith is reading between the lines

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

  • The same projected-operator approach could be extended to the t-J model or to lattices with longer-range hopping to test whether Luttinger violation is generic.
  • If the truncation proves accurate, the method offers a controlled route to compute dynamical response functions in the projected space without explicit slave-particle fields.
  • Violation of Luttinger's theorem at accessible densities suggests that standard Fermi-surface counting arguments may fail in a broader class of strongly projected models.

Load-bearing premise

The chosen truncation of the functional renormalization group flow remains quantitatively reliable without higher-order vertex corrections over the full density range examined.

What would settle it

A direct numerical comparison of the momentum-resolved spectral function or the integrated particle number versus chemical potential against exact diagonalization on clusters or auxiliary-field quantum Monte Carlo at infinite U would confirm or refute the reported renormalization and Luttinger violation.

Figures

Figures reproduced from arXiv: 2512.15437 by Andreas R\"uckriegel, Jonas Arnold, Peter Kopietz.

Figure 1
Figure 1. Figure 1: FIG. 1. Temperature-density phase diagram of the [PITH_FULL_IMAGE:figures/full_fig_p002_1.png] view at source ↗
Figure 2
Figure 2. Figure 2: FIG. 2. Diagrammatic flow equations of (a) holon self-energy Σ [PITH_FULL_IMAGE:figures/full_fig_p005_2.png] view at source ↗
Figure 3
Figure 3. Figure 3: FIG. 3. Diagrammatic flow equations of (a) the su [PITH_FULL_IMAGE:figures/full_fig_p006_3.png] view at source ↗
Figure 4
Figure 4. Figure 4: FIG. 4. Momentum dependence of the static interaction channels within the first Brillouin zone, evaluated for four selected [PITH_FULL_IMAGE:figures/full_fig_p009_4.png] view at source ↗
Figure 5
Figure 5. Figure 5: FIG. 5. (a)-(c) Static magnetic susceptibility [PITH_FULL_IMAGE:figures/full_fig_p010_5.png] view at source ↗
Figure 6
Figure 6. Figure 6: FIG. 6. (a) Chemical potential [PITH_FULL_IMAGE:figures/full_fig_p010_6.png] view at source ↗
Figure 7
Figure 7. Figure 7: FIG. 7. Electronic spectral function [PITH_FULL_IMAGE:figures/full_fig_p012_7.png] view at source ↗
Figure 8
Figure 8. Figure 8: FIG. 8. (a) Damping [PITH_FULL_IMAGE:figures/full_fig_p013_8.png] view at source ↗
Figure 9
Figure 9. Figure 9: FIG. 9. Electronic spectral function [PITH_FULL_IMAGE:figures/full_fig_p014_9.png] view at source ↗
Figure 10
Figure 10. Figure 10: FIG. 10. (a) Damping [PITH_FULL_IMAGE:figures/full_fig_p015_10.png] view at source ↗
Figure 11
Figure 11. Figure 11: FIG. 11. Electronic spectral function [PITH_FULL_IMAGE:figures/full_fig_p016_11.png] view at source ↗
Figure 13
Figure 13. Figure 13: FIG. 13. Temperature dependence of the quasi-particle [PITH_FULL_IMAGE:figures/full_fig_p017_13.png] view at source ↗
Figure 12
Figure 12. Figure 12: FIG. 12. (a) Damping [PITH_FULL_IMAGE:figures/full_fig_p017_12.png] view at source ↗
Figure 14
Figure 14. Figure 14: FIG. 14. Single-particle electronic bandwidth [PITH_FULL_IMAGE:figures/full_fig_p018_14.png] view at source ↗
Figure 16
Figure 16. Figure 16: FIG. 16. Contour plot of the gradient of the occupation num [PITH_FULL_IMAGE:figures/full_fig_p018_16.png] view at source ↗
Figure 9
Figure 9. Figure 9: At high density n = 0.85 the picture has quali- [PITH_FULL_IMAGE:figures/full_fig_p018_9.png] view at source ↗
Figure 17
Figure 17. Figure 17: FIG. 17. Occupation number [PITH_FULL_IMAGE:figures/full_fig_p019_17.png] view at source ↗
Figure 19
Figure 19. Figure 19: FIG. 19. (a) Imaginary and (b) real parts of the holon propa [PITH_FULL_IMAGE:figures/full_fig_p022_19.png] view at source ↗
Figure 18
Figure 18. Figure 18: FIG. 18. Magnetic spectral function defined in Eq. (C4) in [PITH_FULL_IMAGE:figures/full_fig_p022_18.png] view at source ↗
Figure 20
Figure 20. Figure 20: FIG. 20. Slope ∆Im [Σ( [PITH_FULL_IMAGE:figures/full_fig_p023_20.png] view at source ↗
Figure 21
Figure 21. Figure 21: FIG. 21. Matsubara frequency dependence of the imaginary [PITH_FULL_IMAGE:figures/full_fig_p023_21.png] view at source ↗
Figure 23
Figure 23. Figure 23: FIG. 23. Relative error ∆ [PITH_FULL_IMAGE:figures/full_fig_p024_23.png] view at source ↗
Figure 25
Figure 25. Figure 25: FIG. 25. Systematic error [PITH_FULL_IMAGE:figures/full_fig_p024_25.png] view at source ↗
read the original abstract

At strong on-site repulsion $ U $, the fermionic Hubbard model realizes an extremely correlated electron system. In this regime, it is natural to derive the low-energy physics with the help of non-canonical operators acting on a projected Hilbert space without double occupancies. Using a strong-coupling functional renormalization group technique, we study the physics of such extreme correlations in the strict $ U = \infty $ limit, where only kinematic interactions due to the Hilbert space projection remain. For nearest-neighbor hopping on a square lattice, we find that the electronic spectrum is significantly renormalized, with bandwidth and quasi-particle residue strongly decreasing with increasing electron density. On the other hand, damping and particle-hole asymmetry increase, while a polaronic continuum forms in the hole sector, below the single-particle band. Fermi liquid phenomenology applies only at low densities, where the system remains paramagnetic. At higher densities, we find a bad metal with strong magnetic correlations, indicating that the ground state is the Nagaoka ferromagnet at high densities and a stripe antiferromagnet at intermediate densities. Both in the paramagnetic and the ferromagnetic regimes, we observe a violation of Luttinger's theorem.

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 develops a strong-coupling functional renormalization group (fRG) technique for the Hubbard model in the strict U=∞ limit, employing non-canonical operators to enforce the projected no-double-occupancy Hilbert space. For nearest-neighbor hopping on the square lattice, it reports strong density-dependent renormalization of the single-particle spectrum (bandwidth and quasiparticle residue decreasing with filling), increasing damping and particle-hole asymmetry, formation of a polaronic continuum below the band in the hole sector, bad-metal behavior with strong magnetic correlations at intermediate-to-high densities (Nagaoka ferromagnet at high density, stripe antiferromagnet at intermediate density), and explicit violation of Luttinger's theorem in both paramagnetic and ferromagnetic regimes.

Significance. If the truncation of the flow equations can be shown to be controlled, the work would supply a parameter-free, microscopic route to extremely correlated electrons that generates renormalization, bad-metal phenomenology, and magnetic ordering directly from the projected Hamiltonian without fitting. The ability to access the full density range within a single framework is a notable strength, though the absence of benchmarks against exact methods leaves the quantitative reliability open.

major comments (3)
  1. [Flow equations and truncation] The truncation scheme for the strong-coupling fRG hierarchy (typically at the two-particle vertex level) is not specified with an explicit order, error estimate, or convergence test against higher-order vertex corrections. Because the non-canonical operator representation modifies the usual Ward identities that protect Luttinger's theorem, omitted diagrams could restore the theorem at intermediate fillings; this directly undermines the central claim of a robust violation in both paramagnetic and ferromagnetic regimes.
  2. [Numerical results on spectrum and Luttinger's theorem] No comparison is provided to exact diagonalization on small clusters or other non-perturbative methods at the same densities where Luttinger's theorem violation and the polaronic continuum are reported. Such benchmarks are required to establish that the observed Fermi-surface volume mismatch and spectral features are not truncation artifacts.
  3. [Density-dependent results] The transition from paramagnetic Fermi-liquid behavior at low density to bad-metal behavior with magnetic ordering at higher density rests on the same truncated flow; without a controlled error analysis, it is unclear whether the reported density dependence of the quasiparticle residue and damping is quantitatively reliable.
minor comments (2)
  1. [Method] The definition and commutation relations of the non-canonical operators in the projected space would benefit from an explicit early section or appendix to aid reproducibility.
  2. [Figures] Figure captions for the spectral functions and Fermi-surface plots should explicitly state the truncation level and any cutoff parameters used in the flow.

Simulated Author's Rebuttal

3 responses · 1 unresolved

We thank the referee for the careful reading and constructive comments on our manuscript. We have revised the text to explicitly detail the truncation scheme, add discussion of its limitations, and include comparisons to known limits. Below we respond point by point to the major comments.

read point-by-point responses

  1. Referee: [Flow equations and truncation] The truncation scheme for the strong-coupling fRG hierarchy (typically at the two-particle vertex level) is not specified with an explicit order, error estimate, or convergence test against higher-order vertex corrections. Because the non-canonical operator representation modifies the usual Ward identities that protect Luttinger's theorem, omitted diagrams could restore the theorem at intermediate fillings; this directly undermines the central claim of a robust violation in both paramagnetic and ferromagnetic regimes.

    Authors: The flow equations are truncated at the two-particle vertex level, which is the standard approximation employed in fRG treatments of the Hubbard model. We have added an explicit description of the truncation, the neglected higher-order terms, and a qualitative discussion of expected accuracy in the revised methods section. We agree that the non-canonical operators alter the usual Ward identities and that omitted diagrams could in principle restore Luttinger's theorem; we have therefore added a paragraph noting this as a limitation of the current truncation and identifying higher-order extensions as future work. The violation we report is a consistent outcome within the adopted approximation. revision: partial

  2. Referee: [Numerical results on spectrum and Luttinger's theorem] No comparison is provided to exact diagonalization on small clusters or other non-perturbative methods at the same densities where Luttinger's theorem violation and the polaronic continuum are reported. Such benchmarks are required to establish that the observed Fermi-surface volume mismatch and spectral features are not truncation artifacts.

    Authors: We have added comparisons in the revised manuscript to exact results in the low-density regime, where the method recovers Fermi-liquid behavior and satisfaction of Luttinger's theorem, consistent with small-cluster ED and other approaches. For the polaronic continuum and violation at intermediate densities, we discuss consistency with variational Monte Carlo and DMFT results for the magnetic phases. Direct ED benchmarks at the relevant system sizes remain computationally prohibitive in the projected Hilbert space; we therefore acknowledge the lack of such benchmarks at the reported densities as a limitation of the present study. revision: partial

  3. Referee: [Density-dependent results] The transition from paramagnetic Fermi-liquid behavior at low density to bad-metal behavior with magnetic ordering at higher density rests on the same truncated flow; without a controlled error analysis, it is unclear whether the reported density dependence of the quasiparticle residue and damping is quantitatively reliable.

    Authors: The density dependence arises directly from the renormalization-group flow of the spectrum and vertices. In the revision we have added an analysis of flow convergence (monitoring the scale dependence of the vertex functions) together with a qualitative estimate of truncation error obtained by comparing the two-particle truncation to the one-loop level. The qualitative trends—decrease of quasiparticle residue and increase of damping with density—are robust within the approximation, while we emphasize that quantitative values carry the uncertainty inherent to the truncation. revision: partial

standing simulated objections not resolved
  • Direct benchmarks against exact diagonalization or other non-perturbative methods at the intermediate densities where Luttinger violation and the polaronic continuum are reported.

Circularity Check

0 steps flagged

No circularity: results generated from projected Hamiltonian via fRG flow

full rationale

The paper starts from the microscopic Hubbard model at U=∞ using non-canonical operators on the projected Hilbert space and applies a truncated strong-coupling functional renormalization group flow to compute the self-energy and spectral functions. The reported density-dependent bandwidth renormalization, quasi-particle residue drop, polaronic continuum, and Luttinger theorem violation are obtained by numerically integrating the flow equations for nearest-neighbor hopping on the square lattice. No parameters are fitted to the target observables, no self-definitional loops appear in the equations, and no load-bearing self-citations reduce the central claims to prior inputs. The truncation is explicitly an approximation whose validity is assumed rather than derived by construction from the outputs.

Axiom & Free-Parameter Ledger

0 free parameters · 1 axioms · 0 invented entities

The central claim rests on the validity of the projected Hilbert space and the controlled truncation of the FRG hierarchy; no additional free parameters or invented entities are introduced in the abstract.

axioms (1)
  • domain assumption The infinite-U projection forbidding double occupancy is faithfully represented by non-canonical operators whose algebra is preserved under the renormalization flow.
    This is the foundational premise that converts the original Hubbard interaction into purely kinematic constraints.

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Works this paper leans on

153 extracted references · 153 canonical work pages · 2 internal anchors

  1. [1]

    Paramagnetic regime For the low-density regimen < n c,1, we discussn= 0.2 as a representative example for the qualitative behav- ior of the spectral properties. In Fig. 7 we show the electronic spectral function along the high symmetry path of the first Brillouin-zone, following both the Γ- M-diagonal, as well as theX-Xdiagonal along the mag- netic Brillo...

    work page

  2. [2]

    Stripe regime Moving into the intermediate density regimen c,1 ≤ n= 0.56< n c,2, the band narrows significantly and the Fermi surface becomes less defined; see Fig. 9. The spec- tral weight is shifted to the Γ-point at finite positive fre- quencies. In the vicinity of the Fermi energy the excita- tions broaden and leak spectral weight into an incoherent c...

    work page

  3. [3]

    Nagaoka polarons

    Ferromagnetic regime For densitiesn≥n c,2 the static susceptibility sig- nals an instability towards a ferromagnetic ground state. However, we already argued in Sec. III B that there is an additional qualitative change at densityn c,3 = 0.85 that separates two distinct ferromagnetic phases. As repre- sentative examples for these two regimes, we therefore ...

    work page 1970

  4. [4]

    For all densities,Z k decreases significantly with decreasing temperature

    Quasi-particle weight and bandwidth Figure 13 shows the temperature dependence of the quasi-particle weightZ k evaluated at the nodal Fermi momentumk ∗ F (i.e., the Fermi momentum on the high symmetry path Γ→Min the Brillouin zone) in the four different density regimes. For all densities,Z k decreases significantly with decreasing temperature. Forn < n c,...

    work page

  5. [5]

    Luttinger’s theorem may fail at strong couplingU≫Wbecause the Hubbard model is no longer adiabatically connected to theU= 0 limit of free fermions [14, 15, 22–24]

    and much later also non-perturbatively with topo- logical arguments [87, 88]. Luttinger’s theorem may fail at strong couplingU≫Wbecause the Hubbard model is no longer adiabatically connected to theU= 0 limit of free fermions [14, 15, 22–24]. This disconnection is embodied by the Hilbert space projection in thet-Jand tmodels, which ejects doubly occupied s...

    work page

  6. [6]

    (B3) This symmetry is satisfied by choosing the three channel matrices such that S⊤ Λ(Q) =S Λ(Q),(B4a) M⊤ Λ(Q) =M Λ(−Q),(B4b) C⊤ Λ(Q) =C Λ(−Q).(B4c)

    Crossing symmetry.The 2-body interaction must be symmetric under Qpp →Q pp , Q ex → −Qex , Q fs → −Qfs ,(B1) which implies UΛ(K ′ 1, K′ 2;K 2, K1) =U Λ(K ′ 2, K′ 1;K 1, K2).(B2) Inserting the channel decomposition (25) then yields the following matrix equation for the channels: 0 = 1 2 h MΛ(Qfs)−M ⊤ Λ(−Qfs)−C Λ(Qfs) +C ⊤ Λ(−Qfs) i +M Λ(Qex)−M ⊤ Λ(−Qex)−S ...

    work page

  7. [7]

    Time-reversal symmetry.The 2-body interaction must be symmetric under Qpp →Q pp , Q ex →Q ex , Q fs → −Qfs ,(B5) which implies UΛ(K ′ 1, K′ 2;K 2, K1) =U Λ(K1, K2;K ′ 2, K′ 1).(B6) When inserting the channel decomposition (25), this symmetry cannot be cast into a matrix form. It explicitly yields 0 =−Ω fs S21 Λ (Qpp)−S 12 Λ (Qpp) + iΩex Z S22 Λ (Qpp) + Ωf...

    work page

  8. [8]

    Hubbard,Electron correlations in narrow energy bands, Proc

    J. Hubbard,Electron correlations in narrow energy bands, Proc. Roy. Soc. (London) A276, 238 (1963)

    work page 1963

  9. [9]

    Auerbach,Interacting Electrons and Quantum Mag- netism, (Springer, Berlin, 1994)

    A. Auerbach,Interacting Electrons and Quantum Mag- netism, (Springer, Berlin, 1994)

    work page 1994

  10. [10]

    Fulde,Electron Correlations in Molecules and Solids, (Springer, Berlin, Third Enlarged Edition, 1995)

    P. Fulde,Electron Correlations in Molecules and Solids, (Springer, Berlin, Third Enlarged Edition, 1995)

    work page 1995

  11. [11]

    Fazekas,Lecture Notes on Electron Correlation and Magnetism, (World Scientific, Singapore, 1999)

    P. Fazekas,Lecture Notes on Electron Correlation and Magnetism, (World Scientific, Singapore, 1999)

    work page 1999

  12. [12]

    S. G. Ovchinnikov and V. V. Val’kov,Hubbard Operators in the Theory of Strongly Correlated Electrons, (Impe- rial College Press, London, 2004)

    work page 2004

  13. [13]

    Shankar,Renormalization-group approach to inter- acting fermions, Rev

    R. Shankar,Renormalization-group approach to inter- acting fermions, Rev. Mod. Phys.66, 129 (1994)

    work page 1994

  14. [14]

    Van Houcke, E

    K. Van Houcke, E. Kozik, N. Prokof’ev, and B. Svis- tunov,Diagrammatic Monte Carlo, Phys. Procedia6, 95 (2010)

    work page 2010

  15. [15]

    Wetterich,Exact evolution equation for the effective potential, Phys

    C. Wetterich,Exact evolution equation for the effective potential, Phys. Lett. B301, 90 (1993)

    work page 1993

  16. [16]

    Berges, N

    J. Berges, N. Tetradis, and C. Wetterich,Non- perturbative renormalization flow in quantum field the- ory and statistical physics, Phys. Rep.363, 223 (2002)

    work page 2002

  17. [17]

    J. M. Pawlowski,Aspects of the functional renormalisa- tion group, Ann. Phys.322, 2831 (2007)

    work page 2007

  18. [18]

    Kopietz, L

    P. Kopietz, L. Bartosch, and F. Sch¨ utz,Introduction to the Functional Renormalization Group(Springer, Berlin, 2010)

    work page 2010

  19. [19]

    Metzner, M

    W. Metzner, M. Salmhofer, C. Honerkamp, V. Meden, and K. Sch¨ onhammer,Functional renormalization group approach to correlated fermion systems, Rev. Mod. Phys.84, 299 (2012)

    work page 2012

  20. [20]

    Dupuis, L

    N. Dupuis, L. Canet, A. Eichhorn, W. Metzner, J. M. Pawlowski, M. Tissier, and N. Wschebor,The nonper- turbative functional renormalization group and its ap- plications, Phys. Rep.910, 1 (2021)

    work page 2021

  21. [21]

    B. S. Shastry,Extremely correlated quantum liquids, Phys. Rev. B81, 045121 (2010)

    work page 2010

  22. [22]

    Chiappe, E

    G. Chiappe, E. Louis, J. Gal´ an, F. Guinea, and J. A. Verg´ es,Ground-state properties of the U=∞Hubbard model on a4×4cluster, Phys. Rev. B48, 16539 (1993)

    work page 1993

  23. [23]

    [5]) and in our previous work [76], the language of Hubbard X- operatorsX ab i =|i, a⟩ ⟨i, b|is often used to formulate the strong-coupling problem

    Both in the literature (see, for example, Ref. [5]) and in our previous work [76], the language of Hubbard X- operatorsX ab i =|i, a⟩ ⟨i, b|is often used to formulate the strong-coupling problem. Here,a, b∈ {0,↑,↓}label the three states of the atomic Hilbert space. As we only require a small portion of the set of X-operators we in- troduce the more concis...

    work page

  24. [24]

    F. C. Zhang and T. M. Rice,Effective Hamiltonian for the superconducting Cu oxides, Phys. Rev. B37, 3759(R) (1988)

    work page 1988

  25. [25]

    D. S. Dessau, Z.-X. Shen, D. M. King, D. S. Mar- shall, L. W. Lombardo, P. H. Dickinson, A. G. Loeser, J. DiCarlo, C.-H. Park, A. Kapitulnik, and W. E. Spicer,Key features in the measured band structure of Bi2Sr2CaCu2O8+δ: Flat bands at E F and Fermi surface nesting, Phys. Rev. Lett.71, 2781 (1993)

    work page 1993

  26. [26]

    M. R. Norman, H. Ding, M. Randeria, J. C. Cam- puzano, T. Yokoya, T. Takeuchi, T. Takahashi, T. Mochiku, K. Kadowaki, P. Guptasarma, and D. G. Hinks,Destruction of the Fermi surface in underdoped high-Tc superconductors, Nature392, 157 (1998)

    work page 1998

  27. [27]

    K. M. Shen, F. Ronning, D. H. Lu, F. Baumberger, N. J. C. Ingle, W. S. Lee, W. Meevasana, Y. Kohsaka, M. Azuma, M. Takano, H. Takagi, and Z.-X. Shen, Nodal Quasiparticles and Antinodal Charge Ordering in Ca2−xNaxCuO2Cl2, Science307, 901 (2005)

    work page 2005

  28. [28]

    Kanigel, U

    A. Kanigel, U. Chatterjee, M. Randeria, M. R. Norman, S. Souma, M. Shi1, Z. Z. Li, H. Raffy, and J. C. Cam- puzano,Protected Nodes and the Collapse of Fermi Arcs in High-T c Cuprate Superconductors, Phys. Rev. Lett. 99, 157001 (2007)

    work page 2007

  29. [29]

    P. W. Anderson,Hidden Fermi liquid: The secret of high-Tc cuprates, Phys. Rev. B78, 174505 (2008)

    work page 2008

  30. [30]

    P. W. Anderson and P. A. Casey,Transport anomalies of the strange metal: Resolution by hidden Fermi liquid theory, Phys. Rev. B80, 094508 (2009)

    work page 2009

  31. [31]

    P. A. Casey and P. W. Anderson,Hidden Fermi Liquid: Self-Consistent Theory for the Normal State of High-T c Superconductors, Phys. Rev. Lett.106, 097002 (2011)

    work page 2011

  32. [32]

    H.-B. Yang, J. D. Rameau, Z.-H. Pan, G. D. Gu, P. D. Johnson, H. Claus, D. G. Hinks, and T. E. Kidd,Reconstructed Fermi Surface of Un- derdopedBi 2Sr2CaCu2O8+δ Cuprate Superconductors, Phys. Rev. Lett.107, 047003 (2011)

    work page 2011

  33. [33]

    Keimer, S

    B. Keimer, S. A. Kivelson, M. R. Norman, S. Uchida, and J. Zaanen,From quantum matter to high- temperature superconductivity in copper oxides, Nature 518, 179 (2015)

    work page 2015

  34. [34]

    Sachdev,The foot, the fan, and the cuprate phase diagram: Fermi-volume-changing quantum phase tran- sitions, Physica C633, 1354707 (2025)

    S. Sachdev,The foot, the fan, and the cuprate phase diagram: Fermi-volume-changing quantum phase tran- sitions, Physica C633, 1354707 (2025)

    work page 2025

  35. [35]

    Sherman and M

    A. Sherman and M. Schreiber,Two-dimensional t-J model at moderate doping, Eur. Phys. J. B32, 203 (2003)

    work page 2003

  36. [36]

    ˇSimkovic IV, R

    F. ˇSimkovic IV, R. Rossi, A. Georges, and M. Ferrero, Origin and fate of the pseudogap in the doped Hubbard model, Science385, eade9194 (2024)

    work page 2024

  37. [37]

    Nagaoka,Ground state of correlated electrons in a narrow almost half-filled s-band, Solid State Commun

    Y. Nagaoka,Ground state of correlated electrons in a narrow almost half-filled s-band, Solid State Commun. 3, 409 (1965)

    work page 1965

  38. [38]

    Nagaoka,Ferromagnetism in a Narrow, Almost Half- Filld s Band, Phys

    Y. Nagaoka,Ferromagnetism in a Narrow, Almost Half- Filld s Band, Phys. Rev.147, 392 (1966)

    work page 1966

  39. [39]

    Kollar, R

    M. Kollar, R. Strack, and D. Vollhardt,Ferromagnetism in correlated electron systems: Generalization of Na- gaoka’s theorem, Phys. Rev. B53, 9225 (1996)

    work page 1996

  40. [40]

    Tasaki,From Nagaoka’s Ferromagnetism to Flat- Band Ferromagnetism and Beyond, Prog

    H. Tasaki,From Nagaoka’s Ferromagnetism to Flat- Band Ferromagnetism and Beyond, Prog. Theor. Phys. 99, 489 (1998)

    work page 1998

  41. [41]

    E. H. Lieb,Two theorems on the Hubbard model, Phys. Rev. Lett.62, 1201 (1989); Erratum Phys. Rev. Lett. 62, 1927 (1989)

    work page 1989

  42. [42]

    L. M. Roth,Spin wave stability of the ferromagnetic state for a narrow s-band, Journal of Physics and Chem- istry of Solids,28, 1549 (1967)

    work page 1967

  43. [43]

    W. F. Brinkman and T. M. Rice,Single-Particle Ex- citations in Magnetic Insulators, Phys. Rev. B2, 1324 26 (1970)

    work page 1970

  44. [44]

    B. S. Shastry, H. R. Krishnamurthy, and P. W. Ander- son,Instability of the Nagaoka ferromagnetic state of the U=∞Hubbard model, Phys. Rev. B41, 2375 (1990)

    work page 1990

  45. [45]

    Yu. A. Izyumov and B. M. Letfulov,A diagram tech- nique for Hubbard operators: the magnetic phase dia- gram in the (t-J) model, J. Phys.: Condens. Matter2 8905 (1990)

    work page 1990

  46. [46]

    A. G. Basile and V. Elser,Stability of the ferromag- netic state with respect to a single spin flip: Variational calculations for the U=∞Hubbard model on the square lattice, Phys. Rev. B41, 4842(R) (1990)

    work page 1990

  47. [47]

    Kotrla and V

    M. Kotrla and V. Drchal,Mean-Field Solution of Strongly Correlated Systems Using Hubbard Atomic Op- erators, phys. stat. sol. (b)167, 635 (1990)

    work page 1990

  48. [48]

    J. C. Angl` es d’Auriac, B. Doucot, and R. Rammal, Infinite-U Hubbard model in the large-spin regime: ex- act diagonalization study, J. Phys.: Condens. Matter3, 3973 (1991)

    work page 1991

  49. [50]

    W. O. Putikka, M. U. Luchini, and M. Ogata,Ferromag- netism in the two-dimensionalt-Jmodel, Phys. Rev. Lett.69, 2288 (1992)

    work page 1992

  50. [51]

    Hanisch and E

    Th. Hanisch and E. M¨ uller-Hartmann,Ferromagnetism in the Hubbard model: instability of the Nagaoka state on the square lattice, Ann. Physik2, 381 (1993)

    work page 1993

  51. [52]

    M. W. Long and X. Zotos,Hole-hole correlations in the U=∞limit of the Hubbard model and the stability of the Nagaoka state, Phys. Rev. B48, 317 (1993)

    work page 1993

  52. [53]

    Wurth and E

    P. Wurth and E. M¨ uller-Hartmann,Ferromagnetism in the Hubbard model: Spin waves and instability of the Nagaoka state, Ann. Phys.507, 144 (1995)

    work page 1995

  53. [54]

    Obermeier, T

    T. Obermeier, T. Pruschke, and J. Keller,Ferromag- netism in the large-UHubbard model, Phys. Rev. B56, R8479(R) (1997)

    work page 1997

  54. [55]

    E. V. Kuz’min,The ground state problem in the infinite- U Hubbard model, Phys. Solid State39, 169–178 (1997)

    work page 1997

  55. [56]

    Becca and S

    F. Becca and S. Sorella,Nagaoka Ferromagnetism in the Two-Dimensional Infinite-UHubbard Model, Phys. Rev. Lett.86, 3396 (2001)

    work page 2001

  56. [57]

    Zitzler, Th

    R. Zitzler, Th. Pruschke, and R. Bulla,Magnetism and phase separation in the ground state of the Hubbard model, Eur. Phys. J. B27, 473-481 (2002)

    work page 2002

  57. [58]

    Coleman and C

    P. Coleman and C. P´ epin,Supersymmetric approach to the infinite U Hubbard model, Physica B: Cond. Mat. 312, 539 (2002)

    work page 2002

  58. [59]

    H. Park, K. Haule, C. A. Marianetti, and G. Kotliar, Dynamical mean-field theory study of Nagaoka ferro- magnetism, Phys. Rev. B77, 035107 (2008)

    work page 2008

  59. [60]

    Carleo, S

    G. Carleo, S. Moroni, F. Becca, and S. Baroni,Itinerant ferromagnetic phase of the Hubbard model, Phys. Rev. B83, 060411(R) (2011)

    work page 2011

  60. [61]

    L. Liu, H. Yao, E. Berg, S. R. White, and S. A. Kivel- son,Phases of the InfiniteUHubbard Model on Square Lattices, Phys. Rev. Lett.108, 126406 (2012)

    work page 2012

  61. [62]

    Ivantsov, A

    I. Ivantsov, A. Ferraz, and E. Kochetov,Breakdown of the Nagaoka phase at finite doping, Phys. Rev. B95, 155115 (2017)

    work page 2017

  62. [63]

    G. G. Blesio, M. G. Gonzalez, and F. T. Lisandrini, Magnetic phase diagram of the infinite-UHubbard model with nearest- and next-nearest-neighbor hoppings, Phys. Rev. B99, 174411 (2019)

    work page 2019

  63. [64]

    Morera, M

    I. Morera, M. Kan´ asz-Nagy, T. Smolenski, L. Ciorciaro, A. Imamo˘ glu, and E. Demler,High-temperature kinetic magnetism in triangular lattices, Phys. Rev. Research 5, L022048 (2023)

    work page 2023

  64. [65]

    Samajdar and R

    R. Samajdar and R. N. Bhatt,Polaronic mechanism of Nagaoka ferromagnetism in Hubbard models, Phys. Rev. B109, 235128 (2024)

    work page 2024

  65. [66]

    R. C. Newby and E. Khatami,Finite-temperature kinetic ferromagnetism in the square-lattice Hubbard model, Phys. Rev. B111, 245120 (2025)

    work page 2025

  66. [67]

    Instability of Nagaoka State and Quantum Phase Transition via Kinetic Frustration Control

    P. Sharma, Y. Peng, D. N. Sheng, H. J. Changlani, and Y. Wang,Instability of Nagaoka State and Quan- tum Phase Transition via Kinetic Frustration Control, arXiv:2508.08410 [cond-mat.str-el]

    work page internal anchor Pith review Pith/arXiv arXiv

  67. [68]

    L. W. Cheuk, M. A. Nichols, K. R. Lawrence, M. Okan, H. Zhang, E. Khatami, N. Trivedi, T. Paiva, M. Rigol, and M. W. Zwierlein,Observation of Spatial Charge and Spin Correlations in the 2D Fermi-Hubbard Model, Sci- ence353, 1260 (2016)

    work page 2016

  68. [69]

    J. P. Dehollain, U. Mukhopadhyay, V. P. Michal, Y. Wang, B. Wunsch, C. Reichl, W. Wegscheider, M. S. Rudner, E. Demler, and L. M. K. Vandersypen,Na- gaoka ferromagnetism observed in a quantum dot pla- quette, Nature579, 528 (2020)

    work page 2020

  69. [70]

    Bohrdt, L

    A. Bohrdt, L. Homeier, C. Reinmoser, E. Demler, and F. Grusdt,Exploration of doped quantum magnets with ultracold atoms, Annals of Physics,435, 168651 (2021)

    work page 2021

  70. [71]

    B. M. Spar, E. Guardado-Sanchez, S. Chi, Z. Z. Yan, and W. S. Bakr,Realization of a Fermi-Hubbard Optical Tweezer Array, Phys. Rev. Lett.128, 223202 (2022)

    work page 2022

  71. [72]

    Lebrat, M

    M. Lebrat, M. Xu, L. H. Kendrick, A. Kale, Y. Gang, P. Seetharaman, I. Morera, E. Khatami, E. Demler, and M. Greiner,Observation of Nagaoka Polarons in a Fermi-Hubbard Quantum Simulator, Nature629, 317 (2024)

    work page 2024

  72. [73]

    M. L. Prichard, B. M. Spar, I. Morera, E. Demler, Z. Z. Yan, and W. S. Bakr,Directly imaging spin polarons in a kinetically frustrated Hubbard system, Nature629, 323 (2024)

    work page 2024

  73. [74]

    L. H. Kendrick, A. Kale, Y. Gang, A. D. Deters, M. Lebrat, A. W. Young, and M. Greiner,Pseudogap in a Fermi-Hubbard quantum simulator, arXiv:2509.18075

    work page arXiv

  74. [75]

    M. M. Ma´ ska, M. Mierzejewski, E. A. Kochetov, L. Vid- mar, J. Bonˇ ca, and O. P. Sushkov,Effective approach to the Nagaoka regime of the two-dimensionalt-Jmodel, Phys. Rev. B85, 245113 (2012)

    work page 2012

  75. [76]

    Oitmaa, C

    J. Oitmaa, C. Hamer, and W. Zhang,Series Expansion Methods for Strongly Interacting Lattice Models(Cam- bridge University Press, Cambridge, 2006)

    work page 2006

  76. [77]

    Metzner,Linked-cluster expansion around the atomic limit of the Hubbard model, Phys

    W. Metzner,Linked-cluster expansion around the atomic limit of the Hubbard model, Phys. Rev. B43, 8549 (1991)

    work page 1991

  77. [78]

    R. O. Zaitsev,Diagram technique and gas approxima- tion in the Hubbard model, Zh. Eksp. Teor. Fiz.70, 1100 (1976), [Sov. Phys. JETP43, 574 (1976)]

    work page 1976

  78. [79]

    Yu. A. Izyumov, B. M. Letfulov, E. V. Shipitsyn, M. Bartkowiak, and K. A. Chao,Theory of strongly cor- related electron systems on the basis of a diagrammatic technique for Hubbard operators, Phys. Rev. B46, 15697 (1992)

    work page 1992

  79. [80]

    Yu. A. Izyumov, N. I. Chaschin, D. S. Alexeev, and F. Mancini,A generating functional approach to the Hub- bard model, Eur. Phys. J. B45, 69 (2005)

    work page 2005

  80. [81]

    Perepelitsky and B

    E. Perepelitsky and B. S. Shastry,Diagrammaticλse- 27 ries for extremely correlated Fermi liquids, Ann. Phys. 357, 1 (2015)

    work page 2015

Showing first 80 references.