pith. sign in

arxiv: 2507.10670 · v3 · submitted 2025-07-14 · ❄️ cond-mat.str-el · cond-mat.mtrl-sci

Band structure picture for topology in strongly correlated systems with the ghost Gutzwiller ansatz

Ivan Pasqua , Antonio Maria Tagliente , Gabriele Bellomia , Bartomeu Monserrat , Michele Fabrizio , Carlos Mejuto-Zaera This is my paper

Pith reviewed 2026-05-19 04:25 UTC · model grok-4.3

classification ❄️ cond-mat.str-el cond-mat.mtrl-sci
keywords ghost Gutzwiller ansatzHubbard bandstopological edge statescorrelated topologyBernevig-Hughes-Zhang modelstrongly correlated electronsmagnetization control
0
0 comments X

The pith

The ghost Gutzwiller ansatz maps strongly correlated topology onto an effective band structure with nontrivial Hubbard bands.

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

The paper uses the ghost Gutzwiller variational framework to translate the topology of strongly correlated electrons into an interpretable band picture. Applied to the interacting Bernevig-Hughes-Zhang model, this method shows that the lower and upper Hubbard bands each acquire their own topological character and support distinct edge states. The same framework indicates that a finite magnetization provides a practical control knob over these edge states. A sympathetic reader would see this as a route to compute and interpret momentum-resolved spectra in real correlated topological materials without losing the essential interaction effects.

Core claim

By embedding the interacting Bernevig-Hughes-Zhang model in the ghost Gutzwiller ansatz, the authors obtain an effective single-particle band structure in which the Hubbard bands themselves become topologically nontrivial and each hosts its own protected edge states; finite magnetization further allows these edge states to be manipulated while the overall framework remains computationally tractable and directly comparable with spectroscopic measurements.

What carries the argument

The ghost Gutzwiller variational embedding framework, which augments the Hilbert space with auxiliary quasiparticle degrees of freedom to recover an effective band-structure description of the correlated system.

If this is right

  • Topological invariants can be assigned separately to the lower and upper Hubbard bands.
  • Edge states associated with each Hubbard band become visible in energy-momentum resolved spectra.
  • Finite magnetization offers a tunable parameter that can move or gap the Hubbard-band edge states.
  • The method reproduces established non-interacting and weakly correlated limits while extending them to strong coupling.

Where Pith is reading between the lines

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

  • Similar ghost-Gutzwiller treatments could be applied to other lattice models known to host correlated topological phases, such as the Kane-Mele or Haldane models with Hubbard interactions.
  • The resulting Hubbard-band topology may survive in three-dimensional or layered materials and could be searched for in existing candidate compounds.
  • If the edge states inside Hubbard bands remain robust to disorder, they might enable new transport signatures distinct from conventional topological insulators.

Load-bearing premise

The auxiliary quasiparticles introduced by the ghost Gutzwiller ansatz preserve the topological invariants and edge-state structure of the original interacting electrons without adding spurious band crossings or artifacts.

What would settle it

Angle-resolved photoemission or scanning tunneling spectroscopy on a strongly correlated realization of the Bernevig-Hughes-Zhang model that either detects or fails to detect edge-state signatures lying inside the Hubbard-band energy windows rather than only at the original non-interacting band edges.

Figures

Figures reproduced from arXiv: 2507.10670 by Antonio Maria Tagliente, Bartomeu Monserrat, Carlos Mejuto-Zaera, Gabriele Bellomia, Ivan Pasqua, Michele Fabrizio.

Figure 1
Figure 1. Figure 1: FIG. 1. Comparison between different methods on two rep [PITH_FULL_IMAGE:figures/full_fig_p006_1.png] view at source ↗
Figure 3
Figure 3. Figure 3: FIG. 3. Quasiparticle spectrum of [PITH_FULL_IMAGE:figures/full_fig_p007_3.png] view at source ↗
Figure 4
Figure 4. Figure 4: FIG. 4. Determinant of the quasiparticle residue matrices [PITH_FULL_IMAGE:figures/full_fig_p008_4.png] view at source ↗
Figure 5
Figure 5. Figure 5: FIG. 5. Quasiparticle band structure of [PITH_FULL_IMAGE:figures/full_fig_p009_5.png] view at source ↗
Figure 6
Figure 6. Figure 6: FIG. 6. Magnetic susceptibility [PITH_FULL_IMAGE:figures/full_fig_p010_6.png] view at source ↗
Figure 7
Figure 7. Figure 7: FIG. 7. Quasiparticle band structure of [PITH_FULL_IMAGE:figures/full_fig_p011_7.png] view at source ↗
read the original abstract

Understanding the interplay between electronic correlations and band topology remains a central challenge in condensed matter physics, primarily hindered by a language mismatch problem. While band topology is naturally formulated within a single-particle band theory, strong correlations typically elude such an effective one-body description. In this work, we bridge this gap leveraging the ghost Gutzwiller (gGut) variational embedding framework, which introduces auxiliary quasiparticle degrees of freedom to recover an effective band structure description of strongly correlated systems. This approach enables an interpretable and computationally efficient treatment of correlated topological phases, resulting in energy- and momentum-resolved topological features that are directly comparable with experimental spectra. We exemplify the advantages of this framework through a detailed study of the interacting Bernevig-Hughes-Zhang model. Not only does the gGut description reproduce established results, but it also reveals previously inaccessible aspects: most notably, the emergence of topologically nontrivial Hubbard bands hosting their own edge states, as well as possible ways to manipulate these through a finite magnetization. These results position the gGut framework as a promising tool for the predictive modeling of correlated topological materials.

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 introduces the ghost Gutzwiller (gGut) variational embedding method to recover an effective single-particle band-structure description of topology in strongly correlated systems. Applied to the interacting Bernevig-Hughes-Zhang model, the approach is claimed to reproduce established results on correlated topological phases while revealing new features, including topologically nontrivial Hubbard bands that host their own edge states and the possibility of manipulating these states through finite magnetization.

Significance. If the auxiliary quasiparticle degrees of freedom accurately encode the poles of the interacting Green's function without altering topological invariants or generating spurious boundary modes, the gGut framework would provide a computationally efficient and interpretable route to energy- and momentum-resolved topological features in correlated materials, directly comparable to experimental spectra.

major comments (3)
  1. [§3.2] §3.2 (effective Hamiltonian construction): the topological invariants (e.g., Chern numbers) assigned to individual Hubbard bands are computed in the enlarged space that includes ghost orbitals; it is not demonstrated that these invariants remain unchanged when the auxiliary modes are projected out or that they match the physical many-body topology.
  2. [Edge-state analysis] Edge-state analysis (results section on open-boundary spectra): the reported edge states localized on Hubbard bands lack explicit cross-validation against exact diagonalization or DMFT benchmarks for the interacting BHZ model at the same parameters; the variational embedding could introduce artifacts that mimic or modify boundary modes.
  3. [Magnetization-control subsection] Magnetization-control subsection: the claim that finite magnetization manipulates the Hubbard-band topology is obtained after self-consistent optimization of the gGut variational parameters; a sensitivity study showing that the reported edge-state structure and invariants are robust to small changes in these parameters is needed to address potential circularity.
minor comments (2)
  1. [Abstract] The abstract states that 'established results' are reproduced but does not list the specific quantities or parameter regimes used for validation, which would help readers assess the scope of the method's reliability.
  2. [Notation] Notation for the ghost quasiparticle operators and their coupling to physical orbitals is introduced without a compact summary table; adding such a table would improve readability of the enlarged Hilbert space.

Simulated Author's Rebuttal

3 responses · 0 unresolved

We thank the referee for their careful reading of the manuscript and for the constructive comments. We address each major point below, indicating where revisions have been made to strengthen the presentation.

read point-by-point responses

  1. Referee: [§3.2] §3.2 (effective Hamiltonian construction): the topological invariants (e.g., Chern numbers) assigned to individual Hubbard bands are computed in the enlarged space that includes ghost orbitals; it is not demonstrated that these invariants remain unchanged when the auxiliary modes are projected out or that they match the physical many-body topology.

    Authors: We agree that explicit verification is needed. In the gGut construction the ghost orbitals serve as auxiliary modes that encode the poles of the physical Green's function; the effective Hamiltonian is derived such that the physical quasiparticle bands retain the correct spectral weight and dispersion. In the revised manuscript we have added an explicit projection procedure that removes the ghost components from the eigenvectors and recomputes the Chern numbers on the resulting physical subspace. These projected invariants are shown to be identical to those obtained in the enlarged space and to agree with the known many-body topological characterization of the interacting BHZ model reported in the literature. revision: yes

  2. Referee: [Edge-state analysis] Edge-state analysis (results section on open-boundary spectra): the reported edge states localized on Hubbard bands lack explicit cross-validation against exact diagonalization or DMFT benchmarks for the interacting BHZ model at the same parameters; the variational embedding could introduce artifacts that mimic or modify boundary modes.

    Authors: We acknowledge the value of direct benchmarks. The gGut spectra reproduce the bulk phase boundaries previously obtained by DMFT and other methods. For the open-boundary edge states we have added, in the revision, a comparison of the local spectral function against DMFT at the same interaction and magnetization values; the edge-mode dispersions are consistent with the bulk-boundary correspondence applied to the effective bands. Full exact diagonalization of 2D open-boundary systems at the studied sizes remains computationally prohibitive, but we include supporting cluster calculations on smaller lattices that confirm the absence of spurious boundary modes introduced by the embedding. revision: partial

  3. Referee: [Magnetization-control subsection] Magnetization-control subsection: the claim that finite magnetization manipulates the Hubbard-band topology is obtained after self-consistent optimization of the gGut variational parameters; a sensitivity study showing that the reported edge-state structure and invariants are robust to small changes in these parameters is needed to address potential circularity.

    Authors: We appreciate the concern regarding robustness. In the revised manuscript we now include a dedicated sensitivity analysis: the converged variational parameters are perturbed by small relative amounts (1–5 %) while keeping the same self-consistency loop, and the resulting edge-state spectra and Chern numbers are recomputed. The Hubbard-band edge modes and their topological character remain qualitatively unchanged under these perturbations, confirming that the reported manipulation by finite magnetization is not an artifact of the particular converged solution. revision: yes

Circularity Check

0 steps flagged

gGut effective Hamiltonian yields independent topological invariants for Hubbard bands in interacting BHZ

full rationale

The paper applies the established ghost Gutzwiller variational embedding to construct an enlarged single-particle Hamiltonian whose poles recover the interacting Green's function for the Bernevig-Hughes-Zhang model. Topology (Chern numbers, edge states) is then computed directly on the resulting effective bands, including the Hubbard bands. The abstract explicitly states that established results are reproduced, providing an external benchmark, while the new claims about magnetization-tunable Hubbard-band edge states follow from diagonalizing the variational effective Hamiltonian. No equation reduces a reported prediction to a fitted parameter by construction, and the gGut framework is treated as an input method whose validity is cross-checked rather than assumed via unverified self-citation chains. The derivation chain therefore remains self-contained against the model's own spectral functions and known limits.

Axiom & Free-Parameter Ledger

1 free parameters · 1 axioms · 1 invented entities

The central claim rests on the ghost Gutzwiller ansatz being able to embed strong correlations into an effective band picture; this introduces auxiliary quasiparticles whose variational parameters are not independently constrained by external benchmarks in the provided abstract.

free parameters (1)
  • variational parameters of the ghost Gutzwiller ansatz
    Used to recover the effective band structure description of the correlated system
axioms (1)
  • domain assumption The ghost Gutzwiller variational embedding accurately recovers topological features of strongly correlated systems
    Invoked to bridge single-particle band topology with strong correlations
invented entities (1)
  • ghost quasiparticle degrees of freedom no independent evidence
    purpose: To restore an effective band structure description
    Auxiliary degrees of freedom introduced by the framework

pith-pipeline@v0.9.0 · 5748 in / 1198 out tokens · 27160 ms · 2026-05-19T04:25:07.831029+00:00 · methodology

discussion (0)

Sign in with ORCID, Apple, or X to comment. Anyone can read and Pith papers without signing in.

Lean theorems connected to this paper

Citations machine-checked in the Pith Canon. Every link opens the source theorem in the public Lean library.

What do these tags mean?
matches
The paper's claim is directly supported by a theorem in the formal canon.
supports
The theorem supports part of the paper's argument, but the paper may add assumptions or extra steps.
extends
The paper goes beyond the formal theorem; the theorem is a base layer rather than the whole result.
uses
The paper appears to rely on the theorem as machinery.
contradicts
The paper's claim conflicts with a theorem or certificate in the canon.
unclear
Pith found a possible connection, but the passage is too broad, indirect, or ambiguous to say the theorem truly supports the claim.

Reference graph

Works this paper leans on

107 extracted references · 107 canonical work pages · 2 internal anchors

  1. [1]

    The quasiparticle Hamiltonian Hqp is formed using the current R and λ according to Eq. (A2). Its ground state local one-body reduced density matrix ∆qp ab = ⟨d† 0ad0b⟩qp is evaluated

    work page

  2. [2]

    The partial derivative in the equation for λc acts only on the square-root term inside the trace

    The impurity model bath parameters V and λc can then be evaluated following V = 1 VBZ hp ∆qp · (I − ∆qp) i−1 · X k ∆T k · R† · ϵk, λc ab = −λab + ∂ ∂∆qp ab Tr h R · p ∆qp · (I − ∆qp) · V i + h.c., (A5) where VBZ is the volume of the Brillouin zone of the quasiparticle model, ∆ k;ab = ⟨d† kadkb⟩ and the · denotes matrix products in orbital space. The parti...

    work page

  3. [3]

    (A3), whose ground state one-body density matrix is evaluated

    The computed V and λc determine the impurity model in Eq. (A3), whose ground state one-body density matrix is evaluated. In particular, we are interested in the ⟨c† αda⟩imp and ⟨d† adb⟩imp compo- nents. In this work, we employ an exact diagonal- ization solver

    work page

  4. [4]

    Finally, we can close the iteration by proposing a new pair R, λ from the impurity model density ma- trix, according to I − ⟨d† adb⟩imp = ∆qp ab , ⟨c† αdb⟩imp = X a Rαa hp ∆qp · (I − ∆qp) Ti ab . (A6)

    work page

  5. [5]

    To speed up convergence, we employ a DIIS algorithm [102] to propose new parameters in each iteration

    The iteration is repeated from step 1 until the R and λ matrices are converged within some toler- ance. To speed up convergence, we employ a DIIS algorithm [102] to propose new parameters in each iteration. Given the spatial translational symmetry in our pe- riodic lattices, we typically only solve a single impurity model per iteration. In the multi-layer...

    work page

  6. [6]

    M. Z. Hasan and C. L. Kane, Rev. Mod. Phys. 82, 3045 (2010)

    work page 2010

  7. [7]

    Qi and S.-C

    X.-L. Qi and S.-C. Zhang, Rev. Mod. Phys. 83, 1057 (2011)

    work page 2011

  8. [8]

    P. A. Lee, N. Nagaosa, and X.-G. Wen, Rev. Mod. Phys. 78, 17 (2006)

    work page 2006

  9. [9]

    Georges, G

    A. Georges, G. Kotliar, W. Krauth, and M. J. Rozen- berg, Rev. Mod. Phys. 68, 13 (1996)

    work page 1996

  10. [10]

    Imada, A

    M. Imada, A. Fujimori, and Y. Tokura, Rev. Mod. Phys. 70, 1039 (1998)

    work page 1998

  11. [11]

    Tokura, Reports on Progress in Physics 69, 797 (2006)

    Y. Tokura, Reports on Progress in Physics 69, 797 (2006)

    work page 2006

  12. [12]

    C. A. F. Vaz, J. Hoffman, C. H. Ahn, and R. Ramesh, Advanced Materials 22, 2900–2918 (2010)

    work page 2010

  13. [13]

    Th¨ ole, A

    F. Th¨ ole, A. Keliri, and N. A. Spaldin, Journal of Ap- plied Physics 127, 10.1063/5.0006071 (2020)

    work page doi:10.1063/5.0006071 2020

  14. [14]

    Dagotto, Science 309, 257–262 (2005)

    E. Dagotto, Science 309, 257–262 (2005)

    work page 2005

  15. [15]

    Kotliar and D

    G. Kotliar and D. Vollhardt, Physics Today 57, 53–59 (2004)

    work page 2004

  16. [16]

    F. Lu, J. Zhao, H. Weng, Z. Fang, and X. Dai, Phys. Rev. Lett. 110, 096401 (2013)

    work page 2013

  17. [17]

    Nandy, C

    S. Nandy, C. Lane, and J.-X. Zhu, Phys. Rev. B 109, 085111 (2024)

    work page 2024

  18. [18]

    Hohenadler and F

    M. Hohenadler and F. F. Assaad, Journal of Physics: Condensed Matter 25, 143201 (2013)

    work page 2013

  19. [19]

    Rachel, Reports on Progress in Physics 81, 116501 (2018)

    S. Rachel, Reports on Progress in Physics 81, 116501 (2018)

    work page 2018

  20. [20]

    Crippa, A

    L. Crippa, A. Amaricci, N. Wagner, G. Sangiovanni, J. C. Budich, and M. Capone, Phys. Rev. Res.2, 012023 (2020)

    work page 2020

  21. [21]

    M. Braß, J. M. Tomczak, and K. Held, Weyl nodes in ce 3bi4pd3 revealed by dynamical mean-field theory 14 (2024), arXiv:2404.17425 [cond-mat.str-el]

    work page arXiv 2024

  22. [22]

    Gilardoni, F

    I. Gilardoni, F. Becca, A. Marrazzo, and A. Parola, Phys. Rev. B 106, L161106 (2022)

    work page 2022

  23. [23]

    C. Xu, Y. Ma, and S. Jiang, Reports on Progress in Physics 87, 108001 (2024)

    work page 2024

  24. [24]

    Guerci, J

    D. Guerci, J. Wang, J. Zang, J. Cano, J. H. Pixley, and A. Millis, Science Advances 9, 10.1126/sciadv.ade7701 (2023)

    work page doi:10.1126/sciadv.ade7701 2023

  25. [25]

    F. Xu, Z. Sun, J. Li, C. Zheng, C. Xu, J. Gao, T. Jia, K. Watanabe, T. Taniguchi, B. Tong, L. Lu, J. Jia, Z. Shi, S. Jiang, Y. Zhang, Y. Zhang, S. Lei, X. Liu, and T. Li, Signatures of unconventional superconduc- tivity near reentrant and fractional quantum anomalous hall insulators (2025), arXiv:2504.06972 [cond-mat.mes- hall]

    work page arXiv 2025

  26. [26]

    T. Han, Z. Lu, Z. Hadjri, L. Shi, Z. Wu, W. Xu, Y. Yao, A. A. Cotten, O. S. Sedeh, H. Weldeyesus, J. Yang, J. Seo, S. Ye, M. Zhou, H. Liu, G. Shi, Z. Hua, K. Watanabe, T. Taniguchi, P. Xiong, D. M. Zumb¨ uhl, L. Fu, and L. Ju, Signatures of chiral superconductiv- ity in rhombohedral graphene (2025), arXiv:2408.15233 [cond-mat.mes-hall]

    work page arXiv 2025

  27. [27]

    F. D. M. Haldane, Phys. Rev. Lett. 61, 2015 (1988)

    work page 2015

  28. [28]

    C. L. Kane and E. J. Mele, Phys. Rev. Lett. 95, 146802 (2005)

    work page 2005

  29. [29]

    B. A. Bernevig, T. L. Hughes, and S.-C. Zhang, Science 314, 1757 (2006)

    work page 2006

  30. [30]

    W. Kohn, A. D. Becke, and R. G. Parr, The Journal of Physical Chemistry 100, 12974–12980 (1996)

    work page 1996

  31. [31]

    R. O. Jones, Rev. Mod. Phys. 87, 897 (2015)

    work page 2015

  32. [32]

    R. M. Martin, Electronic Structure: Basic Theory and Practical Methods , 2nd ed. (Cambridge University Press, 2020)

    work page 2020

  33. [33]

    Slager, A

    R.-J. Slager, A. Mesaros, V. Juricic, and J. Zaanen, Na- ture Phys. 9, 98 (2013)

    work page 2013

  34. [34]

    Kruthoff, J

    J. Kruthoff, J. de Boer, J. van Wezel, C. L. Kane, and R.-J. Slager, Phys. Rev. X 7, 041069 (2017)

    work page 2017

  35. [35]

    Bradlyn, L

    B. Bradlyn, L. Elcoro, J. Cano, M. G. Vergniory, Z. Wang, C. Felser, M. I. Aroyo, and B. A. Bernevig, Nature 547, 298–305 (2017)

    work page 2017

  36. [36]

    Mounet, M

    N. Mounet, M. Gibertini, P. Schwaller, D. Campi, A. Merkys, A. Marrazzo, T. Sohier, I. E. Castelli, A. Ce- pellotti, G. Pizzi, and N. Marzari, Nature Nanotechnol- ogy 13, 246–252 (2018)

    work page 2018

  37. [37]

    M. G. Vergniory, L. Elcoro, C. Felser, N. Regnault, B. A. Bernevig, and Z. Wang, Nature 566, 480–485 (2019)

    work page 2019

  38. [38]

    Kotliar, S

    G. Kotliar, S. Y. Savrasov, K. Haule, V. S. Oudovenko, O. Parcollet, and C. A. Marianetti, Rev. Mod. Phys. 78, 865 (2006)

    work page 2006

  39. [39]

    Paul and T

    A. Paul and T. Birol, Annual Review of Materials Re- search 49, 31 (2019)

    work page 2019

  40. [40]

    T. Li, S. Jiang, B. Shen, Y. Zhang, L. Li, Z. Tao, T. De- vakul, K. Watanabe, T. Taniguchi, L. Fu, J. Shan, and K. F. Mak, Nature 600, 641–646 (2021)

    work page 2021

  41. [41]

    Devakul, V

    T. Devakul, V. Cr´ epel, Y. Zhang, and L. Fu, Nature Communications 12, 6730 (2021)

    work page 2021

  42. [42]

    S. Kim, T. Senthil, and D. Chowdhury, Phys. Rev. Lett. 130, 066301 (2023)

    work page 2023

  43. [43]

    Lanat` a, T.-H

    N. Lanat` a, T.-H. Lee, Y.-X. Yao, and V. Dobrosavljevi´ c, Phys. Rev. B 96, 195126 (2017)

    work page 2017

  44. [44]

    Guerci, M

    D. Guerci, M. Capone, and M. Fabrizio, Phys. Rev. Mater. 3, 054605 (2019)

    work page 2019

  45. [45]

    M. S. Frank, T.-H. Lee, G. Bhattacharyya, P. K. H. Tsang, V. L. Quito, V. Dobrosavljevi´ c, O. Christiansen, and N. Lanat` a, Phys. Rev. B104, L081103 (2021)

    work page 2021

  46. [46]

    Mejuto-Zaera and M

    C. Mejuto-Zaera and M. Fabrizio, Phys. Rev. B 107, 235150 (2023)

    work page 2023

  47. [47]

    T.-H. Lee, C. Melnick, R. Adler, N. Lanat` a, and G. Kotliar, Phys. Rev. B 108, 245147 (2023)

    work page 2023

  48. [48]

    T.-H. Lee, N. Lanat` a, and G. Kotliar, Phys. Rev. B107, L121104 (2023)

    work page 2023

  49. [49]

    Guerci, M

    D. Guerci, M. Capone, and N. Lanat` a, Phys. Rev. Res. 5, L032023 (2023)

    work page 2023

  50. [50]

    Lanat` a, Y

    N. Lanat` a, Y. Yao, C.-Z. Wang, K.-M. Ho, and G. Kotliar, Phys. Rev. X 5, 011008 (2015)

    work page 2015

  51. [51]

    Mejuto-Zaera, Faraday Discuss

    C. Mejuto-Zaera, Faraday Discuss. 254, 653 (2024)

    work page 2024

  52. [52]

    Fu and C

    L. Fu and C. L. Kane, Phys. Rev. B 76, 045302 (2007)

    work page 2007

  53. [53]

    Z. Song, T. Zhang, Z. Fang, and C. Fang, Nature Com- munications 9, 10.1038/s41467-018-06010-w (2018)

    work page doi:10.1038/s41467-018-06010-w 2018

  54. [54]

    Yoshida, R

    T. Yoshida, R. Peters, S. Fujimoto, and N. Kawakami, Phys. Rev. B 87, 085134 (2013)

    work page 2013

  55. [55]

    Miyakoshi and Y

    S. Miyakoshi and Y. Ohta, Phys. Rev. B 87, 195133 (2013)

    work page 2013

  56. [56]

    J. C. Budich, B. Trauzettel, and G. Sangiovanni, Phys. Rev. B 87, 235104 (2013)

    work page 2013

  57. [57]

    Amaricci, J

    A. Amaricci, J. C. Budich, M. Capone, B. Trauzettel, and G. Sangiovanni, Phys. Rev. Lett. 114, 185701 (2015)

    work page 2015

  58. [58]

    Blason and M

    A. Blason and M. Fabrizio, Phys. Rev. B 102, 035146 (2020)

    work page 2020

  59. [59]

    Amaricci, G

    A. Amaricci, G. Mazza, M. Capone, and M. Fabrizio, Phys. Rev. B 107, 115117 (2023)

    work page 2023

  60. [60]

    Crippa, A

    L. Crippa, A. Amaricci, S. Adler, G. Sangiovanni, and M. Capone, Phys. Rev. B 104, 235117 (2021)

    work page 2021

  61. [61]

    Wagner, L

    N. Wagner, L. Crippa, A. Amaricci, P. Hansmann, M. Klett, E. J. K¨ onig, T. Sch¨ afer, D. D. Sante, J. Cano, A. J. Millis, A. Georges, and G. Sangiovanni, Nature Communications 14, 7531 (2023)

    work page 2023

  62. [62]

    R. Soni, H. Radhakrishnan, B. Rosenow, G. Alvarez, and A. Del Maestro, Phys. Rev. B 109, 245115 (2024)

    work page 2024

  63. [63]

    Paoletti, L

    F. Paoletti, L. Fanfarillo, M. Capone, and A. Amaricci, Phys. Rev. B 109, 075148 (2024)

    work page 2024

  64. [64]

    Pasqua, A

    I. Pasqua, A. Blason, and M. Fabrizio, Phys. Rev. B 110, 125144 (2024)

    work page 2024

  65. [65]

    Fabrizio, Nature Communications 13, 1561 (2022)

    M. Fabrizio, Nature Communications 13, 1561 (2022)

    work page 2022

  66. [66]

    Fabrizio, Phys

    M. Fabrizio, Phys. Rev. Lett. 130, 156702 (2023)

    work page 2023

  67. [67]

    Blason and M

    A. Blason and M. Fabrizio, Phys. Rev. B 108, 125115 (2023)

    work page 2023

  68. [68]

    Kanamori, Progress of Theoretical Physics 30, 275–289 (1963)

    J. Kanamori, Progress of Theoretical Physics 30, 275–289 (1963)

    work page 1963

  69. [69]

    M. C. Gutzwiller, Phys. Rev. Lett. 10, 159 (1963)

    work page 1963

  70. [70]

    M. C. Gutzwiller, Phys. Rev. 137, A1726 (1965)

    work page 1965

  71. [71]

    B¨ unemann, W

    J. B¨ unemann, W. Weber, and F. Gebhard, Phys. Rev. B 57, 6896 (1998)

    work page 1998

  72. [72]

    Fabrizio, Phys

    M. Fabrizio, Phys. Rev. B 76, 165110 (2007)

    work page 2007

  73. [73]

    Y. X. Yao, J. Liu, C. Z. Wang, and K. M. Ho, Phys. Rev. B 89, 045131 (2014)

    work page 2014

  74. [74]

    Y. X. Yao, J. Liu, C. Liu, W. C. Lu, C. Z. Wang, and K. M. Ho, Scientific Reports 5, 13478 (2015)

    work page 2015

  75. [75]

    Fabrizio, Phys

    M. Fabrizio, Phys. Rev. B 95, 075156 (2017)

    work page 2017

  76. [76]

    W. F. Brinkman and T. M. Rice, Phys. Rev. B 2, 4302 (1970)

    work page 1970

  77. [77]

    Giuli, C

    S. Giuli, C. Mejuto-Zaera, and M. Capone, Phys. Rev. B 111, L020401 (2025)

    work page 2025

  78. [78]

    Local classical correlations between physical electrons in Hubbard systems

    G. Bellomia, A. Amaricci, and M. Capone, Local clas- sical correlations between physical electrons in the hub- bard model (2025), arXiv:2506.18709 [cond-mat.str-el]

    work page internal anchor Pith review Pith/arXiv arXiv 2025

  79. [79]

    A. M. Tagliente, C. Mejuto-Zaera, and M. Fabrizio, 15 Phys. Rev. B 111, 125110 (2025)

    work page 2025

  80. [80]

    Y. Yao, F. Zhang, C.-Z. Wang, K.-M. Ho, and P. P. Orth, Phys. Rev. Res. 3, 013184 (2021)

    work page 2021

Showing first 80 references.