Pith. sign in

REVIEW 3 major objections 3 minor 1 cited by

Self-consistent dynamical Hubbard functional for correlated solids

T0 review · 3 major / 3 minor · reviewed 2026-08-05 · deepseek-v4-flash

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

Pith's one-line read A fully self-consistent dynamical Hubbard functional now reproduces the spectrum of SrVO3 and improves its computed volume and bulk modulus.

desk verdict A plausible and significant advance in dynamical Hubbard functionals, but only the abstract was reviewed; the load-bearing inversion method remains unverified. read the letter →

arxiv 2508.18194 v1 pith:DMAUTMHL submitted 2025-08-25 cond-mat.str-el cond-mat.mtrl-sci

Tommaso Chiarotti , Matteo Quinzi , Andrea Pintus , Mario Caserta , Andrea Ferretti , Nicola Marzari This is my paper
classification cond-mat.str-elcond-mat.mtrl-sci
keywords dynamicalHubbardfunctionalself-consistentGreen'sfunctionfrequency-dependentUSrVO3correlatedsolidsequilibriumvolumebulkmodulussum-over-polesrepresentation
verification ladder T0 review T1 audit T2 compute T3 formal

The pith

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

The reading

The paper aims to remove the long-standing barrier of full self-consistency for dynamical many-body functionals in solids. It builds the dynamical Hubbard functional—a frequency-dependent generalization of DFT+U—and drives it to self-consistency using a sum-over-poles algorithmic inversion. Applied to the correlated metal SrVO3, the scheme retains the accurate spectral features known from one-shot calculations while shifting the equilibrium volume and bulk modulus significantly toward experiment. The result matters because spectral and thermodynamic properties, normally computed in separate ways, are here obtained from one self-consistent functional.

What carries the argument

The key machinery is the dynamical Hubbard functional—a functional of the Green's function that generalizes DFT+U by letting the Hubbard correction depend on frequency, so that screening in the localized d or f shells is treated dynamically. To reach self-consistency, the paper employs an algorithmic-inversion method based on a sum-over-poles representation of the frequency dependence. This representation makes the self-consistency equations tractable and numerically accurate for frequency-integrated quantities while preserving a real-frequency axis for spectral quantities.

What would settle it

Perform the same self-consistent calculation for SrVO3 with a much larger or differently distributed set of poles, or with an independent frequency-grid solver, and check whether the equilibrium volume and bulk modulus move by more than a few percent; a strong dependence on the pole representation would indicate the reported improvements are artifacts of the inversion.

Watch

Extended reading notes

Core claim

The central claim is that a fully self-consistent dynamical Hubbard functional is achievable for realistic solids, and that it fixes a previously known trade-off: one-shot dynamical functionals gave reliable spectra but unreliable total energies. By expressing the frequency-dependent Hubbard interaction as a sum over poles and inverting the resulting self-consistency equations, the authors solve the dynamical functional for the Green's function and thermodynamic observables. For SrVO3, the self-consistent solution reproduces the quasiparticle and satellite structure seen in ARPES, essentially confirming earlier one-shot results, and improves the equilibrium volume and bulk modulus relative t

Load-bearing premise

The accuracy of the result rests on the sum-over-poles inversion faithfully representing the full frequency dependence of the Hubbard interaction; if the pole expansion misses essential frequency structure, the improved equilibrium properties could be numerical artifacts.

Editorial extensions

If this is right

  • Fully self-consistent spectral and thermodynamic predictions become feasible for correlated solids, not just one-shot spectra.
  • Equilibrium lattice properties of correlated materials, such as volume and bulk modulus, can be computed from the same functional that gives the spectrum, removing a major inconsistency.
  • The SrVO3 results confirm previous one-shot spectral predictions, validating that self-consistency preserves spectral accuracy while improving energetics.
  • The method opens the way to predictive calculations for d- and f-electron materials where static DFT+U is insufficient.

Reading between the lines

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

  • If the algorithmic inversion is as accurate as claimed, the same framework could be applied to other dynamical functionals beyond the Hubbard functional, such as self-consistent GW-like corrections, where frequency dependence also blocks full self-consistency.
  • The improved bulk modulus suggests that phase-stability predictions for correlated oxides and intermetallics could shift when lattice degrees of freedom are relaxed with the dynamical functional—an implication the paper does not pursue.
  • A testable extension: apply the same sum-over-poles self-consistency to a correlated metal with stronger hybridization, where one-shot spectra are known to deviate from experiment, and see whether simultaneous spectral and thermodynamic accuracy still holds.
Share X Bluesky LinkedIn Reddit HN

Editorial analysis

A structured set of objections, weighed in public.

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

Referee Report

3 major / 3 minor

Summary. The paper proposes a fully self-consistent implementation of the dynamical Hubbard functional for solids, using an algorithmic-inversion method based on a sum-over-poles representation. The authors report that, for SrVO3, the method reproduces the experimentally observed spectral features, consistent with previous one-shot predictions, and improves the equilibrium volume and bulk modulus relative to experiment. The manuscript text provided for review consists of the abstract only; no derivations, algorithmic details, numerical data, convergence tests, or comparisons are included.

Significance. If fully substantiated, this would be a significant advance in first-principles correlated-electron methods: a fully self-consistent dynamical functional capable of simultaneously describing real-axis spectra and thermodynamic properties would move beyond one-shot dynamical-mean-field-like schemes and would be of broad interest in condensed-matter theory. The practical demonstration on SrVO3, a paradigmatic correlated metal, is well chosen. However, the significance is conditional: with only the abstract available, the correctness and numerical robustness of the central claims cannot be assessed. No machine-checked proofs, reproducible code, or parameter-free derivations are visible in the supplied text.

major comments (3)
  1. [Abstract / overall manuscript] The central claim of a 'numerically accurate self-consistent scheme' is not supported by any evidence in the available manuscript: there are no derivations, no definitions of the algorithmic-inversion method or the sum-over-poles representation, no convergence tests with respect to the number of poles or the frequency grid, and no error bars on the reported equilibrium volume and bulk modulus. These are load-bearing omissions because the validity of the pole representation is precisely what determines whether the frequency-integrated and real-axis results are artifacts of truncation.
  2. [Abstract, 'algorithmic-inversion method based on a sum-over-poles representation'] The abstract identifies the sum-over-poles representation as the enabler of the fully self-consistent scheme, but no details are provided about how the inversion is performed, how the pole positions and residues are determined, or how the accuracy of this representation is validated. In particular, no comparison is shown to other frequency representations (e.g., fine grids or Padé approximants) that would establish that the reported spectrum and thermodynamics are independent of the chosen representation. Without such tests, the central technical innovation is unverified.
  3. [Abstract, SrVO3 results] The claim of 'significantly closer' to experimental volume and bulk modulus is not quantified: no numerical values, no experimental references, and no comparison to previous theoretical results are provided. Similarly, 'essentially confirming previous one-shot predictions' is not accompanied by the actual spectra or a quantitative measure of agreement (e.g., peak positions, widths). These omissions prevent any independent check of the reported improvement and of the claim that the self-consistency preserves the earlier one-shot spectral results.
minor comments (3)
  1. [Abstract, terminology] The term 'dynamical Hubbard functional' is used without definition; since the paper presumably extends DFT+U, a precise statement of the functional dependence on the frequency-dependent interaction should be given in the introduction.
  2. [Abstract, 'fully first-principles'] The phrase 'fully first-principles' is asserted but no parameter counts are stated. If the Hubbard U and its frequency dependence are derived from the electronic structure itself (e.g., constrained RPA or similar), this should be explicitly stated; if any external parameter is used, the claim should be qualified.
  3. [Abstract, self-consistency] A mild circularity concern is implicit: if the screening defining the frequency-dependent Hubbard interaction is computed from the same Green's function that the functional then corrects, the self-consistent feedback could bias the results. The manuscript should clarify the construction of the interaction kernel and the self-consistency loop.

Circularity Check

0 steps flagged · score 0.0 of 10

No circularity identified from abstract; the derivation is not shown to reduce to its inputs.

full rationale

The abstract presents a self-consistent dynamical Hubbard functional with frequency-dependent screening. It does not state that any parameter is fitted to the target spectra or equilibrium properties, and it does not invoke a self-citation as the load-bearing justification for its central claim. The sum-over-poles representation and algorithmic-inversion scheme are numerical techniques, but nothing in the abstract shows an equation in which a predicted quantity is identical by construction to an input or fitted value. The SrVO3 results are benchmarked against experimental spectra, volume, and bulk modulus, which are external targets rather than circular restatements of the inputs. The only potential concern visible is numerical convergence of the pole representation, but that is a verification/correctness issue, not circularity. With no detailed equations or derivation chain available, there is no exhibitable reduction of a prediction to a fit or to a self-citation, so the appropriate finding is no significant circularity.

Assumptions & free parameters 0 free parameters · 3 assumptions · 0 invented entities

From the abstract alone, the only stated ingredients are the dynamical Hubbard functional and the pole representation. No new particles, mediators, or conserved quantities are introduced, and no explicit free parameters are named. The axioms listed are the domain assumptions required for the method to apply.

assumptions (3)
  • domain assumption The many-body Green's function functional (dynamical Hubbard) formalism is applicable to solids with localized d/f orbitals.
    The entire method builds on this functional framework, which is taken from prior literature, as stated in the abstract.
  • domain assumption The Hubbard interaction is localized to a small set of d/f orbitals near the Fermi level.
    The abstract states the functional targets materials with d- or f-localized orbitals, which requires the localization assumption.
  • ad hoc to paper The sum-over-poles representation is a sufficiently accurate and complete basis for the frequency-dependent interaction and the self-consistent solution.
    The abstract introduces this as the key enabling approximation but does not justify its completeness in the abstract.

how reviews work

0 comments
Cite this review

Pith. "Pith review of Self-consistent dynamical Hubbard functional for correlated solids." pith.science (2026). https://pith.science/paper/DMAUTMHL

@misc{pith2026250818194,
  author       = {Pith},
  title        = {Pith review of: Self-consistent dynamical Hubbard functional for correlated solids},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/DMAUTMHL}},
  note         = {Machine review of arXiv:2508.18194}
}
abstract

Many-body functionals of the Green's function can provide fundamental advances in electronic-structure calculations, due to their ability to accurately predict both spectral and thermodynamic properties, such as angle-resolved photoemission spectroscopy (ARPES) experiments and total energies of materials. However, fully first-principles, self-consistent calculations with these dynamical functionals remain a major challenge, ultimately limiting their application to thermodynamic quantities, and restricting spectral predictions to one-shot calculations. In this paper, we present a fully self-consistent treatment of the electronic structure of solids using a dynamical functional. Our approach leverages the so-called dynamical Hubbard functional, which generalizes the DFT+$U$ correction by incorporating frequency-dependent screening, augmenting the static density functional to accurately describe both spectral and thermodynamic properties of materials with $d$- or $f$-localized orbitals near the Fermi level. To enable this, we employ the algorithmic-inversion method based on a sum-over-poles representation, resulting in a numerically accurate self-consistent scheme for frequency-integrated properties, while keeping real-axis spectral resolution for dynamically-resolved quantities. Using this framework, we study the paradigmatic correlated solid SrVO$_3$, accurately reproducing its spectral features, essentially confirming previous one-shot predictions, and improving the description of its equilibrium properties, such as the equilibrium volume and bulk modulus, bringing these significantly closer to experimental measurements.

Discussion (0). Sign in to comment.

Forward citations

Cited by 1 Pith paper

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

  1. Dynamical pseudopotentials

    cond-mat.mtrl-sci 2026-05 unverdicted novelty 7.0 of 10

    Dynamical pseudopotentials with sum-over-poles representation reproduce all-electron scattering over wide energy ranges and enable a consistent many-body treatment of all-electron atoms, pseudo-atoms, and solids.

Reference graph

Works this paper leans on

73 extracted references · 41 canonical work pages · cited by 1 Pith paper

  1. [1]

    , " * write output.state after.block =

    ") INTEGERS output.state before.all mid.sentence after.sentence after.block FUNCTION init.state.consts #0 'before.all := #1 'mid.sentence := #2 'after.sentence := #3 'after.block := STRINGS s t FUNCTION output.nonnull 's := output.state mid.sentence = ", " * write output.state after.block = "," * write newline " " write output.state before.all = 'write ad...

  2. [2]

    write newline

    " write newline "" before.all 'output.state := FUNCTION fin.entry add.period write newline FUNCTION new.block output.state before.all = 'skip after.block 'output.state := if FUNCTION new.sentence skip FUNCTION not #0 #1 if FUNCTION and 'skip pop #0 if FUNCTION or pop #1 'skip if FUNCTION new.block.checka empty 'skip 'new.block if FUNCTION new.block.checkb...

    work page

  3. [3]

    Marzari , author A

    author author N. Marzari , author A. Ferretti , \ and\ author C. Wolverton ,\ 10.1038/s41563-021-01013-3 journal journal Nature Materials \ volume 20 ,\ pages 736 ( year 2021 ) NoStop

    work page doi:10.1038/s41563-021-01013-3 2021

  4. [4]

    Onida , author L

    author author G. Onida , author L. Reining , \ and\ author A. Rubio ,\ 10.1103/RevModPhys.74.601 journal journal Reviews of Modern Physics \ volume 74 ,\ pages 601 ( year 2002 ) NoStop

    doi:10.1103/revmodphys.74.601 2002

  5. [5]

    Georges , author G

    author author A. Georges , author G. Kotliar , author W. Krauth , \ and\ author M. J. \ Rozenberg ,\ 10.1103/RevModPhys.68.13 journal journal Reviews of Modern Physics \ volume 68 ,\ pages 13 ( year 1996 ) NoStop

    doi:10.1103/revmodphys.68.13 1996

  6. [6]

    author author J. M. \ Luttinger \ and\ author J. C. \ Ward ,\ 10.1103/PhysRev.118.1417 journal journal Physical Review \ volume 118 ,\ pages 1417 ( year 1960 ) NoStop

    doi:10.1103/physrev.118.1417 1960

  7. [7]

    Baym \ and\ author L

    author author G. Baym \ and\ author L. P. \ Kadanoff ,\ 10.1103/PhysRev.124.287 journal journal Physical Review \ volume 124 ,\ pages 287 ( year 1961 ) NoStop

    doi:10.1103/physrev.124.287 1961

  8. [8]

    Baym ,\ 10.1103/PhysRev.127.1391 journal journal Physical Review \ volume 127 ,\ pages 1391 ( year 1962 ) NoStop

    author author G. Baym ,\ 10.1103/PhysRev.127.1391 journal journal Physical Review \ volume 127 ,\ pages 1391 ( year 1962 ) NoStop

    doi:10.1103/physrev.127.1391 1962

Show all 73 references
  1. [9]

    author author R. M. \ Martin , author L. Reining , \ and\ author D. M. \ Ceperley ,\ 10.1017/CBO9781139050807 title Interacting Electrons : Theory and Computational Approaches , \ ( year 2016 ) NoStop

    2016 doi

  2. [10]

    Stefanucci \ and\ author R

    author author G. Stefanucci \ and\ author R. v. \ Leeuwen ,\ 10.1017/CBO9781139023979 title Nonequilibrium Many - Body Theory of Quantum Systems : A Modern Introduction , \ ( year 2013 ) NoStop

    2013 doi

  3. [11]

    Reining ,\ 10.1002/wcms.1344 journal journal Wiley Interdisciplinary Reviews: Computational Molecular Science \ volume 8 ,\ pages e1344 ( year 2018 ) NoStop

    author author L. Reining ,\ 10.1002/wcms.1344 journal journal Wiley Interdisciplinary Reviews: Computational Molecular Science \ volume 8 ,\ pages e1344 ( year 2018 ) NoStop

    2018 doi

  4. [12]

    van Schilfgaarde , author T

    author author M. van Schilfgaarde , author T. Kotani , \ and\ author S. Faleev ,\ 10.1103/PhysRevLett.96.226402 journal journal Physical Review Letters \ volume 96 ,\ pages 226402 ( year 2006 ) NoStop

    2006 doi

  5. [13]

    Kotani , author M

    author author T. Kotani , author M. van Schilfgaarde , \ and\ author S. V. \ Faleev ,\ 10.1103/PhysRevB.76.165106 journal journal Physical Review B \ volume 76 ,\ pages 165106 ( year 2007 ) NoStop

    2007 doi

  6. [14]

    Kutepov , author S

    author author A. Kutepov , author S. Y. \ Savrasov , \ and\ author G. Kotliar ,\ 10.1103/PhysRevB.80.041103 journal journal Physical Review B \ volume 80 ,\ pages 041103 ( year 2009 ) NoStop

    2009 doi

  7. [15]

    Kutepov , author K

    author author A. Kutepov , author K. Haule , author S. Y. \ Savrasov , \ and\ author G. Kotliar ,\ 10.1103/PhysRevB.85.155129 journal journal Physical Review B \ volume 85 ,\ pages 155129 ( year 2012 ) NoStop

    2012 doi

  8. [16]

    Grumet , author P

    author author M. Grumet , author P. Liu , author M. Kaltak , author J. Klimeš , \ and\ author G. Kresse ,\ 10.1103/PhysRevB.98.155143 journal journal Physical Review B \ volume 98 ,\ pages 155143 ( year 2018 ) NoStop

    2018 doi

  9. [17]

    \ Yeh , author S

    author author C.-N. \ Yeh , author S. Iskakov , author D. Zgid , \ and\ author E. Gull ,\ 10.1103/PhysRevB.106.235104 journal journal Physical Review B \ volume 106 ,\ pages 235104 ( year 2022 ) NoStop

    2022 doi

  10. [18]

    Iskakov , author C.-N

    author author S. Iskakov , author C.-N. \ Yeh , author P. Pokhilko , author Y. Yu , author L. Zhang , author G. Harsha , author V. Abraham , author M. Wen , author M. Wang , author J. Adamski , author T. Chen , author E. Gull , \ and\ author D. Zgid ,\ 10.1016/j.cpc.2024.10938...

    2024

  11. [19]

    Gunnarsson , author M

    author author O. Gunnarsson , author M. W. \ Haverkort , \ and\ author G. Sangiovanni ,\ 10.1103/PhysRevB.82.165125 journal journal Physical Review B \ volume 82 ,\ pages 165125 ( year 2010 ) NoStop

    2010 doi

  12. [20]

    author author A. L. \ Kutepov \ and\ author G. Kotliar ,\ 10.1103/PhysRevB.96.035108 journal journal Physical Review B \ volume 96 ,\ pages 035108 ( year 2017 ) NoStop

    2017 doi

  13. [21]

    Fei , author C.-N

    author author J. Fei , author C.-N. \ Yeh , \ and\ author E. Gull ,\ 10.1103/PhysRevLett.126.056402 journal journal Physical Review Letters \ volume 126 ,\ pages 056402 ( year 2021 ) NoStop

    2021 doi

  14. [22]

    Zhang , author Y

    author author L. Zhang , author Y. Yu , \ and\ author E. Gull ,\ 10.1103/PhysRevB.110.235131 journal journal Physical Review B \ volume 110 ,\ pages 235131 ( year 2024 ) NoStop

    2024 doi

  15. [23]

    Kotliar , author S

    author author G. Kotliar , author S. Y. \ Savrasov , author K. Haule , author V. S. \ Oudovenko , author O. Parcollet , \ and\ author C. A. \ Marianetti ,\ 10.1103/RevModPhys.78.865 journal journal Reviews of Modern Physics \ volume 78 ,\ pages 865 ( year 2006 ) NoStop

    2006 doi

  16. [24]

    author author S. Y. \ Savrasov \ and\ author G. Kotliar ,\ 10.1103/PhysRevB.69.245101 journal journal Physical Review B \ volume 69 ,\ pages 245101 ( year 2004 ) NoStop

    2004 doi

  17. [25]

    https://juser.fz-juelich.de/record/909714 title D ynamical M ean- F ield T heory of C orrelated E lectrons ,\ series Modeling and Simulation , Vol. volume 12 ,\ organization Autumn School on Correlated Electrons, Jülich (Germany), 4 Oct 2022 - 7 Oct 2022 \ ( publisher Forschun...

    2022

  18. [26]

    Paul , author D

    author author S. Paul , author D. Iu s s an , author P. Thunstr\"om , author Y. O. \ Kvashnin , author J. Hellsvik , author M. Pereiro , author A. Delin , author R. Knut , author D. Phuyal , author A. Lindblad , author O. Karis , author B. Sanyal , \ and\ author O. Eriksson ,\...

    2018 doi

  19. [27]

    Mlkvik , author M

    author author P. Mlkvik , author M. E. \ Merkel , author N. A. \ Spaldin , \ and\ author C. Ederer ,\ 10.1103/PhysRevResearch.6.033122 journal journal Phys. Rev. Res. \ volume 6 ,\ pages 033122 ( year 2024 ) NoStop

    2024 doi

  20. [28]

    author author E. B. \ Isaacs \ and\ author C. A. \ Marianetti ,\ 10.1103/PhysRevB.102.045146 journal journal Phys. Rev. B \ volume 102 ,\ pages 045146 ( year 2020 ) NoStop

    2020 doi

  21. [29]

    Boehnke , author F

    author author L. Boehnke , author F. Nilsson , author F. Aryasetiawan , \ and\ author P. Werner ,\ 10.1103/PhysRevB.94.201106 journal journal Physical Review B \ volume 94 ,\ pages 201106 ( year 2016 ) NoStop

    2016 doi

  22. [30]

    Nilsson , author L

    author author F. Nilsson , author L. Boehnke , author P. Werner , \ and\ author F. Aryasetiawan ,\ 10.1103/PhysRevMaterials.1.043803 journal journal Physical Review Materials \ volume 1 ,\ pages 043803 ( year 2017 ) NoStop

    2017 doi

  23. [31]

    author author S. L. \ Dudarev , author G. A. \ Botton , author S. Y. \ Savrasov , author C. J. \ Humphreys , \ and\ author A. P. \ Sutton ,\ 10.1103/PhysRevB.57.1505 journal journal Physical Review B \ volume 57 ,\ pages 1505 ( year 1998 ) NoStop

    1998 doi

  24. [32]

    Chiarotti , author A

    author author T. Chiarotti , author A. Ferretti , \ and\ author N. Marzari ,\ 10.1103/PhysRevResearch.6.L032023 journal journal Physical Review Research \ volume 6 ,\ pages L032023 ( year 2024 ) NoStop

    2024 doi

  25. [33]

    Caserta , author T

    author author M. Caserta , author T. Chiarotti , author M. Vanzini , \ and\ author N. Marzari ,\ 10.48550/arXiv.2503.10893 title Dynamical Hubbard approach to correlated materials: the case of transition-metal monoxides , \ ( year 2025 ),\ note arXiv:2503.10893 [cond-mat] NoStop

    2025 doi arXiv

  26. [34]

    Gatti \ and\ author M

    author author M. Gatti \ and\ author M. Guzzo ,\ 10.1103/PhysRevB.87.155147 journal journal Physical Review B \ volume 87 ,\ pages 155147 ( year 2013 ) NoStop

    2013 doi

  27. [35]

    Chiarotti ,\ title Spectral and thermodynamic properties of interacting electrons with dynamical functionals ,\ https://doi.org/10.5075/epfl-thesis-10201 Ph.D

    author author T. Chiarotti ,\ title Spectral and thermodynamic properties of interacting electrons with dynamical functionals ,\ https://doi.org/10.5075/epfl-thesis-10201 Ph.D. thesis ,\ school EPFL , address Lausanne ( year 2023 ) NoStop

    2023 doi

  28. [36]

    Marzari , author A

    author author N. Marzari , author A. A. \ Mostofi , author J. R. \ Yates , author I. Souza , \ and\ author D. Vanderbilt ,\ 10.1103/RevModPhys.84.1419 journal journal Reviews of Modern Physics \ volume 84 ,\ pages 1419 ( year 2012 ) NoStop

    2012 doi

  29. [37]

    Chiarotti , author N

    author author T. Chiarotti , author N. Marzari , \ and\ author A. Ferretti ,\ 10.1103/PhysRevResearch.4.013242 journal journal Physical Review Research \ volume 4 ,\ pages 013242 ( year 2022 ) NoStop

    2022 doi

  30. [38]

    Ferretti , author T

    author author A. Ferretti , author T. Chiarotti , \ and\ author N. Marzari ,\ 10.1103/PhysRevB.110.045149 journal journal Physical Review B \ volume 110 ,\ pages 045149 ( year 2024 ) NoStop

    2024 doi

  31. [39]

    Quinzi , author T

    author author M. Quinzi , author T. Chiarotti , author M. Gibertini , \ and\ author A. Ferretti ,\ 10.1103/PhysRevB.111.125148 journal journal Physical Review B \ volume 111 ,\ pages 125148 ( year 2025 ) NoStop

    2025 doi

  32. [40]

    author author G. E. \ Engel , author B. Farid , author C. M. M. \ Nex , \ and\ author N. H. \ March ,\ 10.1103/PhysRevB.44.13356 journal journal Physical Review B \ volume 44 ,\ pages 13356 ( year 1991 ) NoStop

    1991 doi

  33. [41]

    note Here, any singular value decomposition suffice to find V_m and V ^ _m . In this work we use _i= _i _i as defined by (omitting the bath index for brevity): = S S^ -1 , with the diagonal matrix of the (principal branch) of the square root of the eigenvalues. Stop

  34. [42]

    note This can be seen from the singular values of the k -dependent dynamical-Hubbard self-energy residues, that, by construction, match those of the local self-energy. Stop

  35. [43]

    author author S. Y. \ Savrasov , author K. Haule , \ and\ author G. Kotliar ,\ 10.1103/PhysRevLett.96.036404 journal journal Physical Review Letters \ volume 96 ,\ pages 036404 ( year 2006 ) NoStop

    2006 doi

  36. [44]

    author author S. J. \ Bintrim \ and\ author T. C. \ Berkelbach ,\ 10.1063/5.0035141 journal journal The Journal of Chemical Physics \ volume 154 ,\ pages 041101 ( year 2021 ) NoStop

    2021 doi

  37. [45]

    author author O. J. \ Backhouse , author A. Santana-Bonilla , \ and\ author G. H. \ Booth ,\ 10.1021/acs.jpclett.1c02383 journal journal The Journal of Physical Chemistry Letters \ volume 12 ,\ pages 7650 ( year 2021 ) NoStop

    2021 doi

  38. [46]

    author author S. J. \ Bintrim \ and\ author T. C. \ Berkelbach ,\ 10.1063/5.0074434 journal journal The Journal of Chemical Physics \ volume 156 ,\ pages 044114 ( year 2022 ) NoStop

    2022 doi

  39. [47]

    author author C. J. C. \ Scott , author O. J. \ Backhouse , \ and\ author G. H. \ Booth ,\ 10.1063/5.0143291 journal journal The Journal of Chemical Physics \ volume 158 ,\ pages 124102 ( year 2023 ) NoStop

    2023 doi

  40. [48]

    Gao , author Z

    author author W. Gao , author Z. Tang , author J. Zhao , \ and\ author J. R. \ Chelikowsky ,\ 10.1103/PhysRevLett.132.126402 journal journal Physical Review Letters \ volume 132 ,\ pages 126402 ( year 2024 ) NoStop

    2024 doi

  41. [49]

    author author D. A. \ Leon , author C. Cardoso , author T. Chiarotti , author D. Varsano , author E. Molinari , \ and\ author A. Ferretti ,\ 10.1103/PhysRevB.104.115157 journal journal Physical Review B \ volume 104 ,\ pages 115157 ( year 2021 ) NoStop

    2021 doi

  42. [50]

    author author D. A. \ Leon , author A. Ferretti , author D. Varsano , author E. Molinari , \ and\ author C. Cardoso ,\ 10.1103/PhysRevB.107.155130 journal journal Physical Review B \ volume 107 ,\ pages 155130 ( year 2023 ) NoStop

    2023 doi

  43. [51]

    author author D. A. \ Leon , author K. Berland , \ and\ author C. Cardoso ,\ 10.1103/PhysRevB.111.195147 journal journal Physical Review B \ volume 111 ,\ pages 195147 ( year 2025 ) NoStop

    2025 doi

  44. [52]

    note The SOP for the self-energy is obtained from the SOP of G _ KS ( ) and U( ) using the Cauchy residue theorem for the convolution of two SOP-propagators chiarotti_unified_2022 . Stop

  45. [53]

    the position of the first t_ 2g quasiparticle peak (BW) and last peak (full), as the center of the peak of the DOS

    @noop note Note that, due to the finite lifetimes, we estimate the occupied bandwidth and effective mass, i.e. the position of the first t_ 2g quasiparticle peak (BW) and last peak (full), as the center of the peak of the DOS. In the figure we do not use an extra broadening fo...

  46. [54]

    Yoshida , author K

    author author T. Yoshida , author K. Tanaka , author H. Yagi , author A. Ino , author H. Eisaki , author A. Fujimori , \ and\ author Z.-X. \ Shen ,\ 10.1103/PhysRevLett.95.146404 journal journal Physical Review Letters \ volume 95 ,\ pages 146404 ( year 2005 ) NoStop

    2005 doi

  47. [55]

    Takizawa , author M

    author author M. Takizawa , author M. Minohara , author H. Kumigashira , author D. Toyota , author M. Oshima , author H. Wadati , author T. Yoshida , author A. Fujimori , author M. Lippmaa , author M. Kawasaki , author H. Koinuma , author G. Sordi , \ and\ author M. Rozenberg ...

    2009 doi

  48. [56]

    Haule \ and\ author T

    author author K. Haule \ and\ author T. Birol ,\ 10.1103/PhysRevLett.115.256402 journal journal Physical Review Letters \ volume 115 ,\ pages 256402 ( year 2015 ) NoStop

    2015 doi

  49. [57]

    Maekawa , author K

    author author T. Maekawa , author K. Kurosaki , \ and\ author S. Yamanaka ,\ 10.1016/j.jallcom.2006.02.026 journal journal Journal of Alloys and Compounds \ volume 426 ,\ pages 46 ( year 2006 ) NoStop

    2006 doi

  50. [58]

    note Please note that here with +V correction we mean we perform a DFT+V (static) calculation with the value of V from linear response timrov_hubbard_2018,timrov_accurate_2022 . Stop

  51. [59]

    note As mentioned in the numerical details, the experimental lattice parameter is extrapolated to zero temperature using the thermal expansion coefficient reported in the same reference. Stop

  52. [60]

    Giannozzi , author S

    author author P. Giannozzi , author S. Baroni , author N. Bonini , author M. Calandra , author R. Car , author C. Cavazzoni , author D. Ceresoli , author G. L. \ Chiarotti , author M. Cococcioni , author I. Dabo , author A. D. \ Corso , author S. d. \ Gironcoli , author S. Fab...

    2009

  53. [61]

    Nakamura , author Y

    author author K. Nakamura , author Y. Yoshimoto , author Y. Nomura , author T. Tadano , author M. Kawamura , author T. Kosugi , author K. Yoshimi , author T. Misawa , \ and\ author Y. Motoyama ,\ 10.1016/j.cpc.2020.107781 journal journal Computer Physics Communications \ volum...

    2020

  54. [62]

    author author D. R. \ Hamann ,\ 10.1103/PhysRevB.88.085117 journal journal Physical Review B \ volume 88 ,\ pages 085117 ( year 2013 ) NoStop

    2013 doi

  55. [63]

    author author M. J. \ van Setten , author M. Giantomassi , author E. Bousquet , author M. J. \ Verstraete , author D. R. \ Hamann , author X. Gonze , \ and\ author G. M. \ Rignanese ,\ 10.1016/j.cpc.2018.01.012 journal journal Computer Physics Communications \ volume 226 ,\ pa...

    2018 doi

  56. [64]

    author author Y. C. \ Lan , author X. L. \ Chen , \ and\ author M. He ,\ 10.1016/S0925-8388(02)01349-X journal journal Journal of Alloys and Compounds \ volume 354 ,\ pages 95 ( year 2003 ) NoStop

    2003 doi

  57. [65]

    Marzari , author D

    author author N. Marzari , author D. Vanderbilt , author A. De Vita , \ and\ author M. C. \ Payne ,\ 10.1103/PhysRevLett.82.3296 journal journal Physical Review Letters \ volume 82 ,\ pages 3296 ( year 1999 ) NoStop

    1999 doi

  58. [66]

    Puig von Friesen , author C

    author author M. Puig von Friesen , author C. Verdozzi , \ and\ author C.-O. \ Almbladh ,\ 10.1103/PhysRevB.82.155108 journal journal Physical Review B \ volume 82 ,\ pages 155108 ( year 2010 ) NoStop

    2010 doi

  59. [67]

    sec:numerical_details for the exact value

    note Please note that for this work we converge total energy differences as we are interested in the equation of state, see Sec. sec:numerical_details for the exact value. Stop

  60. [68]

    author author V. M. \ Galitskii \ and\ author A. B. \ Migdal ,\ https://www.osti.gov/biblio/4348538 journal journal Zhur. Eksptl'. i Teoret. Fiz. \ volume Vol: 34 ( year 1958 ) NoStop

    1958

  61. [69]

    However, the positive semi-definiteness is not guaranteed in general in the case of complex valued poles, and thus we take the absolute value of the trace

    note From the Lehmann representation, the Green's function is expected to have positive semi-definite residues. However, the positive semi-definiteness is not guaranteed in general in the case of complex valued poles, and thus we take the absolute value of the trace. Stop

  62. [70]

    equation NoStop

    note The conservation of the Galitskii-Migdal energy is evident from the expression: equation E_ GM = 1 2 @ d 2 i e^ i0^+ [ +h_0 ] G( ) \, . equation NoStop

  63. [71]

    Hellgren \ and\ author E

    author author M. Hellgren \ and\ author E. K. U. \ Gross ,\ 10.1103/PhysRevA.85.022514 journal journal Physical Review A \ volume 85 ,\ pages 022514 ( year 2012 ) NoStop

    2012 doi

  64. [72]

    Timrov , author N

    author author I. Timrov , author N. Marzari , \ and\ author M. Cococcioni ,\ 10.1103/PhysRevB.98.085127 journal journal Physical Review B \ volume 98 ,\ pages 085127 ( year 2018 ) NoStop

    2018 doi

  65. [73]

    Timrov , author F

    author author I. Timrov , author F. Aquilante , author M. Cococcioni , \ and\ author N. Marzari ,\ 10.1103/PRXEnergy.1.033003 journal journal PRX Energy \ volume 1 ,\ pages 033003 ( year 2022 ) NoStop

    2022 doi

Pith tools

Reviewed August 5, 2026 · model on record in the stance chip above.