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REVIEW 2 major objections 4 minor 69 references

Strong correlations and local self-energies from on-site ensembles

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Pith's one-line read A Boltzmann-weighted average over all static, symmetry-broken Hartree-Fock solutions reproduces the dynamical self-energy of paramagnetic Mott insulators, matching dynamical mean-field theory for NiO and FeO.

desk verdict A genuinely new ensemble construction with honest limits; the NiO/FeO benchmarks are direct and convincing, but SI/code are missing and the saddle-point control is unquantified. read the letter →

arxiv 2607.21490 v1 pith:5QH5KNGG submitted 2026-07-23 cond-mat.str-el

Alberto Carta , Hugo U. R. Strand , Michael Schüler , Nicola Marzari This is my paper · ORCID
classification cond-mat.str-el
keywords Mottinsulatorsdynamicalmean-fieldtheoryself-energysymmetrybreakingcoherent-potentialapproximationlocalmomentson-sitedephasedensembletransition-metaloxides
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

Paramagnetic Mott insulators defeat standard density-functional theory, which predicts metals unless symmetry is artificially broken. This paper introduces the on-site dephased ensemble (DE): instead of picking one Hartree-Fock solution, it forms a Boltzmann average over all accessible static solutions of the local embedding problem. The average produces a frequency-dependent self-energy, and for NiO and FeO the DE self-energy, spectral function, and spin-spin covariance closely match dynamical mean-field theory at a fraction of the cost. The message is that the characteristic frequency structure of 'strong correlations' in gapped Mott systems can be read as the signature of a disordered alloy of symmetry-broken static states.

What carries the argument

The central object is the on-site dephased ensemble (DE), defined by a Boltzmann-weighted sum over all stationary Hartree-Fock self-energies of the local embedding problem: G_DE = sum_s p_s G_s, with p_s proportional to exp(-beta Omega[Sigma_s]). This is mathematically the single-site coherent-potential approximation of an alloy whose 'elements' are symmetry-broken static solutions. The workhorse identity is the stationary-phase reduction of the impurity partition function, which replaces the functional integral over auxiliary fields by a discrete sum over saddle points, converting a dynamical problem into a static statistical mixture. A second identity splits the two-particle covariance int

What would settle it

Compute the Gaussian fluctuation determinant around each stationary Hartree-Fock solution for NiO and reweight the ensemble; if the DE self-energy or spin-spin covariance shifts noticeably away from the dynamical mean-field benchmark, the saddle-point sum underlying the DE is missing physics.

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Extended reading notes

Core claim

The paper's central claim is that the local Green's function of a correlated site is well approximated by a Boltzmann-weighted sum over Green's functions built from each static Hartree-Fock self-energy that is a stationary point of the embedding grand potential. Even though each ingredient is static, the averaged inverse Green's function produces a strongly frequency-dependent effective self-energy. This 'on-site dephased ensemble' is shown to reproduce the dynamical mean-field self-energy and spectral function for paramagnetic NiO and FeO, and the ensemble variance in the two-particle covariance keeps local moments alive at long times, matching dynamical mean-field theory to within a few pe

Load-bearing premise

The construction works only if the local problem's partition function can be represented as a discrete sum over static Hartree-Fock solutions, ignoring quantum fluctuations around each solution and tunneling between them.

Editorial extensions

If this is right

  • For large-gap paramagnetic Mott insulators, DE can replace quantum Monte Carlo impurity solvers, recovering the DMFT self-energy and spectral function at a small fraction of the computational cost.
  • The strong frequency dependence of the local self-energy is reinterpreted as the CPA-like averaging of a disordered alloy of symmetry-broken static states, providing a concrete bridge between the many-body and polymorphous supercell viewpoints.
  • The ensemble variance in the two-particle correlation formula gives a static mechanism for persistent local moments; a single static mean-field solution cannot produce this persistence.
  • Because DE has no fermion sign problem, it opens a route to first-principles treatment of f-electron Mott insulators.
  • DE can be used to precondition DMFT impurity solves and can be extended to cluster schemes for non-local spatial correlations.

Reading between the lines

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

  • If the DE reproduces DMFT generically, the distinction between 'dynamical' and 'static-disorder' origins of Mott gaps becomes a formal duality, and correlation strength in gapped systems could be recast in terms of the density of low-lying symmetry-broken states.
  • The DE's stationary-phase approximation omits Gaussian fluctuations around each saddle; a direct test would be to include those fluctuations and check whether the NiO/FeO weights shift. If they do, the current agreement may partly rely on error cancellation.
  • The temperature dependence of the Boltzmann weights makes DE's ensemble composition—not just occupations—temperature dependent; comparing DE and DMFT across temperatures could reveal how basin structure controls the crossover toward the metallic state.
  • Applying DE to doped Mott insulators or charge-transfer systems with smaller gaps would probe where the static-alloy picture breaks down, since those systems have stronger inter-basin coherences.
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Editorial analysis

A structured set of objections, weighed in public.

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

Referee Report

2 major / 4 minor

Summary. The paper introduces the on-site dephased ensemble (DE) approximation for the local impurity problem in DMFT and related embedding schemes. Instead of keeping a single static Hartree-Fock solution, DE sums over all stationary solutions of the embedding grand potential with Boltzmann weights p_s = exp(-βΩ_s)/Z, producing a CPA-like average Green's function G_DE = Σ_s p_s G_s and hence a frequency-dependent effective self-energy. The authors derive this approximation from a Hubbard-Stratonovich representation of the Anderson impurity model (Appendix A) and apply it to paramagnetic NiO and FeO in a five-orbital model with U=6 eV, J=1 eV. They report quantitative agreement with CTSEG DMFT for the Matsubara self-energy, the real-frequency spectral function, and the spin-spin covariance (within 4–6%). The central interpretive claim is that the strong frequency dependence of Mott-insulator self-energies can be viewed as the signature of a classical alloy of static symmetry-broken states.

Significance. If the DE approximation is reliable in the large-gap Mott regime, it provides a computationally inexpensive, sign-problem-free route to paramagnetic Mott insulators, bypassing QMC impurity solvers and large supercells. The derivation in Appendix A is clean, the CPA analogy is made explicit, and the numerical comparison is direct: the same impurity model is solved with DE and with CTSEG, with no fitting to the DMFT reference. The two-particle covariance prediction in Appendix B is a non-trivial additional validation. The main weakness is that the central saddle-point reduction is not quantitatively controlled; the authors themselves state that intra-basin fluctuations 'become relevant for smaller gaps' and that DE cannot describe correlated metals or the immediate vicinity of the Mott transition.

major comments (2)
  1. [Appendix A, Eq. (7)] The replacement of the exact impurity partition function by a discrete sum over static saddle points omits the Gaussian fluctuation determinant around each saddle and inter-basin tunneling. Since the weights p_s enter Eq. (3) exponentially, even a modest difference in the curvature of the action among the degenerate low-lying states (two for NiO, six for FeO) could alter the ensemble. The text's statement that intra-basin fluctuations 'become relevant for smaller gaps' is not quantitative. Please provide an estimate of the one-loop correction—e.g., by evaluating det(δ²A/δφ²) at each saddle point or by benchmarking against an exact impurity solver for a simplified model—to justify the dephased limit for these materials.
  2. [Eq. (2) and SI Sec. IC1] The DE sum is over 'all accessible stationary points,' and the Ponet et al. protocol is asserted to find them, but no completeness certificate or convergence test is described. If a low-lying stationary state is missed, Z_loc and p_s in Eq. (3) are incomplete. Please report the number of stationary states found, the number of initializations used, and a test of protocol completeness (e.g., random restarts, or exhaustive enumeration for a reduced model).
minor comments (4)
  1. [Eq. (1) and throughout] The symbol U is used both for the interaction tensor U^{ijkl} and for the Hubbard parameter U = 6 eV; please distinguish them (e.g., use a different font or an explicit superindex).
  2. [Fig. 1] In panels (d,e), the labels 'spin-up (positive y-axis)' and 'spin-down (negative y-axis)' are ambiguous; please clarify the plotted quantity and axis labels.
  3. [Appendix A] The text says 'ψ_iσ, ψ†_iσ represent fermionic Grassmann fields', but earlier the spin index was absorbed into a compound index; please make the convention consistent.
  4. [References] Reference [23] lists the DOI '10.1103/zjy7-4jqd', which appears to be a placeholder; please verify.

Circularity Check

0 steps flagged · score 0.0 of 10

No significant circularity: the DE Green's function is constructed from static Hartree-Fock stationary points with thermodynamic weights derived from the embedding grand potential, and the DMFT agreement is an independent benchmark rather than a fitted target.

full rationale

The central object, G_DE in Eq. (3), is not fitted to the DMFT result: it is defined as a Boltzmann-weighted sum over stationary HF self-energies, with weights p_s = Z^{-1} exp(-beta Omega[Sigma_s]) and Omega given by Eq. (1)/(11). None of these parameters is adjusted to reproduce the DMFT self-energy or spin-spin covariance; CTSEG/CT-HYB QMC benchmarks are an external, independent reference. Appendix A does not smuggle in the result: it starts from the exact Hubbard-Stratonovich action and, under the explicitly stated approximation that the functional integral over the auxiliary field is replaced by a discrete sum over static stationary configurations (Eq. (7)), obtains Eq. (3). That is an approximation with uncontrolled one-loop corrections, but it is not a self-definition or a fit. The covariance expression in Eq. (14) is derived from Wick's theorem within each static solution plus the ensemble variance; it is not assumed. Self-citations ([30], [33], [46]) are methodological or peripheral (DFT+U/HF-limit equivalence, saddle-point landscape exploration protocol, software) and do not carry the central claim. No uniqueness theorem from the authors is invoked to force the choice. The paper itself flags the main weaknesses - neglect of intra-basin Gaussian fluctuations and inter-basin tunneling, and inapplicability to correlated metals or the Mott transition - which are correctness/robustness concerns, not circularity. The post hoc agreement with DMFT for NiO/FeO is a validation against an independent solver, not a reduction of the prediction to its inputs. No equation reduces to another by construction, and no fitted parameter is renamed as a prediction.

Assumptions & free parameters 3 free parameters · 6 assumptions · 0 invented entities

No new postulated particles/forces/dimensions. The DE introduces a formal object—the weighted mixture of static self-energies—but it is a computational ansatz within existing single-site embedding theory, not a new entity with independent physical evidence. The main ledger charge is the set of approximation choices (stationary-phase sum, dephasing, landscape completeness) plus hand-chosen interaction parameters U and J.

free parameters (3)
  • Hubbard U = 6 eV
    Standard interaction parameter for TM monoxides taken from previous DFT+DMFT studies; shared by DE and DMFT, so it does not affect the DE-vs-DMFT comparison, but it is a hand-chosen input.
  • Hund coupling J = 1 eV
    Standard value; shared input for both DE and DMFT.
  • Landscape search truncation / set of stationary points = heuristic/undisclosed
    The ensemble is truncated to the stationary points found by the Ponet et al. protocol; no completeness certificate. For NiO the next states are ~1 eV higher, so truncation is safe; generality is assumed.
assumptions (6)
  • standard math Hubbard-Stratonovich transformation of the interacting impurity action, with the auxiliary field restricted to static configurations (phi(tau)->phibar).
    Appendix A, Eqs. (5)-(7); standard Hubbard-Stratonovich decoupling.
  • domain assumption The functional integral over the static auxiliary field is approximated by a discrete sum over stationary points (saddle points) of the action, discarding Gaussian fluctuations around each saddle.
    Appendix A, Eqs. (7)-(8); central approximation; justified by strong-U argument in main text (inter-basin barrier height scales with U) but not controlled quantitatively.
  • domain assumption Inter-basin tunneling between the symmetry-broken states is negligible (dephased limit).
    Main text after Eq. (3); this is what makes the DE a classical mixture rather than a quantum superposition; valid only for large gaps.
  • ad hoc to paper The finite set of stationary solutions found by the Ponet et al. landscape search is complete and representative of all 'accessible' stationary states.
    Numerical methods paragraph: 'adapting the protocol of Ponet et al. to thoroughly explore the landscape'; no completeness proof; FeO landscape has 6 degenerate states; continuous-symmetry integration deferred to SI Sec. ID.
  • domain assumption The local Coulomb interaction is parametrized by Liechtenstein form with scalar U and J, and CTSEG benchmark restricts to density-density interactions W_{ijkl} ~= W_{iikk} delta_{ij} delta_{jk}.
    Main text, model paragraph; standard in DFT+DMFT, but restricts the tested interaction space (rotationally-invariant case tested only in SI on LuNiO3).
  • domain assumption DMFT self-consistency condition (extraction of Weiss field Delta from the lattice Green's function) applies unchanged to DE.
    Approach paragraph: one-shot DFT+DMFT vs DFT+DE, both iterated to self-consistency; standard embedding methodology.

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Pith. "Pith review of Strong correlations and local self-energies from on-site ensembles." pith.science (2026). https://pith.science/paper/5QH5KNGG

@misc{pith2026260721490,
  author       = {Pith},
  title        = {Pith review of: Strong correlations and local self-energies from on-site ensembles},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/5QH5KNGG}},
  note         = {Machine review of arXiv:2607.21490}
}
read the original abstract

Addressing the many-body electronic-structure problem is a central goal of modern condensed-matter physics. Paramagnetic Mott insulators, in particular, have long represented a challenge for standard approaches, such as density-functional theory. Historically, these systems have been tackled either by considering many-body dynamics, as in the case of dynamical mean-field theory (DMFT), or, more recently, by invoking a polymorphous description consisting of large supercells populated with static symmetry-broken motifs whose spatial average restores the paramagnetic state. Inspired by these viewpoints, we introduce the on-site dephased ensemble (DE) approximation, in which the local electronic-structure problem is described by a thermal ensemble of all accessible local static solutions; this gives rise to a strong frequency dependence of the local electronic self-energy, as seen in DMFT or in the coherent-potential approximation of disordered alloys. We show that the DE successfully recovers defining hallmarks of strongly correlated Mott systems, both in terms of the self-energy as well as the persistence of local moments in time, in quantitative agreement with DMFT. By bypassing expensive quantum Monte Carlo solvers or large supercell calculations, this approach offers efficient routes to treating paramagnetic Mott systems in a first-principles setting, and highlights a deeper connection between the physics of strong correlations and that of disorder.

Figures

Figures reproduced from arXiv: 2607.21490 by the authors.

Figure 1
Figure 1. FIG. 1. Paramagnetic state of NiO: (a) embedding grand potential Ω landscape. Marker color scales with Boltzmann weight; [PITH_FULL_IMAGE:figures/full_fig_p003_1.png] view at source ↗
Figure 2
Figure 2. FIG. 2. Paramagnetic state of FeO, 5 orbital model with [PITH_FULL_IMAGE:figures/full_fig_p004_2.png] view at source ↗

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Reference graph

Works this paper leans on

69 extracted references · 5 canonical work pages

  1. [1]

    Kohn and L

    W. Kohn and L. Sham, Self-consistent equations includ- ing exchange and correlation effects, Phys. Rev.140, A1133 (1965)

    1965

  2. [2]

    Hohenberg and W

    P. Hohenberg and W. Kohn, Inhomogeneous electron gas, Phys. Rev.136, B864 (1964)

    1964

  3. [3]

    J. P. Perdew, K. Burke, and M. Ernzerhof, Generalized Gradient Approximation Made Simple, Physical Review Letters77, 3865 (1996)

    1996

  4. [4]

    Trimarchi, Z

    G. Trimarchi, Z. Wang, and A. Zunger, Polymorphous band structure model of gapping in the antiferromag- netic and paramagnetic phases of the Mott insulators MnO, FeO, CoO, and NiO, Physical Review B97, 035107 (2018)

    2018

  5. [5]

    I. I. Mazin and V. I. Anisimov, Insulating gap in FeO: Correlations and covalency, Physical Review B55, 12822 (1997)

    1997

  6. [6]

    Zunger, J.-X

    A. Zunger, J.-X. Xiong, and J. P. Perdew, Symmetry breaking transforms strong to normal correlation and false metals to true insulators (2026), arXiv:2512.18236 [cond-mat]

    arXiv 2026

  7. [7]

    H. K. Bowen, D. Adler, and B. H. Auker, Electrical and optical properties of FeO, Journal of Solid State Chem- istry12, 355 (1975)

    1975

  8. [8]

    W. L. Roth, Magnetic Structures of MnO, FeO, CoO, and NiO, Physical Review110, 1333 (1958)

    1958

Show all 69 references
  1. [9]

    V. I. Anisimov, J. Zaanen, and O. K. Andersen, Band theory and Mott insulators: Hubbard U instead of Stoner I, Physical Review B44, 943 (1991)

    1991

  2. [10]

    V. I. Anisimov, M. A. Korotin, and E. Z. Kurmaev, Band- structure description of Mott insulators (NiO, MnO, FeO, CoO), Journal of Physics: Condensed Matter2, 3973 (1990)

    1990

  3. [11]

    Timrov, F

    I. Timrov, F. Aquilante, M. Cococcioni, and N. Marzari, Accurate Electronic Properties and Intercalation Volt- ages of Olivine-Type Li-Ion Cathode Materials from Ex- tended Hubbard Functionals, PRX Energy1, 033003 (2022)

    2022

  4. [12]

    Timrov, M

    I. Timrov, M. Kotiuga, and N. Marzari, Unraveling the effects of inter-site Hubbard interactions in spinel Li-ion cathode materials, Physical Chemistry Chemical Physics 25, 9061 (2023)

    2023

  5. [13]

    Georges, G

    A. Georges, G. Kotliar, W. Krauth, and M. J. Rozen- berg, Dynamical Mean-Field Theory of Strongly Corre- lated Fermion Systems and the Limit of Infinite Dimen- sions, Reviews of Modern Physics68, 13 (1996). 8

    1996

  6. [14]

    Kotliar, S

    G. Kotliar, S. Y. Savrasov, K. Haule, V. S. Oudovenko, O. Parcollet, and C. A. Marianetti, Electronic structure calculations with dynamical mean-field theory, Reviews of Modern Physics78, 865 (2006)

    2006

  7. [15]

    Held, Electronic structure calculations using dynami- cal mean field theory, Advances in Physics56, 829 (2007)

    K. Held, Electronic structure calculations using dynami- cal mean field theory, Advances in Physics56, 829 (2007)

    2007

  8. [16]

    I. A. Abrikosov, A. V. Ponomareva, P. Steneteg, S. A. Barannikova, and B. Alling, Recent progress in simula- tions of the paramagnetic state of magnetic materials, Current Opinion in Solid State and Materials Science20, 85 (2016)

    2016

  9. [17]

    Alling, T

    B. Alling, T. Marten, and I. A. Abrikosov, Effect of mag- netic disorder and strong electron correlations on the thermodynamics of CrN, Physical Review B82, 184430 (2010)

    2010

  10. [18]

    O. I. Malyi and A. Zunger, Rise and fall of Mott insulat- ing gaps in YNiO3 paramagnets as a reflection of symme- try breaking and remaking, Physical Review Materials7, 044409 (2023)

    2023

  11. [19]

    Varignon, M

    J. Varignon, M. Bibes, and A. Zunger, Mott gapping in 3d ABO3 perovskites without Mott-Hubbard inter- electronic repulsion energy U, Physical Review B100, 035119 (2019)

    2019

  12. [20]

    Cococcioni and S

    M. Cococcioni and S. de Gironcoli, Linear response ap- proach to the calculation of the effective interaction pa- rameters in the LDA+U method, Physical Review B71, 035105 (2005)

    2005

  13. [21]

    J. W. Furness, A. D. Kaplan, J. Ning, J. P. Perdew, and J. Sun, Accurate and Numerically Efficient r2SCAN Meta-Generalized Gradient Approximation, The Journal of Physical Chemistry Letters11, 8208 (2020)

    2020

  14. [22]

    D. D. Rivera, G. M. Dalpian, and J. P. Perdew, Identify- ing strong correlation using only the Kohn-Sham density of one-electron states (2026), arXiv:2604.25125 [cond- mat.str-el]

    2026 arXiv

  15. [23]

    H. Eßl, M. Reitner, E. Kozik, and A. Toschi, Origin of misleading convergence in self-consistent many-electron theories: Fundamental aspects and practical implica- tions, Physical Review Letters137, 10.1103/zjy7-4jqd (2026)

    2026 doi

  16. [24]

    Ferretti and N

    A. Ferretti and N. Marzari, Functional theory of the oc- cupied spectral density (2025)

    2025

  17. [25]

    Ferretti, T

    A. Ferretti, T. Chiarotti, and N. Marzari, Green’s function embedding using sum-over-pole representations, Physical Review B110, 10.1103/physrevb.110.045149 (2024)

    2024 doi

  18. [26]

    S. Y. Savrasov and G. Kotliar, Spectral density function- als for electronic structure calculations, Physical Review B69, 10.1103/physrevb.69.245101 (2004)

    2004 doi

  19. [27]

    Altland and B

    A. Altland and B. D. Simons,Condensed Matter Field Theory, 2nd ed. (Cambridge University Press, Cam- bridge, 2010)

    2010

  20. [28]

    Liechtenstein, V

    A. Liechtenstein, V. Anisimov, and J. Zaanen, Density- functional theory and strong interactions: Orbital order- ing in Mott-Hubbard insulators, Phys. Rev. B52, R5467 (1995)

    1995

  21. [29]

    R. M. Martin, L. Reining, and D. M. Ceperley,Inter- acting Electrons: Theory and Computational Approaches (Cambridge University Press, 2016)

    2016

  22. [30]

    Carta, I

    A. Carta, I. Timrov, P. Mlkvik, A. Hampel, and C. Ed- erer, Explicit demonstration of the equivalence between DFT+U and the Hartree-Fock limit of DFT+DMFT, Physical Review Research7, 013289 (2025)

    2025

  23. [31]

    Coulson and I

    C. Coulson and I. Fischer, Xxxiv. notes on the molecular orbital treatment of the hydrogen molecule, The Lon- don, Edinburgh, and Dublin Philosophical Magazine and Journal of Science40, 386–393 (1949)

    1949

  24. [32]

    R. K. Nesbet, Unrestricted hartree–fock then and now, International Journal of Quantum Chemistry102, 602–605 (2004)

    2004

  25. [33]

    Ponet, E

    L. Ponet, E. Di Lucente, and N. Marzari, The energy landscape of magnetic materials, npj Computational Ma- terials10, 1 (2024)

    2024

  26. [34]

    Haddadi, D

    F. Haddadi, D. Campi, F. J. dos Santos, N. Mounet, L. Ponet, N. Marzari, and M. Gibertini, Explor- ing the Magnetic Landscape of Easily Exfoliable Two-Dimensional Materials, ACS Nano 10.1021/ac- snano.5c16067 (2026)

    2026 doi

  27. [35]

    Dorado, M

    B. Dorado, M. Freyss, B. Amadon, M. Bertolus, G. Jo- mard, and P. Garcia, Advances in first-principles mod- elling of point defects in uo¡sub¿2¡/sub¿: f electron cor- relations and the issue of local energy minima, Journal of Physics: Condensed Matter25, 333201 (2013)

    2013

  28. [36]

    E. R. Ylvisaker, W. E. Pickett, and K. Koepernik, Anisotropy and magnetism in the lsda+u method, Phys- ical Review B79, 10.1103/physrevb.79.035103 (2009)

    2009 doi

  29. [37]

    Velick´ y, S

    B. Velick´ y, S. Kirkpatrick, and H. Ehrenreich, Single-site approximations in the electronic theory of simple binary alloys, Physical Review175, 747 (1968), see Equation (4.16), which defines the CPA self-consistency condition. In their notation,Frepresents the average macros...

    1968

  30. [38]

    Kakehashi, Electron correlations and many-body tech- niques in magnetism, Advances in Physics53, 497 (2004)

    Y. Kakehashi, Electron correlations and many-body tech- niques in magnetism, Advances in Physics53, 497 (2004)

    2004

  31. [39]

    J. P. Perdew, A. Ruzsinszky, G. I. Csonka, O. A. Vy- drov, G. E. Scuseria, L. A. Constantin, X. Zhou, and K. Burke, Restoring the Density-Gradient Expansion for Exchange in Solids and Surfaces, Physical Review Letters 100, 136406 (2008)

    2008

  32. [40]

    Giannozzi, O

    P. Giannozzi, O. Andreussi, T. Brumme, O. Bunau, M. Buongiorno Nardelli, M. Calandra, R. Car, C. Cavaz- zoni, D. Ceresoli, M. Cococcioni, N. Colonna, I. Carn- imeo, A. Dal Corso, S. de Gironcoli, P. Delugas, R. A. DiStasio, A. Ferretti, A. Floris, G. Fratesi, G. Fugallo, R. Ge...

    2017

  33. [41]

    Giannozzi, S

    P. Giannozzi, S. Baroni, N. Bonini, M. Calandra, R. Car, C. Cavazzoni, D. Ceresoli, G. L. Chiarotti, M. Cococ- cioni, I. Dabo, A. Dal Corso, S. de Gironcoli, S. Fabris, G. Fratesi, R. Gebauer, U. Gerstmann, C. Gougoussis, A. Kokalj, M. Lazzeri, L. Martin-Samos, N. Marzari, F. ...

    2009

  34. [42]

    Marzari, A

    N. Marzari, A. A. Mostofi, J. R. Yates, I. Souza, and D. Vanderbilt, Maximally localized Wannier functions: Theory and applications, Reviews of Modern Physics84, 1419 (2012)

    2012

  35. [43]

    Pizzi, V

    G. Pizzi, V. Vitale, R. Arita, S. Bl¨ ugel, F. Freimuth, G. G´ eranton, M. Gibertini, D. Gresch, C. Johnson, T. Koretsune, J. Iba˜ nez-Azpiroz, H. Lee, J.-M. Lihm, D. Marchand, A. Marrazzo, Y. Mokrousov, J. I. Mustafa, Y. Nohara, Y. Nomura, L. Paulatto, S. Ponc´ e, T. Pon- wei...

    2020

  36. [44]

    P. Seth, I. Krivenko, M. Ferrero, and O. Parcollet, TRIQS/CTHYB: A continuous-time quantum Monte Carlo hybridisation expansion solver for quantum impu- rity problems, Computer Physics Communications200, 274 (2016)

    2016

  37. [45]

    Kavokine, H

    N. Kavokine, H. Lu, T. Ayral, M. Ferrero, N. Wentzell, and O. Parcollet, CTSEG: A segment picture quantum impurity solver based on TRIQS, Journal of Open Source Software10, 7425 (2025)

    2025

  38. [46]

    M. E. Merkel, A. Carta, S. Beck, and A. Hampel, Solid dmft: Gray-boxing DFT+DMFT materials simu- lations with TRIQS, Journal of Open Source Software7, 4623 (2022)

    2022

  39. [47]

    Parcollet, M

    O. Parcollet, M. Ferrero, T. Ayral, H. Hafermann, I. Krivenko, L. Messio, and P. Seth, TRIQS: A toolbox for research on interacting quantum systems, Computer Physics Communications196, 398 (2015)

    2015

  40. [48]

    J. Kaye, K. Chen, and O. Parcollet, Discrete lehmann representation of imaginary time green’s functions, Phys. Rev. B105, 235115 (2022)

    2022

  41. [49]

    J. Kaye, K. Chen, and H. U. Strand, libdlr: Efficient imaginary time calculations using the discrete lehmann representation, Comput. Phys. Commun.280, 108458 (2022)

    2022

  42. [50]

    J. Kaye, H. U. R. Strand, and N. Wentzell, cppdlr: Imag- inary time calculations using the discrete lehmann rep- resentation, Journal of Open Source Software9, 6297 (2024)

    2024

  43. [51]

    Kiese, H

    D. Kiese, H. U. R. Strand, K. Chen, N. Wentzell, O. Parcollet, and J. Kaye, Discrete lehmann represen- tation of three-point functions, Physical Review B111, 10.1103/physrevb.111.035135 (2025)

    2025 doi

  44. [52]

    G. J. Kraberger, R. Triebl, M. Zingl, and M. Aichhorn, Maximum entropy formalism for the analytic continua- tion of matrix-valued Green’s functions, Physical Review B96, 155128 (2017)

    2017

  45. [53]

    R. Levy, J. P. F. LeBlanc, and E. Gull, Implementation of the maximum entropy method for analytic continuation, Computer Physics Communications215, 149 (2017)

    2017

  46. [54]

    M. J. Rozenberg, Mott-Hubbard transition in infinite di- mensions, Physical Review Letters69, 1236 (1992)

    1992

  47. [55]

    Vanzini and N

    M. Vanzini and N. Marzari, Towards a minimal descrip- tion of dynamical correlation in metals (2023)

    2023

  48. [56]

    Ferretti, I

    A. Ferretti, I. Dabo, M. Cococcioni, and N. Marzari, Bridging density-functional and many-body per- turbation theory: Orbital-density dependence in electronic-structure functionals, Physical Review B89, 10.1103/physrevb.89.195134 (2014)

    2014 doi

  49. [57]

    Caserta, T

    M. Caserta, T. Chiarotti, M. Vanzini, and N. Marzari, Dynamical Hubbard approach to correlated materi- als: The case of transition-metal monoxides (2025), arXiv:2503.10893 [cond-mat]

    2025 arXiv

  50. [58]

    A. B. Georgescu and A. J. Millis, Quantifying the role of the lattice in metal–insulator phase transitions, Commu- nications Physics5, 10.1038/s42005-022-00909-z (2022)

    2022 doi

  51. [59]

    Han and A

    Q. Han and A. Millis, Lattice energetics and correlation- driven metal-insulator transitions: The case of ca2ruo4, Physical Review Letters121, 10.1103/phys- revlett.121.067601 (2018)

    2018 doi

  52. [60]

    E. M. Makaresz, O. Gingras, T.-H. Lee, N. Lanat` a, B. J. Powell, and H. L. Nourse, Accelerating dynamical mean- field theory convergence by preconditioning with compu- tationally cheaper quantum embedding methods (2026), arXiv:2601.16401 [cond-mat.str-el]

    2026

  53. [61]

    ˇZitko, Convergence acceleration and stabilization of dynamical mean-field theory calculations, Physical Re- view B80, 125125 (2009)

    R. ˇZitko, Convergence acceleration and stabilization of dynamical mean-field theory calculations, Physical Re- view B80, 125125 (2009)

    2009

  54. [62]

    Srinivas, A

    N. Srinivas, A. Krause, S. Kakade, and M. Seeger, Gaus- sian process optimization in the bandit setting: No regret and experimental design, inProceedings of the 27th In- ternational Conference on International Conference on Machine Learning, ICML’10 (Omnipress, Madison, WI, US...

    2010

  55. [63]

    Kleinberg, Nearly Tight Bounds for the Continuum- Armed Bandit Problem, inAdvances in Neural Informa- tion Processing Systems, Vol

    R. Kleinberg, Nearly Tight Bounds for the Continuum- Armed Bandit Problem, inAdvances in Neural Informa- tion Processing Systems, Vol. 17 (MIT Press, 2004)

    2004

  56. [64]

    Chakrabarti, R

    D. Chakrabarti, R. Kumar, F. Radlinski, and E. Up- fal, Mortal Multi-Armed Bandits, inAdvances in Neural Information Processing Systems, Vol. 21 (Curran Asso- ciates, Inc., 2008)

    2008

  57. [65]

    Parisi, Infinite Number of Order Parameters for Spin- Glasses, Physical Review Letters43, 1754 (1979)

    G. Parisi, Infinite Number of Order Parameters for Spin- Glasses, Physical Review Letters43, 1754 (1979)

    1979

  58. [66]

    Quinzi, T

    M. Quinzi, T. Chiarotti, A. Pintus, M. Capone, and N. Marzari (2026), manuscript in preparation

    2026

  59. [67]

    Ryee and M

    S. Ryee and M. J. Han, The effect of double count- ing, spin density, and Hund interaction in the different DFT+U functionals, Scientific Reports8, 9559 (2018)

    2018

  60. [68]

    Kakehashi, T

    Y. Kakehashi, T. Tamashiro, M. A. R. Patoary, and T. Nakamura, First-principles dynamical CPA to finite- temperature magnetism of transition metals, Journal of Physics: Conference Series200, 032030 (2010)

    2010

  61. [69]

    Kakehashi, Many-body coherent potential approx- imation, dynamical coherent potential approximation, and dynamical mean-field theory, Physical Review B66, 104428 (2002)

    Y. Kakehashi, Many-body coherent potential approx- imation, dynamical coherent potential approximation, and dynamical mean-field theory, Physical Review B66, 104428 (2002)

    2002

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