Pith. sign in

REVIEW 1 cited by

Renormalization of States and Quasiparticles in Many-body Downfolding

T0 review · reviewed 2026-08-12 · deepseek-v4-flash

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

Pith's one-line read The renormalization factor Z in downfolding equals the squared overlap between the downfolded eigenvector and the full many-body eigenvector.

desk verdict Solid, interesting paper with a clean core identity that has one sign typo and a heuristic second half; worth peer review. read the letter →

arxiv 2411.13725 v2 pith:63ZLRA4Q submitted 2024-11-20 physics.comp-ph cond-mat.mtrl-sci

Annabelle Canestraight , Zhen Huang , Vojtech Vlcek This is my paper · ORCID
classification physics.comp-phcond-mat.mtrl-sci
keywords Many-bodydownfoldingRenormalizationfactorSchurcomplementQuasiparticlesGreen'sfunctionEnergyscaleseparationSatellitestatesQuantumembedding
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

This paper asks when a reduced, “downfolded” description of a many-body system can be trusted. It shows that the renormalization factor Z—the overlap between the downfolded eigenvector and the true eigenvector of the full Hamiltonian—is exactly given by a formula involving the energy derivative of the self-energy. It then argues that building an effective Hamiltonian from one-body Green's functions requires including not just the main quasiparticle peaks but all satellite peaks, and that the resulting static Hamiltonian is faithful only when the subsystem and its environment are well separated in energy. This matters for embedding methods used on defects, interfaces, and other localized quantum systems, because it turns a heuristic “Z factor” into a rigorous fidelity check and identifies when renormalization by the environment is necessary.

What carries the argument

The central object is the Schur-complement self-energy of a block-partitioned Hamiltonian, Sigma_S(omega) = C(H2 - omega I)^{-1} C^dagger, together with the fixed-point eigenvalue problem omega = H_eff(omega) with H_eff = H1 + Sigma_S(omega). The paper's key identity is Eq. (9), which identifies the renormalization factor Z_i, the residue of the Schur complement at the fixed point, with the squared overlap |<Phi_i|Psi_i>|^2 between the downfolded and full eigenvectors. For the quasiparticle part, the machinery is the spectral representation of the one-body Green's function and the orbitals extracted from it; the renormalized one-body energies are weighted averages over all hole peaks, which is why satellites must be included.

What would settle it

Switch on inter-subsystem hopping in the exactly solvable two-dimer model, rebuild the effective Hamiltonian from the satellite-inclusive one-body Green's function, and compare low-lying eigenvalues and eigenvector overlaps with exact diagonalization; faithful spectra despite strong hopping would refute the claimed need for energy-scale separation, while failure would confirm it.

Watch

Extended reading notes

Core claim

The paper's central result is that for any Hamiltonian partitioned into a subsystem H1, an environment H2, and a coupling C, the renormalization factor of the ith downfolded state equals the squared overlap between the eigenvector of the effective (Schur-complement) Hamiltonian and the corresponding eigenvector of the full Hamiltonian: Zi = |<Phi_i|Psi_i>|^2 = 1 / (1 + <phi_1,i| C (H2 - eps_i I)^{-2} C^dagger |phi_1,i>). This ties a quantity conventionally computed from the slope of the self-energy to a concrete state-fidelity measure. The paper further shows that when the effective Hamiltonian is constructed from the one-body Green's function, the renormalization of single-particle terms must include all satellite solutions of the Green's function, because those satellites carry information about coupling to environment excitations. On exactly solvable two-dimer models, the downfolded quasiparticle Hamiltonian reproduces ground and low-lying excited states faithfully, but accuracy degrades for states whose energy is set by two-body interactions with the environment; no satisfactory renormalized two-body interaction is defined.

Load-bearing premise

The load-bearing premise is that the environment's influence on the subsystem can be represented by renormalizing only one-body terms, with the environment fixed in its ground state and no hopping between subsystem and environment; if hopping or renormalized two-body interactions are important, the downfolded quasiparticle Hamiltonian can miss the states it targets.

Editorial extensions

If this is right

  • A downfolded calculation can report a per-state fidelity: when Z is close to 1, the excitation is essentially contained in the downfolded subspace and the product-state form of the eigenvector is trustworthy.
  • Static quasiparticle Hamiltonians built from one-body Green's functions are reliable for ground and low-lying excited states only when the subsystem and environment have well-separated energy scales; otherwise intruder states with small Z appear.
  • Renormalizing one-body terms requires including all satellite peaks of the Green's function; in the two-dimer model this lowers the one-body environment self-energy by up to 42 percent at the largest interaction strength.
  • States whose energies are dominated by two-body interactions between subsystem and environment are the ones a one-body renormalization fails to correct, and no satisfactory renormalized two-body interaction is currently defined.
  • The position and height of satellite peaks serve as a practical diagnostic for whether downfolded eigenvectors are reliable, replacing the need to compute the many-body Z factor directly.

Reading between the lines

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

  • The fidelity formula suggests a cheap stopping criterion for embedding workflows: evaluate Z for each targeted state and treat states with Z well below 1 as unresolved rather than accurate.
  • Because the failure is concentrated in two-body-dominated states, a natural next step is to define a renormalized two-body interaction from the two-particle propagator and test it on the same exactly solvable models; the paper identifies this as an open problem.
  • The random-congruent-basis result implies that randomized downfolding could be used to recover the full spectrum in large systems, with Z tracking which recovered states are physically interpretable.
  • For practical Green's-function approximations, the satellite requirement implies that methods producing only a single quasiparticle peak will systematically underestimate environment renormalization; checking the multipole structure of the computed Green's function should precede any downfolding.
Share X Bluesky LinkedIn Reddit HN

Signed reviews

No signed human review yet.

Editorial analysis

A structured set of objections, weighed in public.

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

Circularity Check

0 steps flagged · score 0.0 of 10

No significant circularity: the central Section II identity is a parameter-free linear-algebra result verified against exact diagonalization, and the Section III/IV quasiparticle analysis uses external ED benchmarks rather than fitting its own target quantities.

full rationale

The central derivation in Section II is a parameter-free matrix identity. The paper constructs the Schur-complement self-energy Σ_S(ω)=C(ωI−H2)^{-1}C†, introduces Z in Eq. (3) as the standard residue, derives the eigenvector relation in Eqs. (7)-(8), and obtains Eq. (9) for the overlap. The identification with the derivative in Eq. (10) is a claimed algebraic step (Hellman-Feynman), not a fit or an input-output tautology. The numerical proof in Fig. 2(c) uses exact diagonalization as an external benchmark, computing both sides independently. The Section III/IV construction (satellite-inclusive one-body self-energy from the Green's function, then diagonalization of the effective Hamiltonian) is benchmarked against ED eigenvalues; the self-energy is not fitted to those eigenvalues. Self-citations ([1], [3], [5], [36]-[37], [46]-[47]) provide context and algorithms but do not supply the target equality. A separate, non-circular correctness concern: Eq. (10) as printed states ∂ω⟨ϕ1,i|ΣS(ω)|ϕ1,i⟩ = ⟨ϕ1,i|C(H2−ωI)^{−2}C†|ϕ1,i⟩, which conflicts with Eq. (2) by a sign (the derivative of C(ω−H2)^{-1}C† is negative); this is a correctness defect, not a circular reduction. The paper's own limitations (Section IV: 'there is no obvious and simple route to define a renormalized two-body interaction'; Section II: exact Schur complement construction 'is equivalent to solving the full many-body problem') are acknowledged scope restrictions, not circular steps. No load-bearing claim reduces by construction to its inputs, so the circularity score is 0.

Assumptions & free parameters 0 free parameters · 5 assumptions · 0 invented entities

The central derivation relies on standard block-matrix identities and on modeling assumptions that restrict the scope. U and t_env are scanned model inputs, not fitted parameters. No new physical entities are introduced.

assumptions (5)
  • standard math Schur complement/Lowdin downfolding captures all eigenvalues when (I*omega - H2) is invertible and no eigenvector is orthogonal to the subspace.
    Invoked in Section II; the paper notes inaccessible eigenvalues when Zi = 0 and assumes a random congruent transform solves this in practice.
  • domain assumption Product-form eigenstates |Psi_N> = |S_N> (x) |R_N> with the environment held in its ground state.
    Used in Section III B, Eq. (20), to define the downfolding subspace and interpret Green's function satellites.
  • domain assumption No hopping between the subsystem and the environment in the Green's function analysis.
    Explicit in Section III B, footnote [44]; if violated, the satellite structure of the one-body Green's function changes and the simple product-state interpretation breaks down.
  • domain assumption Only one-body terms of the effective Hamiltonian are renormalized; two-body renormalization is not defined.
    Section IV states there is no obvious simple route to a renormalized two-body interaction, so the scope of the numerical demonstration is limited.
  • standard math Hellmann-Feynman theorem for the omega-dependent eigenvector relation in Eq. 10.
    Used to equate the derivative of the self-energy expectation value with the rest-space overlap denominator.

how reviews work

0 comments
Cite this review

Pith. "Pith review of Renormalization of States and Quasiparticles in Many-body Downfolding." pith.science (2026). https://pith.science/paper/63ZLRA4Q

@misc{pith2026241113725,
  author       = {Pith},
  title        = {Pith review of: Renormalization of States and Quasiparticles in Many-body Downfolding},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/63ZLRA4Q}},
  note         = {Machine review of arXiv:2411.13725}
}
read the original abstract

We explore the principles of many-body Hamiltonian complexity reduction via downfolding on an effective low-dimensional representation. We present a unique measure of fidelity between the effective (reduced-rank) description and the full many-body treatment for arbitrary (i.e., ground and excited) states. When the entire problem is mapped on a system of interacting quasiparticles [npj Computational Materials 9 (1), 126, 2023], the effective Hamiltonians can faithfully reproduce the physics only when a clear energy scale separation exists between the subsystems and its environment. We also demonstrate that it is necessary to include quasiparticle renormalization at distinct energy scales, capturing the distinct interaction between subsystems and their surrounding environments. Numerical results from simple, exactly solvable models highlight the limitations and strengths of this approach, particularly for ground and low-lying excited states. This work lays the groundwork for applying dynamical downfolding techniques to problems concerned with (quantum) interfaces.

Figures

Figures reproduced from arXiv: 2411.13725 by the authors.

Figure 1
Figure 1. FIG. 1. The fixed point solution for the eigenvalue is solved at the red point. The tangent line to this point gives the [PITH_FULL_IMAGE:figures/full_fig_p003_1.png] view at source ↗
Figure 2
Figure 2. FIG. 2. a. We show a fixed point solution where some ED solutions are missing due to the orthogonality of the eigenvectors to [PITH_FULL_IMAGE:figures/full_fig_p011_2.png] view at source ↗
Figure 3
Figure 3. FIG. 3. a. A portion of the eigenvalue spectrum is given, with the color bar indicating the [PITH_FULL_IMAGE:figures/full_fig_p011_3.png] view at source ↗
Figures from the paper (1 more)
Figure 4
Figure 4. Figure 4: FIG. 4 [PITH_FULL_IMAGE:figures/full_fig_p012_4.png]

Discussion (0). Continue with ORCID to comment.

Forward citations

Cited by 1 Pith paper

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

  1. Theory of ab initio downfolding with arbitrary range electron-phonon coupling

    cond-mat.mtrl-sci 2025-01 conditional novelty 7.0 of 10

    A first-principles downfolding framework that includes short- and long-range electron-phonon coupling predicts large phonon screening of electron interactions, including an attractive nearest-neighbor interaction in GeTe.

Reference graph

Works this paper leans on

56 extracted references · 47 canonical work pages · cited by 1 Pith paper

  1. [1]

    Romanova, G

    M. Romanova, G. Weng, A. Apelian, and V. Vlˇ cek, Dy- namical downfolding for localized quantum states, npj Computational Materials 9, 126 (2023)

    work page 2023

  2. [2]

    Muechler, D

    L. Muechler, D. I. Badrtdinov, A. Hampel, J. Cano, M. R¨ osner, and C. E. Dreyer, Quantum embedding meth- ods for correlated excited states of point defects: Case studies and challenges, Phys. Rev. B 105, 235104 (2022)

    2022

  3. [3]

    Canestraight, X

    A. Canestraight, X. Lei, K. Z. Ibrahim, and V. Vlˇ cek, Efficient quasiparticle determination beyond the diagonal approximation via random compression, Journal of Chemical Theory and Computation 20, 551 (2024), pMID: 38175913, https://doi.org/10.1021/acs.jctc.3c01069

    work page doi:10.1021/acs.jctc.3c01069 2024

  4. [4]

    Rignanese, X

    G.-M. Rignanese, X. Blase, and S. Louie, Quasiparticle effects on tunneling currents: A study of c 2 h 4 adsorbed on the si (001)-(2× 1) surface, Physical review letters 86, 2110 (2001)

    work page 2001

  5. [5]

    X. Lei, A. Canestraight, and V. Vlcek, Excep- tional spatial variation of charge injection ener- gies on plasmonic surfaces, The Journal of Physi- cal Chemistry Letters 0, 8470 (0), pMID: 37721434, https://doi.org/10.1021/acs.jpclett.3c02223

    work page doi:10.1021/acs.jpclett.3c02223

  6. [6]

    D. A. Egger, Z.-F. Liu, J. B. Neaton, and L. Kronik, Reliable energy level alignment at physisorbed molecule– metal interfaces from density functional theory, Nano let- ters 15, 2448 (2015)

    work page 2015

  7. [7]

    Renormalized density matrix downfolding: A rigorous framework in learning emergent models from ab initio many-body calculations

    Y. Chang, S. Joshi, and L. K. Wagner, Learning emergent models from ab initio many-body calculations (2023), arXiv:2302.02899 [cond-mat.str-el]

    work page Pith review arXiv 2023

  8. [8]

    H. Q. Pham, M. R. Hermes, and L. Gagliardi, Periodic electronic structure calculations with the density matrix embedding theory, J. Chem. Theory Comput. 16, 130 (2020)

    work page 2020

Show all 56 references
  1. [9]

    A. A. Rusakov, S. Iskakov, L. N. Tran, and D. Zgid, Self- Energy embedding theory (SEET) for periodic systems, J. Chem. Theory Comput. 15, 229 (2019)

    2019

  2. [10]

    Sun and G

    Q. Sun and G. K.-L. Chan, Quantum embedding theo- ries, Acc. Chem. Res. 49, 2705 (2016)

    2016

  3. [11]

    L¨ owdin, Studies in perturbation theory: Part i

    P.-O. L¨ owdin, Studies in perturbation theory: Part i. an elementary iteration-variation procedure for solving the schr¨ odinger equation by partitioning technique, Journal of Molecular Spectroscopy 10, 12 (1963)

    1963

  4. [12]

    L¨ owdin, Studies in Perturbation Theory

    P. L¨ owdin, Studies in Perturbation Theory. IV. So- lution of Eigenvalue Problem by Projection Oper- ator Formalism, Journal of Mathematical Physics 3, 969 (1962), https://pubs.aip.org/aip/jmp/article- pdf/3/5/969/19196745/969 1 online.pdf

    1962

  5. [13]

    Bekas and Y

    C. Bekas and Y. Saad, Computation of smallest eigenvalues using spectral schur complements, SIAM Journal on Scientific Computing 27, 458 (2005), https://doi.org/10.1137/040603528

    2005 doi

  6. [14]

    Dvorak and P

    M. Dvorak and P. Rinke, Dynamical configuration inter- action: Quantum embedding that combines wave func- tions and green’s functions, Phys. Rev. B 99, 115134 (2019)

    2019

  7. [15]

    Li and J

    J. Li and J. Yang, Downfolded configuration interac- tion for chemically accurate electron correlation, J. Phys. Chem. Lett. 13, 10042 (2022)

    2022

  8. [16]

    Dvorak, D

    M. Dvorak, D. Golze, and P. Rinke, Quantum embedding theory in the screened coulomb interaction: Combin- ing configuration interaction with gw/BSE, Phys. Rev. Mater. 3, 070801 (2019)

    2019

  9. [17]

    Authier and P.-F

    J. Authier and P.-F. Loos, Dynamical kernels for opti- cal excitations, The Journal of Chemical Physics 153, 184105 (2020)

    2020

  10. [18]

    Eskridge, H

    B. Eskridge, H. Krakauer, and S. Zhang, Local em- bedding and effective downfolding in the auxiliary-field quantum monte carlo method, Journal of Chemical The- ory and Computation 15, 3949 (2019), pMID: 31244125, https://doi.org/10.1021/acs.jctc.8b01244

    2019 doi

  11. [19]

    Aryasetiawan, J

    F. Aryasetiawan, J. M. Tomczak, T. Miyake, and R. Sakuma, Downfolded self-energy of many-electron sys- tems, Phys. Rev. Lett. 102, 176402 (2009). 9

    2009

  12. [20]

    Miyake, F

    T. Miyake, F. Aryasetiawan, and M. Imada, Ab initio procedure for constructing effective models of correlated materials with entangled band structure, Phys. Rev. B 80, 155134 (2009)

    2009

  13. [21]

    Aryasetiawan, M

    F. Aryasetiawan, M. Imada, A. Georges, G. Kotliar, S. Biermann, and A. I. Lichtenstein, Frequency- dependent local interactions and low-energy effective models from electronic structure calculations, Phys. Rev. B 70, 195104 (2004)

    2004

  14. [22]

    Chang, E

    Y. Chang, E. G. C. P. van Loon, B. Eskridge, B. Buse- meyer, M. A. Morales, C. E. Dreyer, A. J. Millis, S. Zhang, T. O. Wehling, L. K. Wagner, and M. R¨ osner, Downfolding from ab initio to interacting model hamilto- nians: comprehensive analysis and benchmarking of the dft+cr...

    2024

  15. [23]

    Bockstedte, F

    M. Bockstedte, F. Sch¨ utz, T. Garratt, V. Iv´ ady, and A. Gali, Ab initio description of highly correlated states in defects for realizing quantum bits, npj Quantum Ma- terials 3, 31 (2018)

    2018

  16. [24]

    Sheng, C

    N. Sheng, C. Vorwerk, M. Govoni, and G. Galli, Green’s function formulation of quantum defect embedding the- ory, J. Chem. Theory Comput. 18, 3512 (2022)

    2022

  17. [25]

    H. Ma, N. Sheng, M. Govoni, and G. Galli, Quantum embedding theory for strongly correlated states in mate- rials, J. Chem. Theory Comput. 17, 2116 (2021)

    2021

  18. [26]

    Sakuma, P

    R. Sakuma, P. Werner, and F. Aryasetiawan, Electronic structure of srvo 3 within gw+dmft, Phys. Rev. B 88, 235110 (2013)

    2013

  19. [27]

    Werner and A

    P. Werner and A. J. Millis, Dynamical screening in cor- related electron materials, Phys. Rev. Lett. 104, 146401 (2010)

    2010

  20. [28]

    Casula, P

    M. Casula, P. Werner, L. Vaugier, F. Aryasetiawan, T. Miyake, A. J. Millis, and S. Biermann, Low-energy models for correlated materials: Bandwidth renormal- ization from coulombic screening, Phys. Rev. Lett. 109, 126408 (2012)

    2012

  21. [29]

    N. P. Bauman, G. H. Low, and K. Kowal- ski, Quantum simulations of excited states with active-space downfolded Hamiltonians, The Journal of Chemical Physics 151, 234114 (2019), https://pubs.aip.org/aip/jcp/article- pdf/doi/10.1063/1.5128103/15566753/234114 1 online.pdf

    2019 doi

  22. [30]

    N. P. Bauman and K. Kowalski, Coupled cluster down- folding theory: towards universal many-body algorithms for dimensionality reduction of composite quantum sys- tems in chemistry and materials science, Materials The- ory 6, 17 (2022)

    2022

  23. [31]

    N. P. Bauman, E. J. Bylaska, S. Krishnamoorthy, G. H. Low, N. Wiebe, C. E. Granade, M. Roet- teler, M. Troyer, and K. Kowalski, Downfolding of many-body Hamiltonians using active-space models: Extension of the sub-system embedding sub-algebras approach to unitary coupled clust...

    2019 doi

  24. [32]

    Kowalski, Dimensionality reduction of the many-body problem using coupled-cluster subsystem flow equations: Classical and quantum computing perspective, Phys

    K. Kowalski, Dimensionality reduction of the many-body problem using coupled-cluster subsystem flow equations: Classical and quantum computing perspective, Phys. Rev. A 104, 032804 (2021)

    2021

  25. [33]

    A. Shee, F. M. Faulstich, B. Whaley, L. Lin, and M. Head-Gordon, A static quantum embedding scheme based on coupled cluster theory, arXiv preprint arXiv:2404.09078 (2024)

    2024 arXiv

  26. [34]

    C. Li, S. Mao, R. Huang, and F. A. Evangelista, Frozen natural orbitals for the State-Averaged driven similarity renormalization group, J. Chem. Theory Comput. 20, 4170 (2024)

    2024

  27. [35]

    He and F

    N. He and F. A. Evangelista, A zeroth-order active-space frozen-orbital embedding scheme for multireference cal- culations, The Journal of Chemical Physics 152, 094107 (2020)

    2020

  28. [36]

    V. c. v. Vlˇ cek, W. Li, R. Baer, E. Rabani, and D. Neuhauser, Swift gw beyond 10,000 electrons using sparse stochastic compression, Phys. Rev. B 98, 075107 (2018)

    2018

  29. [37]

    Vlˇ cek, E

    V. Vlˇ cek, E. Rabani, D. Neuhauser, and R. Baer, Stochastic GW calculations for molecules, J. Chem. The- ory Comput. 13, 4997 (2017)

    2017

  30. [38]

    S. J. Gustafson and I. M. Sigal, Mathematical concepts of quantum mechanics, 3rd ed., Universitext (Springer Nature, Cham, Switzerland, 2020)

    2020

  31. [39]

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

    2016

  32. [40]

    A. L. Fetter and J. D. Walecka, Quantum Theory of Many-Particle Systems (McGraw-Hill, Boston, 1971)

    1971

  33. [41]

    R. P. Feynman, Forces in molecules, Physical review 56, 340 (1939)

    1939

  34. [42]

    We note that Dyson orbitals naturally form a non- orthogonal basis owing to the frequency dependence of the quasiparticle Hamiltonian

  35. [43]

    Manne and T

    R. Manne and T. ˚Aberg, Koopmans’ theorem for inner- shell ionization, Chemical Physics Letters 7, 282 (1970)

    1970

  36. [44]

    Consequently, the two GFs we compute are identical and Σ env ij = 0 ∀ i, j

    When there are no interactions between subsystems, a particle created or annihilated in the subsystem of inter- est does not affect the environment, which remains in its ground state. Consequently, the two GFs we compute are identical and Σ env ij = 0 ∀ i, j

  37. [45]

    In the case of the |1⟩ eigenvector, this state is always a product state and is always the same across all values of U

  38. [46]

    Mejuto-Zaera and V

    C. Mejuto-Zaera and V. c. v. Vlˇ cek, Self-consistency in gwΓ formalism leading to quasiparticle-quasiparticle cou- plings, Phys. Rev. B 106, 165129 (2022)

    2022

  39. [47]

    G. Weng, R. Mallarapu, and V. Vlˇ cek, Embedding vertex corrections in GW self-energy: Theory, implementation, and outlook, J Chem Phys 158, 144105 (2023)

    2023

  40. [48]

    A. L. Kutepov, Full versus quasiparticle self-consistency in vertex-corrected gw approaches, Phys. Rev. B 105, 045124 (2022)

    2022

  41. [49]

    Maggio and G

    E. Maggio and G. Kresse, GW vertex corrected calcula- tions for molecular systems, J. Chem. Theory Comput. 13, 4765 (2017)

    2017

  42. [50]

    Gr¨ uneis, G

    A. Gr¨ uneis, G. Kresse, Y. Hinuma, and F. Oba, Ioniza- tion potentials of solids: The importance of vertex cor- rections, Phys. Rev. Lett. 112, 096401 (2014)

    2014

  43. [51]

    Crisostomo, E

    S. Crisostomo, E. K. U. Gross, and K. Burke, Exchange- correlation energy from green’s functions, Phys. Rev. Lett. 133, 086401 (2024)

    2024

  44. [52]

    El-Sahili, F

    A. El-Sahili, F. Sottile, and L. Reining, Total energy be- yond gw: Exact results and guidelines for approxima- tions, Journal of Chemical Theory and Computation 20, 1972 (2024)

    2024

  45. [53]

    Mejuto-Zaera and M

    C. Mejuto-Zaera and M. Fabrizio, Efficient computa- tional screening of strongly correlated materials: Mul- tiorbital phenomenology within the ghost gutzwiller ap- 10 proximation, Phys. Rev. B 107, 235150 (2023)

    2023

  46. [54]

    Lanat` a, Derivation of the ghost gutzwiller approxi- mation from quantum embedding principles: Ghost den- sity matrix embedding theory, Phys

    N. Lanat` a, Derivation of the ghost gutzwiller approxi- mation from quantum embedding principles: Ghost den- sity matrix embedding theory, Phys. Rev. B 108, 235112 (2023)

    2023

  47. [55]

    T.-H. Lee, N. Lanat` a, M. Kim, and G. Kotliar, Effi- cient slave-boson approach for multiorbital two-particle response functions and superconductivity, Phys. Rev. X 11, 041040 (2021)

    2021

  48. [56]

    intruder

    F. Lechermann, A. Georges, G. Kotliar, and O. Parcol- let, Rotationally invariant slave-boson formalism and mo- mentum dependence of the quasiparticle weight, Phys. Rev. B 76, 155102 (2007). 11 FIG. 2. a. We show a fixed point solution where some ED solutions are missing due t...

    2007

Pith tools

Reviewed August 12, 2026 · model on record in the stance chip above.