pith. sign in

arxiv: 2606.11095 · v1 · pith:IW26K4MPnew · submitted 2026-06-09 · ❄️ cond-mat.str-el

Hybrid Hamiltonian-diagrammatic quantum impurity solver

Yang Yu , Gaurav Harsha , Lei Zhang , Agnieszka Ja\.zd\.zewska , Dominika Zgid , Xinyang Dong , Emanuel Gull This is my paper

Pith reviewed 2026-06-27 11:20 UTC · model grok-4.3

classification ❄️ cond-mat.str-el
keywords quantum impurity modelsdiagrammatic perturbation theoryauxiliary bathsign problemstrongly correlated electronshybrid solverlow-order perturbation
0
0 comments X

The pith

Adding a small auxiliary bath to diagrammatic solvers reduces the residual problem to one where low-order perturbation theory converges rapidly and accurately.

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

The paper establishes that quantum impurity models can be solved by combining an explicit small auxiliary bath with diagrammatic perturbation theory on what remains. This hybrid reduces the interacting part to a regime where low-order expansions are both accurate and free of large truncation errors. In benchmarks the resulting precision exceeds that of bold-line diagrammatic calculations by several orders of magnitude, while a two-orbital model with a severe sign problem reaches convergence at roughly one-thousandth the cost of competing approaches. The same acceleration appears in a realistic case whose exact answer is unknown. A reader cares because impurity models sit at the heart of strongly correlated electron physics and current methods are either limited by bath size, entanglement, or sign problems.

Core claim

Augmenting a diagrammatic expansion with a small auxiliary bath discretization reduces the residual quantum impurity problem to a regime in which low-order perturbation theory becomes highly accurate and rapidly convergent. In a simple benchmark this hybrid yields precision several orders of magnitude above bold-line calculations; for a strongly interacting two-orbital model with a severe sign problem, convergence occurs at three orders of magnitude lower computational cost; and convergence to the unknown exact result accelerates markedly in a difficult realistic problem.

What carries the argument

The auxiliary bath that is added to the diagrammatic expansion so that the remaining interaction is weak enough for low-order perturbation theory to suffice.

If this is right

  • Precision several orders of magnitude above bold-line diagrammatic results is obtained on simple benchmarks.
  • A two-orbital model with severe sign problem converges at three orders of magnitude lower cost than existing methods.
  • Convergence to the exact result accelerates rapidly in difficult realistic impurity problems.
  • The approach supplies a practical route to high-precision solutions for quantum impurity models in correlated systems.

Where Pith is reading between the lines

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

  • The same bath-augmentation idea could be tested on other diagrammatic expansions that currently suffer from slow convergence or sign problems.
  • Optimizing the auxiliary bath choice might further reduce the number of sites needed while preserving accuracy.
  • The hybrid construction suggests a general strategy for turning intractable diagrammatic series into controllable perturbative ones by controlled discretization of part of the environment.

Load-bearing premise

A small auxiliary bath can be chosen so that the leftover diagrammatic problem enters a regime of rapid, accurate low-order convergence without the bath itself introducing uncontrolled systematic errors into the final impurity solution.

What would settle it

A controlled test on a model with a known exact solution in which the hybrid result, after systematic enlargement of the auxiliary bath, deviates from the exact value by more than the claimed improvement over pure diagrammatic methods.

Figures

Figures reproduced from arXiv: 2606.11095 by Agnieszka Ja\.zd\.zewska, Dominika Zgid, Emanuel Gull, Gaurav Harsha, Lei Zhang, Xinyang Dong, Yang Yu.

Figure 1
Figure 1. Figure 1: FIG. 1. Spinless, non-interacting impurity model coupled to [PITH_FULL_IMAGE:figures/full_fig_p003_1.png] view at source ↗
Figure 3
Figure 3. Figure 3: FIG. 3. Spinless, non-interacting impurity model coupled to [PITH_FULL_IMAGE:figures/full_fig_p003_3.png] view at source ↗
Figure 5
Figure 5. Figure 5: FIG. 5. NiO SEET impurity result (first iteration) at [PITH_FULL_IMAGE:figures/full_fig_p004_5.png] view at source ↗
read the original abstract

Quantum impurity models, which describe the coupling between interacting orbitals and a non-interacting bath, play a central role in the physics of strongly correlated electron systems. Solving a quantum impurity model in general requires the use of non-perturbative numerical methods. Hamiltonian-based approaches, which rely on an explicit bath discretization, are typically limited to a small number of bath sites or small entanglement, and diagrammatic methods suffer from sign problems, slow convergence, or diagram truncation approximations. Here we show that these two classes of methods can be combined: augmenting diagrammatic methods with a small auxiliary bath can reduce the residual problem to a regime where low-order perturbation theory is highly accurate and rapidly converging. In a simple benchmark, the precision of the hybrid approach surpasses bold-line calculations by several orders of magnitude; for a strongly interacting two-orbital model with a severe sign problem, convergence is achieved at three orders of magnitude lower computational cost than competing methods; and convergence to the unknown exact result is rapidly accelerated in a difficult realistic problem. Our results establish a practical route to high-precision quantum impurity solutions in correlated quantum systems.

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, simulated authors' rebuttal, and a circularity audit. Tearing a paper down is the easy half of reading it; the pith above is the substance, this is the friction.

Referee Report

1 major / 0 minor

Summary. The manuscript proposes a hybrid quantum impurity solver that augments diagrammatic perturbation theory with a small auxiliary bath obtained from Hamiltonian discretization. This is claimed to reduce the residual problem to a regime where low-order perturbation theory becomes highly accurate and rapidly convergent, yielding several orders of magnitude better precision than bold-line diagrammatic calculations in a simple benchmark, three orders of magnitude lower computational cost for a strongly interacting two-orbital model with a severe sign problem, and accelerated convergence in a realistic problem.

Significance. If the central claim holds, the hybrid method would provide a practical route to high-precision solutions for quantum impurity models that are difficult for either pure Hamiltonian or pure diagrammatic approaches, with potential applications in DMFT calculations for correlated materials. The reported numerical gains on sign-problematic cases would be a notable advance if they can be shown to arise from controlled suppression of the residual diagrammatic series rather than uncontrolled cancellations.

major comments (1)
  1. [Abstract and method description] The central claim rests on the existence of a small auxiliary bath such that the residual diagrammatic series after hybridization is both rapidly convergent and free of truncation bias. No systematic criterion, a-posteriori error estimator, or convergence bound with respect to bath size or diagram order is supplied that would certify this for arbitrary models; the benchmarks demonstrate numerical improvement but do not isolate whether the observed precision gain is due to genuine suppression of the residual or to partial cancellation between bath-induced bias and PT truncation error.

Simulated Author's Rebuttal

1 responses · 0 unresolved

We thank the referee for the careful reading and constructive feedback. We address the single major comment below.

read point-by-point responses

  1. Referee: [Abstract and method description] The central claim rests on the existence of a small auxiliary bath such that the residual diagrammatic series after hybridization is both rapidly convergent and free of truncation bias. No systematic criterion, a-posteriori error estimator, or convergence bound with respect to bath size or diagram order is supplied that would certify this for arbitrary models; the benchmarks demonstrate numerical improvement but do not isolate whether the observed precision gain is due to genuine suppression of the residual or to partial cancellation between bath-induced bias and PT truncation error.

    Authors: We agree that no general systematic criterion, a-posteriori estimator, or model-independent convergence bound is supplied; deriving such a bound lies outside the scope of the present work and would be highly model-dependent. The benchmarks nevertheless allow isolation of the effect in at least one case: the simple benchmark compares directly against the known exact solution and shows that the hybrid solver achieves several orders of magnitude higher precision than bold-line diagrammatic calculations at the same diagram order, consistent with genuine suppression of the residual series rather than cancellation. The two-orbital and realistic-model benchmarks further show accelerated convergence to results obtained by independent methods. We will revise the manuscript to add an explicit discussion of these points and of the absence of a general bound. revision: yes

Circularity Check

0 steps flagged

No significant circularity; derivation self-contained via external benchmarks

full rationale

The paper proposes combining Hamiltonian discretization with diagrammatic perturbation theory via an auxiliary bath, claiming improved convergence on external benchmarks (simple model, two-orbital sign-problem case, realistic problem). No quoted equations or steps reduce a claimed prediction to a fitted parameter by construction, invoke self-citations as uniqueness theorems, or rename known results. The auxiliary-bath choice and low-order truncation are presented as empirical improvements validated against independent reference calculations, with no load-bearing self-referential definitions or ansatzes smuggled via prior author work. The derivation chain therefore remains independent of its own outputs.

Axiom & Free-Parameter Ledger

0 free parameters · 1 axioms · 0 invented entities

The central claim rests on the domain assumption that an auxiliary bath can be introduced without spoiling the diagrammatic expansion while rendering low-order perturbation theory accurate; no free parameters or invented entities are mentioned in the abstract.

axioms (1)
  • domain assumption A small auxiliary bath can be chosen so that the residual problem lies in a regime where low-order perturbation theory is highly accurate.
    This is the load-bearing premise that enables the hybrid method to outperform pure diagrammatic or Hamiltonian approaches.

pith-pipeline@v0.9.1-grok · 5743 in / 1271 out tokens · 22259 ms · 2026-06-27T11:20:47.077594+00:00 · methodology

discussion (0)

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

Reference graph

Works this paper leans on

75 extracted references · 2 canonical work pages

  1. [1]

    While the impurity Green’s functionGis problem-specific (and exactly known in the current example), the hybridization strength ∆R depends on the number of counterterms

    of the bare hybridization expansion, which is given by⟨k⟩=− P 12 ∆R 12G21 [63]. While the impurity Green’s functionGis problem-specific (and exactly known in the current example), the hybridization strength ∆R depends on the number of counterterms. The left panel of Fig. 3 shows the magnitude of this residual hybridization ∆ R for the example of Fig. 1, t...

  2. [2]

    P. W. Anderson, Localized Magnetic States in Metals, Physical Review124, 41 (1961)

    1961

  3. [3]

    Hanson, Spins in few-electron quantum dots, Reviews of Modern Physics79, 1217 (2007)

    R. Hanson, Spins in few-electron quantum dots, Reviews of Modern Physics79, 1217 (2007)

    2007

  4. [4]

    D. C. Langreth, Derivation of a master equation for charge-transfer processes in atom-surface collisions, Physical Review B43, 2541 (1991)

    1991

  5. [5]

    Georges, G

    A. Georges, G. Kotliar, W. Krauth, and M. J. Rozen- berg, Dynamical mean-field theory of strongly correlated fermion systems and the limit of infinite dimensions, Re- views of Modern Physics68, 13 (1996)

    1996

  6. [6]

    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. [7]

    Zgid and E

    D. Zgid and E. Gull, Finite temperature quantum em- bedding theories for correlated systems, New Journal of Physics19, 023047 (2017)

    2017

  8. [8]

    A. A. Rusakov, S. Iskakov, L. N. Tran, and D. Zgid, Self- Energy Embedding Theory (SEET) for Periodic Systems, Journal of Chemical Theory and Computation15, 229 (2019)

    2019

  9. [9]

    L. N. Tran, N. L. Nguyen, S. Iskakov, and D. Zgid, Gen- eralized self-energy embedding theory, The Journal of Physical Chemistry Letters8, 1859 (2017)

    2017

  10. [10]

    Caffarel and W

    M. Caffarel and W. Krauth, Exact diagonalization ap- proach to correlated fermions in infinite dimensions: Mott transition and superconductivity, Physical Review Letters72, 1545 (1994)

    1994

  11. [11]

    Zgid and G

    D. Zgid and G. K.-L. Chan, Dynamical mean-field theory from a quantum chemical perspective, The Journal of Chemical Physics134, 094115 (2011)

    2011

  12. [12]

    D. Zgid, E. Gull, and G. K.-L. Chan, Truncated config- uration interaction expansions as solvers for correlated quantum impurity models and dynamical mean-field the- ory, Physical Review B86, 165128 (2012)

    2012

  13. [13]

    Shee and D

    A. Shee and D. Zgid, Coupled Cluster as an Impu- rity Solver for Green’s Function Embedding Methods, Journal of Chemical Theory and Computation15, 6010 (2019)

    2019

  14. [14]

    Barra and P

    T. Zhu, Coupled-cluster impurity solvers for dynamical mean-field theory, Physical Review B100, 10.1103/Phys- RevB.100.115154 (2019)

    work page doi:10.1103/phys- 2019

  15. [15]

    Nishimoto and E

    S. Nishimoto and E. Jeckelmann, Density-matrix renor- malization group approach to quantum impurity prob- lems, Journal of Physics: Condensed Matter16, 613 (2004)

    2004

  16. [16]

    D. J. Garc´ ıa, K. Hallberg, and M. J. Rozenberg, Dynam- ical Mean Field Theory with the Density Matrix Renor- malization Group, Physical Review Letters93, 246403 (2004)

    2004

  17. [17]

    X. Cao, Y. Lu, E. M. Stoudenmire, and O. Parcollet, Dynamical correlation functions from complex time evo- lution, Physical Review B109, 235110 (2024)

    2024

  18. [18]

    Grundner, P

    M. Grundner, P. Westhoff, F. B. Kugler, O. Parcollet, and U. Schollw¨ ock, Complex time evolution in tensor networks and time-dependent Green’s functions, Phys- ical Review B109, 155124 (2024)

    2024

  19. [19]

    Y. Yu, L. Zhang, E. Gull, X. Cao, and X. Dong, Multi- orbital dynamical mean-field theory with a complex-time solver, Physical Review Research8, 023142 (2026)

    2026

  20. [20]

    Y. Lu, M. H¨ oppner, O. Gunnarsson, and M. W. Haverkort, Efficient real-frequency solver for dynamical mean-field theory, Phys. Rev. B90, 085102 (2014)

    2014

  21. [21]

    Lu and M

    Y. Lu and M. W. Haverkort, Exact diagonalization as an impurity solver in dynamical mean field theory, The Eu- ropean Physical Journal Special Topics226, 2549 (2017)

    2017

  22. [22]

    A. N. Rubtsov, V. V. Savkin, and A. I. Lichten- stein, Continuous-time quantum Monte Carlo method for fermions, Physical Review B72, 035122 (2005)

    2005

  23. [23]

    Werner, A

    P. Werner, A. Comanac, L. de’ Medici, M. Troyer, and A. J. Millis, Continuous-time solver for quantum impu- rity models, Physical Review Letters97, 076405 (2006)

    2006

  24. [24]

    E. Gull, P. Werner, O. Parcollet, and M. Troyer, Continuous-time auxiliary-field Monte Carlo for quantum 6 impurity models, EPL (Europhysics Letters)82, 57003 (2008)

    2008

  25. [25]

    E. Gull, D. R. Reichman, and A. J. Millis, Bold-line di- agrammatic Monte Carlo method: General formulation and application to expansion around the noncrossing ap- proximation, Physical Review B82, 075109 (2010)

    2010

  26. [26]

    E. Gull, A. J. Millis, A. I. Lichtenstein, A. N. Rubtsov, M. Troyer, and P. Werner, Continuous-time Monte Carlo methods for quantum impurity models, Reviews of Mod- ern Physics83, 349 (2011)

    2011

  27. [27]

    Eidelstein, E

    E. Eidelstein, E. Gull, and G. Cohen, Multiorbital Quantum Impurity Solver for General Interactions and Hybridizations, Physical Review Letters124, 206405 (2020)

    2020

  28. [28]

    Keiter and J

    H. Keiter and J. C. Kimball, Perturbation Technique for the Anderson Hamiltonian, Physical Review Letters25, 672 (1970)

    1970

  29. [29]

    Pruschke and N

    Th. Pruschke and N. Grewe, The Anderson model with finite Coulomb repulsion, Zeitschrift f¨ ur Physik B Con- densed Matter74, 439 (1989)

    1989

  30. [30]

    N´ u˜ nez Fern´ andez, M

    Y. N´ u˜ nez Fern´ andez, M. Jeannin, P. T. Dumitrescu, T. Kloss, J. Kaye, O. Parcollet, and X. Waintal, Learning Feynman Diagrams with Tensor Trains, Physical Review X12, 041018 (2022)

    2022

  31. [31]

    Y. Yu, A. Erpenbeck, D. Zgid, G. Cohen, O. Parcollet, and E. Gull, Inchworm tensor train hybridization expan- sion quantum impurity solver, Physical Review B112, 085120 (2025)

    2025

  32. [32]

    Erpenbeck, W.-T

    A. Erpenbeck, W.-T. Lin, T. Blommel, L. Zhang, S. Iskakov, L. Bernheimer, Y. N´ u˜ nez-Fern´ andez, G. Co- hen, O. Parcollet, X. Waintal, and E. Gull, Tensor train continuous time solver for quantum impurity models, Physical Review B107, 245135 (2023)

    2023

  33. [33]

    J. Kaye, Z. Huang, H. U. R. Strand, and D. Goleˇ z, Decomposing Imaginary-Time Feynman Diagrams Using Separable Basis Functions: Anderson Impurity Model Strong-Coupling Expansion, Physical Review X14, 031034 (2024)

    2024

  34. [34]

    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

  35. [35]

    Huang, D

    Z. Huang, D. Golez, H. U. R. Strand, and J. Kaye, Auto- mated evaluation of imaginary time strong coupling dia- grams by sum-of-exponentials hybridization fitting, Sci- Post Physics19, 121 (2025)

    2025

  36. [36]

    Pollet, N

    L. Pollet, N. V. Prokof’ev, and B. V. Svistunov, Regu- larization of Diagrammatic Series with Zero Convergence Radius, Physical Review Letters105, 210601 (2010)

    2010

  37. [37]

    Rossi, F

    R. Rossi, F. Werner, N. Prokof’ev, and B. Svistunov, Shifted-action expansion and applicability of dressed di- agrammatic schemes, Physical Review B93, 161102 (2016)

    2016

  38. [38]

    Rossi, Determinant Diagrammatic Monte Carlo Al- gorithm in the Thermodynamic Limit, Physical Review Letters119, 045701 (2017)

    R. Rossi, Determinant Diagrammatic Monte Carlo Al- gorithm in the Thermodynamic Limit, Physical Review Letters119, 045701 (2017)

    2017

  39. [39]

    A. J. Kim, N. V. Prokof’ev, B. V. Svistunov, and E. Kozik, Homotopic Action: A Pathway to Convergent Diagrammatic Theories, Physical Review Letters126, 257001 (2021)

    2021

  40. [40]

    Wang and K

    Y. Wang and K. Haule, Variational Diagrammatic Monte Carlo Built on Dynamical Mean-Field Theory, Physical Review Letters135, 176501 (2025)

    2025

  41. [41]

    J. Li, M. Wallerberger, and E. Gull, Diagrammatic Monte Carlo method for impurity models with general interac- tions and hybridizations, Physical Review Research2, 033211 (2020)

    2020

  42. [42]

    J. Li, Y. Yu, E. Gull, and G. Cohen, Interaction- expansion inchworm Monte Carlo solver for lattice and impurity models, Physical Review B105, 165133 (2022)

    2022

  43. [43]

    A. N. Rubtsov, M. I. Katsnelson, and A. I. Lichtenstein, Dual fermion approach to nonlocal correlations in the Hubbard model, Physical Review B77, 033101 (2008)

    2008

  44. [44]

    Rohringer, H

    G. Rohringer, H. Hafermann, A. Toschi, A. A. Katanin, A. E. Antipov, M. I. Katsnelson, A. I. Lichtenstein, A. N. Rubtsov, and K. Held, Diagrammatic routes to nonlo- cal correlations beyond dynamical mean field theory, Re- views of Modern Physics90, 025003 (2018)

    2018

  45. [45]

    See the Supplemental Material at XXX for the deriva- tion of the formulas presented in the main text, along with supplemental numerical results, which included Refs. [45–51]. (n.d.)

  46. [46]

    C. G. BROYDEN, The Convergence of a Class of Double- rank Minimization Algorithms 1. General Considera- tions, IMA Journal of Applied Mathematics6, 76 (1970)

    1970

  47. [47]

    M. J. D. Powell,The BOBYQA Algorithm for Bound Constrained Optimization without Derivatives, Technical Report NA2009/06 (Department of Applied Mathemat- ics and Theoretical Physics, Cambridge University, Cam- bridge, England, 2009)

    2009

  48. [48]

    Roy and T

    R. Roy and T. Kailath, ESPRIT-estimation of signal parameters via rotational invariance techniques, IEEE Transactions on Acoustics, Speech, and Signal Process- ing37, 984 (1989)

    1989

  49. [49]

    Hua and T

    Y. Hua and T. Sarkar, Matrix pencil method for estimat- ing parameters of exponentially damped/undamped sinu- soids in noise, IEEE Transactions on Acoustics, Speech, and Signal Processing38, 814 (1990)

    1990

  50. [50]

    Sarkar and O

    T. Sarkar and O. Pereira, Using the matrix pencil method to estimate the parameters of a sum of complex exponen- tials, IEEE Antennas and Propagation Magazine37, 48 (1995)

    1995

  51. [51]

    Fei, C.-N

    J. Fei, C.-N. Yeh, D. Zgid, and E. Gull, Analytical con- tinuation of matrix-valued functions: Carath´ eodory for- malism, Physical Review B104, 165111 (2021)

    2021

  52. [52]

    Nakatsukasa, O

    Y. Nakatsukasa, O. S` ete, and L. N. Trefethen, The AAA Algorithm for Rational Approximation, SIAM Journal on Scientific Computing40, A1494 (2018)

    2018

  53. [53]

    Mejuto-Zaera, L

    C. Mejuto-Zaera, L. Zepeda-N´ u˜ nez, M. Lindsey, N. Tub- man, B. Whaley, and L. Lin, Efficient hybridization fit- ting for dynamical mean-field theory via semi-definite re- laxation, Physical Review B101, 035143 (2020)

    2020

  54. [54]

    Huang, E

    Z. Huang, E. Gull, and L. Lin, Robust analytic contin- uation of Green’s functions via projection, pole estima- tion, and semidefinite relaxation, Physical Review B107, 075151 (2023)

    2023

  55. [55]

    Zhang and E

    L. Zhang and E. Gull, Minimal pole representation and controlled analytic continuation of Matsubara response functions, Physical Review B110, 035154 (2024)

    2024

  56. [56]

    Zhang, Y

    L. Zhang, Y. Yu, and E. Gull, Minimal pole representa- tion and analytic continuation of matrix-valued correla- tion functions, Physical Review B110, 235131 (2024)

    2024

  57. [57]

    Zhang, A

    L. Zhang, A. Erpenbeck, Y. Yu, and E. Gull, Minimal pole representation for spectral functions, The Journal of Chemical Physics162, 214111 (2025)

    2025

  58. [58]

    Ying, Pole Recovery From Noisy Data on Imaginary Axis, Journal of Scientific Computing92, 107 (2022)

    L. Ying, Pole Recovery From Noisy Data on Imaginary Axis, Journal of Scientific Computing92, 107 (2022)

    2022

  59. [59]

    Ying, Analytic continuation from limited noisy Mat- 7 subara data, Journal of Computational Physics469, 111549 (2022)

    L. Ying, Analytic continuation from limited noisy Mat- 7 subara data, Journal of Computational Physics469, 111549 (2022)

    2022

  60. [60]

    Ostmeyer and C

    J. Ostmeyer and C. Urbach, The Truncated Hankel Cor- relator Method (2025), arXiv:2510.15500 [hep-lat]

    arXiv 2025

  61. [61]

    E. Gull, P. Werner, A. Millis, and M. Troyer, Perfor- mance analysis of continuous-time solvers for quantum impurity models, Physical Review B76, 235123 (2007)

    2007

  62. [62]

    J. Kaye, K. Chen, and O. Parcollet, Discrete Lehmann representation of imaginary time Green’s functions, Physical Review B105, 235115 (2022)

    2022

  63. [63]

    J. Kaye, K. Chen, and H. U. R. Strand, Libdlr: Efficient imaginary time calculations using the discrete Lehmann representation, Computer Physics Communications280, 108458 (2022)

    2022

  64. [64]

    K. Haule, Quantum Monte Carlo impurity solver for clus- ter dynamical mean-field theory and electronic structure calculations with adjustable cluster base, Physical Re- view B75, 155113 (2007)

    2007

  65. [65]

    Kanamori, Electron correlation and ferromagnetism of transition metals, Progress of Theoretical Physics30, 275 (1963)

    J. Kanamori, Electron correlation and ferromagnetism of transition metals, Progress of Theoretical Physics30, 275 (1963)

    1963

  66. [66]

    Werner, E

    P. Werner, E. Gull, M. Troyer, and A. J. Millis, Spin Freezing Transition and Non-Fermi-Liquid Self-Energy in a Three-Orbital Model, Physical Review Letters101, 166405 (2008)

    2008

  67. [67]

    Georges, L

    A. Georges, L. de’ Medici, and J. Mravlje, Strong Cor- relations from Hund’s Coupling, Annual Review of Con- densed Matter Physics4, 137 (2013)

    2013

  68. [68]

    Iskakov, C.-N

    S. Iskakov, C.-N. Yeh, E. Gull, and D. Zgid, Ab initio self-energy embedding for the photoemission spectra of NiO and MnO, Physical Review B102, 085105 (2020)

    2020

  69. [69]

    A. A. Kananenka, E. Gull, and D. Zgid, Systematically improvable multiscale solver for correlated electron sys- tems, Physical Review B91, 121111 (2015)

    2015

  70. [70]

    C.-N. Yeh, S. Iskakov, D. Zgid, and E. Gull, Fully self- consistent finite-temperature$GW$in Gaussian Bloch orbitals for solids, Physical Review B106, 235104 (2022)

    2022

  71. [71]

    Iskakov, C.-N

    S. Iskakov, C.-N. Yeh, P. Pokhilko, Y. Yu, L. Zhang, G. Harsha, V. Abraham, M. Wen, M. Wang, J. Adamski, T. Chen, E. Gull, and D. Zgid, Green/WeakCoupling: Implementation of fully self-consistent finite-temperature many-body perturbation theory for molecules and solids, Computer Physics Communications306, 109380 (2025)

    2025

  72. [72]

    Iskakov and M

    S. Iskakov and M. Danilov, Exact diagonalization library for quantum electron models, Computer Physics Com- munications225, 128 (2018)

    2018

  73. [73]

    Gaenko, A

    A. Gaenko, A. E. Antipov, G. Carcassi, T. Chen, X. Chen, Q. Dong, L. Gamper, J. Gukelberger, R. Igarashi, S. Iskakov, M. K¨ onz, J. P. F. LeBlanc, R. Levy, P. N. Ma, J. E. Paki, H. Shinaoka, S. Todo, M. Troyer, and E. Gull, Updated core libraries of the ALPS project, Computer Physics Communications213, 235 (2017)

    2017

  74. [74]

    Cohen, E

    G. Cohen, E. Gull, D. R. Reichman, and A. J. Millis, Taming the dynamical sign problem in real-time evolu- tion of quantum many-body problems, Physical Review Letters115, 266802 (2015)

    2015

  75. [75]

    Hybrid Hamiltonian- diagrammatic quantum impurity solver

    Y. Yu, G. Harsha, L. Zhang, A. Ja˙ zd˙ zewska, D. Zgid, X. Dong, and E. Gull, Dataset for publication “Hybrid Hamiltonian- diagrammatic quantum impurity solver”, https://doi.org/10.5281/zenodo.20150672(2026)

    work page doi:10.5281/zenodo.20150672(2026 2026