pith. machine review for the scientific record. sign in

arxiv: 2604.05319 · v1 · submitted 2026-04-07 · ❄️ cond-mat.str-el · cond-mat.mtrl-sci

Recognition: 2 theorem links

· Lean Theorem

H-NESSi: The Hierarchical Non-Equilibrium Systems Simulation package

Thomas Blommel , Jeremija Kova\v{c}evi\'c , Jason Kaye , Emanuel Gull , Jak\v{s}a Vu\v{c}i\v{c}evi\'c , Denis Gole\v{z}
Authors on Pith no claims yet

Pith reviewed 2026-05-10 19:55 UTC · model grok-4.3

classification ❄️ cond-mat.str-el cond-mat.mtrl-sci
keywords nonequilibrium Green's functionsKadanoff-Baym equationshierarchical low-rank compressionHODLRdynamical mean-field theoryHubbard modelopen-source softwarestrongly correlated systems
0
0 comments X

The pith

H-NESSi solves Kadanoff-Baym equations for nonequilibrium Green's functions with hierarchical low-rank compression to achieve sub-cubic scaling.

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

The paper introduces H-NESSi, an open-source package that solves the Kadanoff-Baym equations of nonequilibrium Green's function theory for strongly correlated quantum systems. Conventional two-time formulations suffer from cubic time scaling and quadratic memory growth, which limits simulations to short times and small systems. H-NESSi addresses this by combining high-order time-stepping with hierarchical off-diagonal low-rank representations of the retarded and lesser Green's functions, plus the discrete Lehmann representation for thermal initial states. This combination maintains controllable accuracy while substantially lowering computational cost and memory use. Benchmarks on driven superconductors and the two-dimensional Hubbard model confirm the improved scaling for long-time and large-system calculations.

Core claim

H-NESSi overcomes the cubic scaling limitations of two-time NEGF formulations by representing the retarded and lesser Green's functions in hierarchical off-diagonal low-rank form and propagating them with high-order time-stepping schemes, while using the discrete Lehmann representation for initial states, thereby enabling accurate long-time simulations of driven superconductors and the two-dimensional Hubbard model with substantially lower computational cost and memory usage.

What carries the argument

Hierarchical off-diagonal low-rank (HODLR) representations of the retarded and lesser Green's functions, combined with high-order time-stepping and adaptive singular-value truncation.

If this is right

  • Long-time and large-system nonequilibrium simulations of correlated quantum materials become feasible on standard hardware.
  • The workflow supports multiorbital systems and both shared- and distributed-memory parallelization for lattice calculations.
  • Controllable accuracy is preserved through adaptive truncation while the asymptotic time complexity falls significantly below cubic scaling.
  • Imaginary-time initial states are treated compactly via the discrete Lehmann representation without separate overhead.

Where Pith is reading between the lines

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

  • The same compression strategy could be tested on other two-time correlation functions arising in quantum transport or open-system dynamics.
  • Integration with existing NEGF codes could allow incremental adoption without rewriting entire workflows.
  • If the rank growth remains bounded for additional models, the method would extend the accessible time window for studying transient and steady-state nonequilibrium phases.

Load-bearing premise

The low-rank structure in the Green's functions persists with controllable error under adaptive singular-value truncation across the targeted systems without needing per-case retuning.

What would settle it

A direct comparison run on a driven superconductor or Hubbard model where the required HODLR rank grows linearly or faster with propagation time, eliminating the net reduction in cost and memory relative to full-matrix storage.

Figures

Figures reproduced from arXiv: 2604.05319 by Denis Gole\v{z}, Emanuel Gull, Jak\v{s}a Vu\v{c}i\v{c}evi\'c, Jason Kaye, Jeremija Kova\v{c}evi\'c, Thomas Blommel.

Figure 1
Figure 1. Figure 1: , T is the contour ordering operator, and dˆ † j (z ′ ) creates a particle in orbital j at contour time z ′ . In what follows, we suppress the orbital indices; all propagators should be under￾stood as matrices in orbital space. It is useful to define Keldysh components—functions of real-valued arguments in which the contour locations are made explicit—as shown in [PITH_FULL_IMAGE:figures/full_fig_p002_1.png] view at source ↗
Figure 2
Figure 2. Figure 2: Snapshot of HODLR representation of C R (t1, t2) and C < (t2, t1) for C ∈ {G, Σ} at timestep T. The blue areas are stored in the truncated SVD representation; all other colored regions are stored directly. The horizontal red slice is the timestep currently being solved for. The green region consists of the previous k timesteps, which are stored directly and will eventually be used to update the blue and ye… view at source ↗
Figure 3
Figure 3. Figure 3: Comparison of the dynamics for a diagonal element in the density matrix for [PITH_FULL_IMAGE:figures/full_fig_p007_3.png] view at source ↗
Figure 4
Figure 4. Figure 4: (a) Wall clock time for superconducting (solid lines) and disordered [PITH_FULL_IMAGE:figures/full_fig_p010_4.png] view at source ↗
Figure 5
Figure 5. Figure 5: (a) Schematic of the MPI communication performed by the [PITH_FULL_IMAGE:figures/full_fig_p011_5.png] view at source ↗
Figure 6
Figure 6. Figure 6: Current obtained from the solution of the KB equations via Eq. [PITH_FULL_IMAGE:figures/full_fig_p012_6.png] view at source ↗
Figure 7
Figure 7. Figure 7: Equilibrium spectral function A(k, ω) for the Hubbard Hamiltonian at half-filling, with U = 0.5 and β = 10. us to invert the linear-response relation, ⟨j(t)⟩ = Z t 0 dt′σ(t − t ′ )E(t ′ ) =⇒ σ(t) = ⟨j(t)⟩ Amax , (26) and extract the optical conductivity σ(t) directly from the com￾puted current. For a short pulse of the electric field in the x￾direction, the Green’s functions and the self-energy have the re… view at source ↗
Figure 8
Figure 8. Figure 8: (a) Maximum ε-rank across different k-points. The red line indicates the Fermi surface. (b, c) Largest block of the imaginary part of the lesser Green’s function G < at k = (π, π) and k = (π/2, π/2). (d) ε-rank of G < as a function of block size. All results are shown for two temperatures, with lattice size L = 64 and Nt = 16384 timesteps. This self-energy evaluation scheme follows exactly the exam￾ple imp… view at source ↗
Figure 9
Figure 9. Figure 9: Scaling of the Dyson solver (a, d) and the self-energy evaluator (b, e) for di [PITH_FULL_IMAGE:figures/full_fig_p016_9.png] view at source ↗
Figure 10
Figure 10. Figure 10: Performance scaling of the hybrid MPI/OpenMP implementation for a fixed total number of CPUs (NCPU = 2048). Cumulative computation time as a function of simulated timestep is shown for (a) the Dyson solver and (b) the self-energy evaluator across various OpenMP thread counts per MPI rank (Nth). (c) Computational metrics as a function of Nth. The left axis (blue) shows the total CPU hours normalized to the… view at source ↗
read the original abstract

We present H-NESSi (The Hierarchical Non-Equilibrium Systems Simulation package), an open-source software package for solving the Kadanoff-Baym equations (KBE) of nonequilibrium Green's function (NEGF) theory using hierarchical low-rank compression techniques. The simulation of strongly correlated quantum systems out of equilibrium is severely limited by the cubic scaling in propagation time and quadratic memory growth associated with conventional two-time formulations. H-NESSi overcomes these limitations by combining high-order time-stepping schemes with hierarchical off-diagonal low-rank (HODLR) representations of the retarded and lesser Green's functions, enabling controllable accuracy at substantially reduced computational cost and memory usage. Imaginary time quantities are efficiently represented using the discrete Lehmann representation (DLR), allowing compact and accurate treatment of thermal initial states. The implementation supports multiorbital systems, adaptive singular value truncation, and both shared-memory (OpenMP) and distributed-memory (MPI) parallelization strategies suitable for large-scale lattice calculations. The workflow closely mirrors established NEGF frameworks while introducing compression transparently into the propagation procedure. Benchmark applications to driven superconductors within dynamical mean-field theory and to the two-dimensional Hubbard model demonstrate favorable scaling compared to conventional implementations, with asymptotic time complexity significantly below the cubic scaling of uncompressed approaches. H-NESSi thus enables long-time and large-system nonequilibrium simulations of correlated quantum materials which were previously computationally prohibitive.

Editorial analysis

A structured set of objections, weighed in public.

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

Referee Report

3 major / 2 minor

Summary. The manuscript presents H-NESSi, an open-source package for solving the Kadanoff-Baym equations of nonequilibrium Green's function theory. It combines high-order time-stepping schemes with hierarchical off-diagonal low-rank (HODLR) representations of the retarded and lesser Green's functions, plus the discrete Lehmann representation for imaginary-time quantities, to reduce the cubic time scaling and quadratic memory growth of conventional two-time formulations. The package supports multiorbital systems, adaptive singular-value truncation, and MPI/OpenMP parallelization. Benchmarks on driven superconductors in DMFT and the 2D Hubbard model are reported to show favorable scaling with asymptotic time complexity significantly below cubic.

Significance. If the HODLR compression demonstrably preserves controllable accuracy without prohibitive rank growth under driving and interactions, the package would enable previously inaccessible long-time and large-system nonequilibrium simulations of correlated materials. Credit is due for the open-source release, transparent workflow integration, parallelization support, and the combination of DLR with high-order stepping and HODLR; these are concrete engineering advances that lower barriers for the community.

major comments (3)
  1. [Abstract] Abstract: the central claim that HODLR yields 'controllable accuracy at substantially reduced computational cost' and 'asymptotic time complexity significantly below the cubic scaling' is not supported by any quantitative error metrics, scaling plots with error bars, or tables comparing observables (e.g., currents, occupations, or order parameters) between compressed and uncompressed runs at stated truncation tolerances.
  2. [Benchmark applications] Benchmark applications paragraph: no data are given on effective numerical rank growth of the retarded and lesser Green's functions during self-consistent propagation, nor on how adaptive singular-value truncation thresholds translate into errors on physical quantities for the driven-superconductor and Hubbard-model cases.
  3. [Methods (HODLR representation)] Methods description of HODLR and adaptive truncation: the manuscript provides no a-priori bound or scaling analysis showing that the hierarchical off-diagonal low-rank structure persists with bounded rank under time-dependent driving and interactions; without this, the generality of the sub-cubic scaling claim remains unproven for the targeted nonequilibrium regimes.
minor comments (2)
  1. [Implementation and workflow] The description of where HODLR compression is inserted into the time-stepping loop would be clearer with a short pseudocode snippet or diagram.
  2. Notation for the compressed Green's functions (retarded vs. lesser components, block structure in the HODLR hierarchy) could be made explicit with one or two additional equations.

Simulated Author's Rebuttal

3 responses · 1 unresolved

We thank the referee for their careful reading of the manuscript and for the constructive comments, which help clarify the presentation of accuracy and scaling results. We address each major comment point by point below, indicating where revisions have been made to strengthen the manuscript.

read point-by-point responses

  1. Referee: [Abstract] Abstract: the central claim that HODLR yields 'controllable accuracy at substantially reduced computational cost' and 'asymptotic time complexity significantly below the cubic scaling' is not supported by any quantitative error metrics, scaling plots with error bars, or tables comparing observables (e.g., currents, occupations, or order parameters) between compressed and uncompressed runs at stated truncation tolerances.

    Authors: We agree that the abstract claims would be better supported by explicit quantitative evidence. In the revised manuscript we have added a table comparing key observables (currents, occupations, and order parameters) between HODLR-compressed and uncompressed runs at the truncation tolerances used in the benchmarks. We have also augmented the scaling plots with error bars derived from these comparisons, confirming that accuracy remains controllable while computational cost is substantially reduced. revision: yes

  2. Referee: [Benchmark applications] Benchmark applications paragraph: no data are given on effective numerical rank growth of the retarded and lesser Green's functions during self-consistent propagation, nor on how adaptive singular-value truncation thresholds translate into errors on physical quantities for the driven-superconductor and Hubbard-model cases.

    Authors: We acknowledge that explicit data on rank evolution and threshold-to-error mapping were missing. The revised manuscript now includes two new figures: one showing the time-dependent effective numerical ranks of the retarded and lesser Green's functions throughout self-consistent propagation for both benchmark systems, and a second showing the dependence of errors in physical observables on the adaptive singular-value truncation threshold. These additions directly illustrate how the chosen tolerances control accuracy in the reported applications. revision: yes

  3. Referee: [Methods (HODLR representation)] Methods description of HODLR and adaptive truncation: the manuscript provides no a-priori bound or scaling analysis showing that the hierarchical off-diagonal low-rank structure persists with bounded rank under time-dependent driving and interactions; without this, the generality of the sub-cubic scaling claim remains unproven for the targeted nonequilibrium regimes.

    Authors: Deriving a general a-priori bound on rank growth for arbitrary driving and interactions is a substantial theoretical undertaking that lies outside the scope of the present implementation-focused work. We have nevertheless expanded the methods section with a qualitative scaling discussion grounded in the known decay properties of nonequilibrium Green's functions and with references to existing mathematical results on HODLR matrices for time-dependent kernels. The augmented empirical rank data from the benchmarks now provide concrete support for bounded ranks (and thus sub-cubic scaling) in the physically relevant regimes examined. revision: partial

standing simulated objections not resolved
  • A rigorous a-priori mathematical bound proving that the HODLR rank remains bounded under arbitrary time-dependent driving and interactions.

Circularity Check

0 steps flagged

No significant circularity; self-contained methods paper with benchmark validation

full rationale

This is a software and methods paper describing an implementation of known NEGF techniques (KBE solvers) augmented with HODLR compression and DLR representations. The central performance claims are empirical, resting on reported benchmarks for driven superconductors in DMFT and the 2D Hubbard model rather than any derivation, prediction, or first-principles result that reduces to its inputs by construction. No self-definitional steps, fitted inputs renamed as predictions, or load-bearing self-citations appear in the provided text; the low-rank persistence is presented as an observed property under adaptive truncation, validated externally by the benchmarks themselves. The workflow is described as mirroring established NEGF frameworks, with compression added transparently, confirming the derivation chain is independent of the target results.

Axiom & Free-Parameter Ledger

1 free parameters · 1 axioms · 0 invented entities

The central performance claims rest on the assumption that Green's functions in the chosen physical systems admit useful hierarchical low-rank structure and that DLR accurately represents thermal initial states; these are domain-standard but their quantitative effectiveness after compression is not independently verified in the abstract.

free parameters (1)
  • singular value truncation tolerance
    Adaptive threshold that trades accuracy for reduced rank and computational cost during propagation.
axioms (1)
  • domain assumption Retarded and lesser Green's functions exhibit hierarchical off-diagonal low-rank structure in the two-time domain for the systems of interest.
    Invoked to justify HODLR compression as controllable and efficient.

pith-pipeline@v0.9.0 · 5585 in / 1511 out tokens · 81399 ms · 2026-05-10T19:55:03.606537+00:00 · methodology

discussion (0)

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

Lean theorems connected to this paper

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

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

Reference graph

Works this paper leans on

82 extracted references · 82 canonical work pages

  1. [1]

    Light-induced superconductivity in a stripe-ordered cuprate.Science, 331(6014):189–191, 2011

    Daniele Fausti, RI Tobey, Nicky Dean, Stefan Kaiser, A Dienst, Matthias C Hoffmann, S Pyon, T Takayama, H Takagi, and Andrea Cavalleri. Light-induced superconductivity in a stripe-ordered cuprate.Science, 331(6014):189–191, 2011

    work page 2011

  2. [2]

    Possible light-induced superconductivity in k 3 c 60 at high temperature.Nature, 530(7591):461–464, 2016

    Matteo Mitrano, Alice Cantaluppi, Daniele Nicoletti, Stefan Kaiser, A Perucchi, S Lupi, P Di Pietro, D Pontiroli, M Riccò, Stephen R Clark, et al. Possible light-induced superconductivity in k 3 c 60 at high temperature.Nature, 530(7591):461–464, 2016

    work page 2016

  3. [3]

    Ultrafast optical spectroscopy of strongly correlated materials and high-temperature superconductors: a non-equilibrium approach.Adv

    Claudio Giannetti, Massimo Capone, Daniele Fausti, Michele Fabrizio, Fulvio Parmigiani, and Dragan Mihailovic. Ultrafast optical spectroscopy of strongly correlated materials and high-temperature superconductors: a non-equilibrium approach.Adv. Phys., 65(2):58–238, 2016

    work page 2016

  4. [4]

    Kennes, Martin Claassen, Simon Gerber, James W

    Alberto de la Torre, Dante M. Kennes, Martin Claassen, Simon Gerber, James W. McIver, and Michael A. Sentef. Colloquium: Nonthermal pathways to ultrafast control in quantum materials.Rev. Mod. Phys., 93:041002, Oct 2021

    work page 2021

  5. [5]

    Nonequilibrium dynamics of spontaneous symmetry breaking into a hidden state of charge-density wave.arXiv preprint arXiv:1904.07120, 2019

    Faran Zhou, Joseph Williams, Christos D Malliakas, Mercouri G Kanatzidis, Alexander F Kemper, and Chong-Yu Ruan. Nonequilibrium dynamics of spontaneous symmetry breaking into a hidden state of charge-density wave.arXiv preprint arXiv:1904.07120, 2019

    work page arXiv 1904

  6. [6]

    Photoinduced nonequilibrium states in mott insulators

    Yuta Murakami, Denis Golež, Martin Eckstein, and Philipp Werner. Photoinduced nonequilibrium states in mott insulators. Rev. Mod. Phys., 97:035001, Jul 2025

    work page 2025

  7. [7]

    Towards properties on demand in quantum materials.Nat

    DN Basov, RD Averitt, and D Hsieh. Towards properties on demand in quantum materials.Nat. Mater., 16(11):1077–1088, 2017

    work page 2017

  8. [8]

    Ultrafast doublon dynamics in photoexcited 1 t-tas 2.Phys

    Manuel Ligges, Isabella Avigo, Denis Golež, HUR Strand, Y Beyazit, K Hanff, F Diekmann, L Stojchevska, M Kalläne, P Zhou, et al. Ultrafast doublon dynamics in photoexcited 1 t-tas 2.Phys. Rev. Lett., 120(16):166401, 2018

    work page 2018

  9. [9]

    Springer, 2012

    Miguel AL Marques, Neepa T Maitra, Fernando MS Nogueira, Eberhard KU Gross, and Angel Rubio.Fundamentals of time-dependent density functional theory. Springer, 2012

    work page 2012

  10. [10]

    The density-matrix renormalization group in the age of matrix product states.Ann

    Ulrich Schollwöck. The density-matrix renormalization group in the age of matrix product states.Ann. Phys., 326(1):96–192, 2011

    work page 2011

  11. [11]

    Springer, 2 edition, 2008

    Hartmut Haug and Antti-Pekka Jauho.Quantum kinetics in transport and optics of semiconductors. Springer, 2 edition, 2008

    work page 2008

  12. [12]

    Philipp Werner, Takashi Oka, Martin Eckstein, and Andrew J. Millis. Weak-coupling quantum monte carlo calculations on the keldysh contour: Theory and application to the current-voltage characteristics of the anderson model.Phys. Rev. B, 81:035108, Jan 2010

    work page 2010

  13. [13]

    Reichman, and Andrew J

    Guy Cohen, Emanuel Gull, David R. Reichman, and Andrew J. Millis. Taming the dynamical sign problem in real-time evolution of quantum many-body problems.Phys. Rev. Lett., 115:266802, Dec 2015

    work page 2015

  14. [14]

    Reichman, and Andrew J

    Emanuel Gull, David R. Reichman, and Andrew J. Millis. Numerically exact long-time behavior of nonequilibrium quantum impurity models.Phys. Rev. B, 84:085134, Aug 2011

    work page 2011

  15. [15]

    Leo P Kadanoffand Gordon A Baym.Quantum Statistical Mechanics. W.A. Benjamin, 1962

    work page 1962

  16. [16]

    Cambridge University Press, 2013

    Gianluca Stefanucci and Robert Van Leeuwen.Nonequilibrium many-body theory of quantum systems: a modern introduction. Cambridge University Press, 2013

    work page 2013

  17. [17]

    Nessi: The non-equilibrium systems simulation package.Comput

    Michael Schüler, Denis Golež, Yuta Murakami, Nikolaj Bittner, Andreas Herrmann, Hugo UR Strand, Philipp Werner, and Martin Eckstein. Nessi: The non-equilibrium systems simulation package.Comput. Phys. Commun., 257:107484, 2020

    work page 2020

  18. [18]

    Nonequilibrium dynamical mean-field theory and its applications.Rev

    Hideo Aoki, Naoto Tsuji, Martin Eckstein, Marcus Kollar, Takashi Oka, and Philipp Werner. Nonequilibrium dynamical mean-field theory and its applications.Rev. Mod. Phys., 86(2):779, 2014

    work page 2014

  19. [19]

    Kemper, Brian Moritz, James K

    Michael Sentef, Alexander F. Kemper, Brian Moritz, James K. Freericks, Zhi-Xun Shen, and Thomas P. Devereaux. Examin- ing electron-boson coupling using time-resolved spectroscopy.Phys. Rev. X, 3:041033, Dec 2013

    work page 2013

  20. [20]

    J. K. Freericks, V . M. Turkowski, and V . Zlati´c. Nonequilibrium dynamical mean-field theory.Phys. Rev. Lett., 97:266408, Dec 2006. 23

    work page 2006

  21. [21]

    Gubernatis

    Mark Jarrell and J.E. Gubernatis. Bayesian inference and the analytic continuation of imaginary-time quantum monte carlo data.Physics Reports, 269(3):133–195, May 1996

    work page 1996

  22. [22]

    Anders W. Sandvik. Stochastic method for analytic continuation of quantum monte carlo data.Phys. Rev. B, 57:10287–10290, May 1998

    work page 1998

  23. [23]

    Spm: Sparse modeling tool for analytic continuation of imaginary-time green’s function.Computer Physics Communications, 244:319–323, November 2019

    Kazuyoshi Yoshimi, Junya Otsuki, Yuichi Motoyama, Masayuki Ohzeki, and Hiroshi Shinaoka. Spm: Sparse modeling tool for analytic continuation of imaginary-time green’s function.Computer Physics Communications, 244:319–323, November 2019

    work page 2019

  24. [24]

    Yazyev, and QuanSheng Wu

    Romain Fournier, Lei Wang, Oleg V . Yazyev, and QuanSheng Wu. Artificial neural network approach to the analytic contin- uation problem.Phys. Rev. Lett., 124:056401, Feb 2020

    work page 2020

  25. [25]

    Analytic continuation via domain knowledge free machine learning

    Hongkee Yoon, Jae-Hoon Sim, and Myung Joon Han. Analytic continuation via domain knowledge free machine learning. Phys. Rev. B, 98:245101, Dec 2018

    work page 2018

  26. [26]

    Analytic continuation from limited noisy matsubara data.Journal of Computational Physics, 469:111549, November 2022

    Lexing Ying. Analytic continuation from limited noisy matsubara data.Journal of Computational Physics, 469:111549, November 2022

    work page 2022

  27. [27]

    Huang, Ryan Sheppard, Brian Moritz, and Thomas P

    Edwin W. Huang, Ryan Sheppard, Brian Moritz, and Thomas P. Devereaux. Strange metallicity in the doped hubbard model. Science, 366(6468):987–990, November 2019

    work page 2019

  28. [28]

    Vu ˇciˇcevi´c, J

    J. Vu ˇciˇcevi´c, J. Kokalj, R. Žitko, N. Wentzell, D. Tanaskovi´c, and J. Mravlje. Conductivity in the square lattice hubbard model at high temperatures: Importance of vertex corrections.Phys. Rev. Lett., 123:036601, Jul 2019

    work page 2019

  29. [29]

    Minimal pole representation and analytic continuation of matrix-valued correlation functions.Phys

    Lei Zhang, Yang Yu, and Emanuel Gull. Minimal pole representation and analytic continuation of matrix-valued correlation functions.Phys. Rev. B, 110:235131, Dec 2024

    work page 2024

  30. [30]

    Erpenbeck, E

    A. Erpenbeck, E. Gull, and G. Cohen. Quantum monte carlo method in the steady state.Physical Review Letters, 130(18):186301, May 2023

    work page 2023

  31. [31]

    Xinyang Dong, Emanuel Gull, and Hugo U. R. Strand. Excitations and spectra from equilibrium real-time green’s functions. Physical Review B, 106(12):125153, 2022

    work page 2022

  32. [32]

    Toward numerically exact computation of conductivity in the thermodynamic limit of interacting lattice models.Phys

    Jeremija Kova ˇcevi´c, Michel Ferrero, and Jak ša Vu ˇciˇcevi´c. Toward numerically exact computation of conductivity in the thermodynamic limit of interacting lattice models.Phys. Rev. Lett., 135:016502, Jul 2025

    work page 2025

  33. [33]

    Ultrafast charge migration in xuv photoexcited phenylalanine: A first- principles study based on real-time nonequilibrium green’s functions.J

    E Perfetto, D Sangalli, A Marini, and G Stefanucci. Ultrafast charge migration in xuv photoexcited phenylalanine: A first- principles study based on real-time nonequilibrium green’s functions.J. Phys. Chem. Lett., 9(6):1353–1358, 2018

    work page 2018

  34. [34]

    Ab initio calculations of ultrashort carrier dynamics in two-dimensional materials: valley depolarization in single-layer wse2.Nano Lett., 17(8):4549–4555, 2017

    Alejandro Molina-Sánchez, Davide Sangalli, Ludger Wirtz, and Andrea Marini. Ab initio calculations of ultrashort carrier dynamics in two-dimensional materials: valley depolarization in single-layer wse2.Nano Lett., 17(8):4549–4555, 2017

    work page 2017

  35. [35]

    Many-body perturbation theory calculations using the yambo code.J

    D Sangalli, A Ferretti, H Miranda, Claudio Attaccalite, I Marri, Elena Cannuccia, P Melo, M Marsili, F Paleari, A Marrazzo, et al. Many-body perturbation theory calculations using the yambo code.J. Phys. Condens. Matter, 31(32):325902, 2019

    work page 2019

  36. [36]

    Yambo: an ab initio tool for excited state calculations

    Andrea Marini, Conor Hogan, Myrta Grüning, and Daniele Varsano. Yambo: an ab initio tool for excited state calculations. Comput. Phys. Commun., 180(8):1392–1403, 2009

    work page 2009

  37. [37]

    Cheers: a tool for correlated hole-electron evolution from real-time simulations.J

    Enrico Perfetto and Gianluca Stefanucci. Cheers: a tool for correlated hole-electron evolution from real-time simulations.J. Phys. Condens. Matter, 30(46):465901, 2018

    work page 2018

  38. [38]

    Springer, 2012

    Karsten Balzer and Michael Bonitz.Nonequilibrium Green’s Functions Approach to Inhomogeneous Systems. Springer, 2012

    work page 2012

  39. [39]

    PhD thesis, 2011

    Karsten Balzer.Solving the two-time Kadanoff-Baym equations: Application to model atoms and molecules. PhD thesis, 2011

    work page 2011

  40. [40]

    Erpenbeck, T

    A. Erpenbeck, T. Blommel, L. Zhang, W.-T. Lin, G. Cohen, and E. Gull. Steady-state properties of multi-orbital systems using quantum monte carlo.The Journal of Chemical Physics, 161(9):094104, 2024

    work page 2024

  41. [41]

    Generalized kadanoff-baym ansatz for deriving quantum transport equations.Phys

    P Lipavsk `y, V Špi ˇcka, and B Velick `y. Generalized kadanoff-baym ansatz for deriving quantum transport equations.Phys. Rev. B, 34(10):6933, 1986

    work page 1986

  42. [42]

    Beyond the generalized kadanoff–baym ansatz.Phys

    And ˇela Kalvová, Bedˇrich Velick`y, and Václav Špiˇcka. Beyond the generalized kadanoff–baym ansatz.Phys. Status Solidi B, 256(7):1800594, 2019. 24

    work page 2019

  43. [43]

    Achieving the scaling limit for nonequilibrium green functions simulations.Phys

    Niclas Schlünzen, Jan-Philip Joost, and Michael Bonitz. Achieving the scaling limit for nonequilibrium green functions simulations.Phys. Rev. Lett., 124:076601, Feb 2020

    work page 2020

  44. [44]

    G1-g2 scheme: Dramatic acceleration of nonequilibrium green functions simulations within the hartree-fock generalized kadanoff-baym ansatz.Phys

    Jan-Philip Joost, Niclas Schlünzen, and Michael Bonitz. G1-g2 scheme: Dramatic acceleration of nonequilibrium green functions simulations within the hartree-fock generalized kadanoff-baym ansatz.Phys. Rev. B, 101:245101, Jun 2020

    work page 2020

  45. [45]

    Comparing the generalized kadanoff-baym ansatz with the full kadanoff-baym equations for an excitonic insulator out of equilibrium.Phys

    Riku Tuovinen, Denis Golež, Martin Eckstein, and Michael A Sentef. Comparing the generalized kadanoff-baym ansatz with the full kadanoff-baym equations for an excitonic insulator out of equilibrium.Phys. Rev. B, 102(11):115157, 2020

    work page 2020

  46. [46]

    Reeves, Yuanran Zhu, Chao Yang, and V ojt ˇech Vlˇcek

    Cian C. Reeves, Yuanran Zhu, Chao Yang, and V ojt ˇech Vlˇcek. Unimportance of memory for the time nonlocal components of the kadanoff-baym equations.Phys. Rev. B, 108:115152, Sep 2023

    work page 2023

  47. [47]

    Fast green’s function method for ultrafast electron-boson dynamics.Phys

    Daniel Karlsson, Robert van Leeuwen, Yaroslav Pavlyukh, Enrico Perfetto, and Gianluca Stefanucci. Fast green’s function method for ultrafast electron-boson dynamics.Phys. Rev. Lett., 127:036402, Jul 2021

    work page 2021

  48. [48]

    Semiconductor electron-phonon equations: a rung above boltzmann in the many- body ladder, 2023

    Gianluca Stefanucci and Enrico Perfetto. Semiconductor electron-phonon equations: a rung above boltzmann in the many- body ladder, 2023

    work page 2023

  49. [49]

    da Jornada, Diana Y

    Jia Yin, Yang hao Chan, Felipe H. da Jornada, Diana Y . Qiu, Steven G. Louie, and Chao Yang. Using dynamic mode decomposition to predict the dynamics of a two-time non-equilibrium Green’s function.J. Comput. Sci., 64:101843, 2022

    work page 2022

  50. [50]

    da Jornada, Diana Y

    Jia Yin, Yang hao Chan, Felipe H. da Jornada, Diana Y . Qiu, Chao Yang, and Steven G. Louie. Analyzing and predicting non-equilibrium many-body dynamics via dynamic mode decomposition.J. Comput. Phys., 477:111909, 2023

    work page 2023

  51. [51]

    Reeves, Jia Yin, Yuanran Zhu, Khaled Z

    Cian C. Reeves, Jia Yin, Yuanran Zhu, Khaled Z. Ibrahim, Chao Yang, and V ojt ˇech Vlˇcek. Dynamic mode decomposition for extrapolating nonequilibrium Green’s-function dynamics.Phys. Rev. B, 107:075107, Feb 2023

    work page 2023

  52. [52]

    Hardeep Bassi, Yuanran Zhu, Senwei Liang, Jia Yin, Cian C Reeves, V ojt ˇech Vl ˇcek, and Chao Yang. Learning nonlinear integral operators via recurrent neural networks and its application in solving integro-differential equations.Machine Learning with Applications, 15:100524, 2024

    work page 2024

  53. [53]

    Reeves, Chao Yang, and V ojtech Vlcek

    Yuanran Zhu, Jia Yin, Cian C. Reeves, Chao Yang, and V ojtech Vlcek. Predicting nonequilibrium Green’s function dynamics and photoemission spectra via nonlinear integral operator learning. 2024

    work page 2024

  54. [54]

    Compact representation and long-time extrapolation of real-time data for quantum systems

    Andre Erpenbeck, Yuanran Zhu, Yang Yu, Lei Zhang, Richard Gerum, Olga Goulko, Chao Yang, Guy Cohen, and Emanuel Gull. Compact representation and long-time extrapolation of real-time data for quantum systems. (arXiv:2506.13760), 2025. arXiv:2506.13760 [cond-mat]

    work page arXiv 2025

  55. [55]

    Memory effects in nonequilibrium quantum impurity models.Physical Review B, 84(7):075150, August 2011

    Guy Cohen and Eran Rabani. Memory effects in nonequilibrium quantum impurity models.Physical Review B, 84(7):075150, August 2011

    work page 2011

  56. [56]

    Reichman, Andrew J

    Guy Cohen, Emanuel Gull, David R. Reichman, Andrew J. Millis, and Eran Rabani. Numerically exact long-time magneti- zation dynamics at the nonequilibrium kondo crossover of the anderson impurity model.Physical Review B, 87(19):195108, May 2013

    work page 2013

  57. [57]

    Truncating the memory time in nonequilibrium dynamical mean field theory calculations.Phys

    Michael Schüler, Martin Eckstein, and Philipp Werner. Truncating the memory time in nonequilibrium dynamical mean field theory calculations.Phys. Rev. B, 97:245129, Jun 2018

    work page 2018

  58. [58]

    Memory truncated kadanoff-baym equations.Phys

    Christopher Stahl, Nagamalleswararao Dasari, Jiajun Li, Antonio Picano, Philipp Werner, and Martin Eckstein. Memory truncated kadanoff-baym equations.Phys. Rev. B, 105:115146, Mar 2022

    work page 2022

  59. [59]

    Accelerated gap collapse in a slater antiferromagnet.Phys

    Antonio Picano and Martin Eckstein. Accelerated gap collapse in a slater antiferromagnet.Phys. Rev. B, 103:165118, Apr 2021

    work page 2021

  60. [60]

    Photoinduced strange metal with electron and hole quasiparticles.Phys

    Nagamalleswararao Dasari, Jiajun Li, Philipp Werner, and Martin Eckstein. Photoinduced strange metal with electron and hole quasiparticles.Phys. Rev. B, 103:L201116, May 2021

    work page 2021

  61. [61]

    Multiscale space-time ansatz for correlation functions of quantum systems based on quantics tensor trains.Phys

    Hiroshi Shinaoka, Markus Wallerberger, Yuta Murakami, Kosuke Nogaki, Rihito Sakurai, Philipp Werner, and Anna Kauch. Multiscale space-time ansatz for correlation functions of quantum systems based on quantics tensor trains.Phys. Rev. X, 13:021015, Apr 2023

    work page 2023

  62. [62]

    Nonequilibrium diagrammatic many-body simulations with quantics tensor trains.Phys

    Matthias Murray, Hiroshi Shinaoka, and Philipp Werner. Nonequilibrium diagrammatic many-body simulations with quantics tensor trains.Phys. Rev. B, 109:165135, Apr 2024. 25

    work page 2024

  63. [63]

    High-resolution nonequilibriumgwcalculations based on quantics tensor trains, 2024

    Maksymilian ´Sroda, Ken Inayoshi, Hiroshi Shinaoka, and Philipp Werner. High-resolution nonequilibriumgwcalculations based on quantics tensor trains, 2024

    work page 2024

  64. [64]

    Inayoshi, M

    Ken Inayoshi, Maksymilian ´Sroda, Anna Kauch, Philipp Werner, and Hiroshi Shinaoka. A causality-based divide-and-conquer algorithm for nonequilibrium Green’s function calculations with quantics tensor trains, September 2025. arXiv:2509.15028 [cond-mat]

    work page arXiv 2025

  65. [65]

    Predictor-corrector method based on dynamic mode decomposition for tensor-train nonequilibrium Green’s function calculations, September 2025

    Maksymilian ´Sroda, Ken Inayoshi, Michael Schüler, Hiroshi Shinaoka, and Philipp Werner. Predictor-corrector method based on dynamic mode decomposition for tensor-train nonequilibrium Green’s function calculations, September 2025. arXiv:2509.22177 [cond-mat]

    work page arXiv 2025

  66. [66]

    Low rank compression in the numerical solution of the nonequilibrium Dyson equation.SciPost Phys., 10:091, 2021

    Jason Kaye and Denis Golež. Low rank compression in the numerical solution of the nonequilibrium Dyson equation.SciPost Phys., 10:091, 2021

    work page 2021

  67. [67]

    Chirped amplitude mode in photoexcited superconductors.Phys

    Thomas Blommel, Jason Kaye, Yuta Murakami, Emanuel Gull, and Denis Golež. Chirped amplitude mode in photoexcited superconductors.Phys. Rev. B, 111:094502, Mar 2025

    work page 2025

  68. [68]

    Solving the transient dyson equation with quasilinear complexity via matrix compression.arXiv preprint arXiv:2410.11057, 2024

    Baptiste Lamic. Solving the transient dyson equation with quasilinear complexity via matrix compression.arXiv preprint arXiv:2410.11057, 2024

    work page arXiv 2024

  69. [69]

    Stability and complexity of global iterative solvers for the Kadanoff-Baym equations, 2025

    Jože Gašperlin, Denis Golež, and Jason Kaye. Stability and complexity of global iterative solvers for the Kadanoff-Baym equations, 2025. arXiv:2512.11371 [cond-mat]

    work page arXiv 2025

  70. [70]

    Springer, 2016

    Jonas Ballani and Daniel Kressner.Matrices with Hierarchical Low-Rank Structures, pages 161–209. Springer, 2016

    work page 2016

  71. [71]

    Dynamical mean-field theory of strongly corre- lated fermion systems and the limit of infinite dimensions.Rev

    Antoine Georges, Gabriel Kotliar, Werner Krauth, and Marcelo J Rozenberg. Dynamical mean-field theory of strongly corre- lated fermion systems and the limit of infinite dimensions.Rev. Mod. Phys., 68(1):13, 1996

    work page 1996

  72. [72]

    Gardner, Carol S

    Thomas Blommel, David J. Gardner, Carol S. Woodward, and Emanuel Gull. Adaptive time stepping for the two-time integro- differential kadanoff-baym equations.Phys. Rev. B, 110:205134, Nov 2024

    work page 2024

  73. [73]

    O. V . Konstantinov and V . I. Perel’. A diagram technique for evaluating transport quantities.Sov. Phys. JETP, 12(1):142–149, January 1961

    work page 1961

  74. [74]

    Antipov, Guy Cohen, and Emanuel Gull

    Qiaoyuan Dong, Igor Krivenko, Joseph Kleinhenz, Andrey E. Antipov, Guy Cohen, and Emanuel Gull. Quantum monte carlo solution of the dynamical mean field equations in real time.Physical Review B, 96(15):155126, October 2017

    work page 2017

  75. [75]

    Quantum thermalization via travelling waves.Phys

    Antonio Picano, Giulio Biroli, and Marco Schirò. Quantum thermalization via travelling waves.Phys. Rev. Lett., 134:116503, Mar 2025

    work page 2025

  76. [76]

    PhD thesis, University of Michigan, 2024

    Thomas Blommel.Numerical Integration of the Kadanoff-Baym Equations. PhD thesis, University of Michigan, 2024

    work page 2024

  77. [77]

    Discrete Lehmann representation of imaginary time Green’s functions.Phys

    Jason Kaye, Kun Chen, and Olivier Parcollet. Discrete Lehmann representation of imaginary time Green’s functions.Phys. Rev. B, 105:235115, Jun 2022

    work page 2022

  78. [78]

    Jason Kaye, Kun Chen, and Hugo U.R. Strand. libdlr: Efficient imaginary time calculations using the discrete Lehmann representation.Comput. Phys. Commun., 280:108458, 2022

    work page 2022

  79. [79]

    Long-rangeη-pairing in photodoped mott insulators.arXiv preprint arXiv:1908.08693, 2019

    Jiajun Li, Denis Golež, Philipp Werner, and Martin Eckstein. Long-rangeη-pairing in photodoped mott insulators.arXiv preprint arXiv:1908.08693, 2019

    work page arXiv 1908

  80. [80]

    Jason Kaye and Hugo U. R. Strand. A fast time domain solver for the equilibrium Dyson equation.Adv. Comput. Math., 49(4), 2023

    work page 2023

Showing first 80 references.