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arxiv: 1907.11302 · v1 · pith:AOVE2AP6new · submitted 2019-07-25 · ❄️ cond-mat.str-el

An introduction to many-body Green's functions in and out of equilibrium

J. K. Freericks This is my paper

Pith reviewed 2026-05-24 15:47 UTC · model grok-4.3

classification ❄️ cond-mat.str-el
keywords many-body Green's functionsnonequilibriumdynamical mean-field theoryKeldysh contourcorrelated electronsDMFTtime-dependent phenomena
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The pith

Dynamical mean-field theory extends to compute many-body Green's functions out of equilibrium.

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

The paper presents an introductory treatment of many-body Green's functions for systems both in and out of equilibrium, with a focus on using dynamical mean-field theory to make the calculations feasible. It supplies the formalism needed to handle time-dependent driving in correlated electron models. A reader would care because this opens a route to model how materials respond to external fields or pulses on ultrafast timescales. The approach stays within a self-consistent impurity framework that remains tractable even when the system is driven far from equilibrium.

Core claim

The paper establishes that dynamical mean-field theory, already successful for equilibrium properties, can be formulated on the Keldysh contour to calculate contour-ordered Green's functions for nonequilibrium situations, thereby providing graduate students with the concrete steps required to obtain spectral functions and other observables under time-dependent perturbations.

What carries the argument

Contour-ordered Green's functions solved self-consistently within dynamical mean-field theory on the Keldysh contour.

If this is right

  • Time-dependent spectral functions become computable for driven Hubbard-like models.
  • Nonequilibrium DMFT supplies a consistent way to treat the impurity problem under time-dependent hybridization.
  • Real-time response functions such as current or magnetization can be extracted directly from the Green's functions.
  • The formalism recovers standard equilibrium DMFT as a special case.

Where Pith is reading between the lines

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

  • The same contour technique might be combined with other impurity solvers beyond the ones presented here.
  • Direct comparison with time-resolved photoemission data on specific materials would test practical accuracy.
  • Extension to include nonlocal correlations could be examined by relaxing the DMFT locality assumption.

Load-bearing premise

Readers already possess a solid background in solid state physics and advanced quantum mechanics.

What would settle it

Explicit reduction of the nonequilibrium DMFT equations to the known equilibrium DMFT result when all external driving fields are switched off.

Figures

Figures reproduced from arXiv: 1907.11302 by J. K. Freericks.

Figure 1
Figure 1. Figure 1: (a) Kadanoff-Baym-Keldysh contour used in the contruction of the contour-ordered Green’s function. The contour starts at −∞, runs out to the maximum of t and t 0 , runs back to −∞ and then runs parallel to the imaginary axis for a distance equal to β. (b) The con￾tour can be “stretched” into a straight line as indicated here, which is convenient for properly implementing time-ordering along the contour [P… view at source ↗
Figure 2
Figure 2. Figure 2: Local lesser self-energy for the Falicov-Kimball model at half-filling and β = 1 and U = 1. The timestep was ∆t = 0.05 and the time range ran from −15 ≤ trel ≤ 15. The blue curve is the exact result and the other colors are different methods for integration over the noninteracting density of states. The inset shows a blow up of the region at large negative times, where the different integration methods sta… view at source ↗
Figure 3
Figure 3. Figure 3: Local lesser self-energy for the Falicov-Kimball model at half-filling and β = 1 and U = 1. Here, we Fourier transform the data from time to frequency. We use different time discretizations for the different curves, while the density of states integration used N = 54 and N = 55 points for Gaussian integration. The oscillations on the discrete calculations come from the oscillations in time shown in [PITH_… view at source ↗
Figure 4
Figure 4. Figure 4: Local lesser Green’s function for the Falicov-Kimball model at half-filling and β = 1 and U = 1.The parameters are the same as the previous figure. The main plot is the imaginary part (which becomes symmetric for the exact result, and the inset is the real part, which becomes antisymmetric. This figure is adapted from Ref. [22]. In [PITH_FULL_IMAGE:figures/full_fig_p020_4.png] view at source ↗
Figure 5
Figure 5. Figure 5: Local density of states for the Falicov-Kimball model in equilibrium and at half-filling. The calculations are in equilibrium, where the density of states is temperature independent in the normal state. The curves are for different U. One can see as U increases we cross through a Mott transition at U ≈ √ 2. We can see this transition occur in [PITH_FULL_IMAGE:figures/full_fig_p021_5.png] view at source ↗
Figure 6
Figure 6. Figure 6: Transient local density of states for the Falicov-Kimball model in a dc electric field with U = 0.5, β = 0.1 and E = 1 at half-filling. The different panels are labelled by the average time of the spectra. One can see that quite quickly after the dc field is turned on, the retarded Green’s function approaches the steady state. These results are adapted from [26] Fourier transform of a periodic function, wh… view at source ↗
Figure 7
Figure 7. Figure 7: Transient current for E = 1, U = 0.5 and β = 0.1. These results use ∆t = 0.1 and are not scaled. Notice how they start off as a Bloch oscillation, but are damped by the scattering due to the interaction U. They die off and then start to have a recurrence at the longest times simulated. At the earliest times the current is nonzero simply because we have not scaled the data. Scaling is needed to achieve a va… view at source ↗
Figure 8
Figure 8. Figure 8: Sum rules for the local retarded Green’s function for E = 1 and U = 2. Here, we illustrate how one can use sum rules to verify the scaling to ∆t → 0 has been done accurately. The zeroth moment sum rule equals 1 and the second moment sum rule equals −(1/2 + U 2/4). We plot the raw data versus time, the exact result, and the extrapolated result. One can see that even if the raw data was off by a huge amount,… view at source ↗
read the original abstract

This is an introductory chapter on how to calculate nonequilibrium Green's functions via dynamical mean-field theory for the Autumn School on Correlated Electrons: Many-Body Methods for Real Materials, 16-20 September 2019, Forschungszentrum Juelich. It is appropriate for graduate students with a solid state physics and advanced quantum mechanics background.

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

0 major / 1 minor

Summary. This manuscript is an introductory chapter (Autumn School lecture notes) on calculating nonequilibrium Green's functions via dynamical mean-field theory. It targets graduate students with solid-state physics and advanced quantum mechanics backgrounds and presents standard DMFT techniques for equilibrium and nonequilibrium cases without introducing new derivations or results.

Significance. As pedagogical material, the work has value in accurately exposing established nonequilibrium DMFT methods to students. No novel claims, parameter-free derivations, or machine-checked results are present; significance rests on clarity and correctness of the exposition of standard techniques.

minor comments (1)
  1. The abstract states the target audience but the manuscript should explicitly list prerequisites (e.g., familiarity with Matsubara formalism or impurity solvers) at the start of the main text for clarity.

Simulated Author's Rebuttal

0 responses · 0 unresolved

We thank the referee for the careful reading and the positive recommendation to accept the manuscript. We are pleased that the work is viewed as a useful pedagogical resource for the intended audience of graduate students.

Circularity Check

0 steps flagged

No significant circularity; purely pedagogical exposition

full rationale

The paper is explicitly an introductory lecture-note chapter presenting standard DMFT techniques for nonequilibrium Green's functions. It contains no novel derivations, quantitative predictions, or load-bearing claims that could reduce to self-definitions, fitted inputs, or self-citation chains. All content is expository of established material, with correctness depending on accurate presentation rather than any internal derivation chain. No steps meet the criteria for circularity.

Axiom & Free-Parameter Ledger

0 free parameters · 2 axioms · 0 invented entities

This introductory chapter relies entirely on standard background from condensed matter physics and quantum mechanics without introducing or fitting new elements.

axioms (2)
  • domain assumption Readers have solid state physics and advanced quantum mechanics background
    Explicitly stated in the abstract as prerequisite for the chapter.
  • domain assumption Dynamical mean-field theory applies to nonequilibrium Green's functions in correlated systems
    The chapter assumes this framework is the appropriate method without deriving it.

pith-pipeline@v0.9.0 · 5569 in / 966 out tokens · 25100 ms · 2026-05-24T15:47:09.995538+00:00 · methodology

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Reference graph

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