Microscopic Origin of Dephasing in Solids from First-Principles Electron-Phonon Interactions

Atsushi Yamada; Kazuhiro Yabana

REVIEW 4 major objections 5 minor 25 references

Microscopic Origin of Dephasing in Solids from First-Principles Electron-Phonon Interactions

T0 review · 4 major / 5 minor · reviewed 2026-08-01 · deepseek-v4-flash

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Pith's one-line read This paper claims that static lattice disorder from thermal and zero-point motion, captured through a single frozen ionic configuration in a supercell, is enough to produce effective dephasing in real-time TDDFT—yielding Drude-like current

desk verdict A useful, clever rt-TDDFT dephasing mechanism with a genuinely new diagnostic, but the headline 10 fs is a finite-size number until proven otherwise. read the letter →

arxiv 2607.17109 v1 pith:SRTF4XF7 submitted 2026-07-19 cond-mat.other

Atsushi Yamada , Kazuhiro Yabana This is my paper · ORCID

classification cond-mat.other

keywords dephasingelectron-phononinteractionreal-timeTDDFTWilliams-LaxformalismDrudedampinghigh-harmonicgenerationbandunfoldingthermaldisorder

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

The authors aim to establish that electron-phonon interactions, treated as frozen static disorder in a supercell, provide a first-principles mechanism for dephasing in solids within real-time time-dependent density functional theory. They argue that a single thermally disordered ionic configuration, without ensemble averaging, reproduces Drude-like exponential current damping in aluminum and produces well-resolved high-harmonic spectra in diamond that otherwise require an ultrashort phenomenological dephasing time. By unfolding the supercell dynamics onto a primitive-cell density matrix, they show that the dominant contribution to this dephasing comes from diagonal population dynamics, not the decay of off-diagonal coherence assumed in conventional T2 pictures. If correct, this removes the need for empirical relaxation parameters in real-time simulations and provides a microscopic interpretation of dephasing as a coarse-graining effect of unitary evolution in a disordered environment.

What carries the argument

The key machinery is the time-domain Williams-Lax framework: ionic positions are frozen in a supercell with displacements sampled from harmonic phonon modes (including zero-point motion), and the time-dependent Kohn-Sham equation is solved for that single configuration. To interpret the dephasing, the authors introduce a time-dependent unfolding procedure that projects supercell wavefunctions onto primitive-cell Bloch states, yielding a primitive-cell density matrix ρ_nn'k(t). This unfolding acts as a spatial average over translational replicas and is what reveals the diagonal population dynamics as the dominant source of the apparent damping.

What would settle it

A concrete falsifier would be to compute the diamond HHG spectrum (or the silicon conductivity) using an explicit ensemble average over many (e.g., 20 or more) independently sampled ionic configurations and compare it to the single-shot result. If the single-shot spectrum is not statistically representative—for instance, if the clean harmonic peaks wash out or the extracted damping time shifts by more than a few femtoseconds under averaging—the single-configuration typicality claim fails. Additionally, running the aluminum conductivity at a 5x5x5 supercell and checking whether the ~10 fs decay

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Extended reading notes

Core claim

The central discovery is that a single frozen ionic displacement pattern, generated from thermal and zero-point phonon amplitudes set to their standard deviations, is sufficient to induce realistic dephasing in real-time TDDFT. In aluminum, supercell calculations with this static disorder produce exponential decay of the time-domain conductivity with a characteristic time of about 10 fs, matching the expected Drude form. In diamond, the same approach suppresses spurious post-pulse current oscillations and yields clean high-harmonic peaks beyond the 20th order without introducing a T2 parameter or propagation effects. A time-dependent unfolding analysis maps the supercell density matrix onto

Load-bearing premise

The load-bearing premise is that a single frozen snapshot of ionic positions, with phonon displacements set to their standard deviations, reproduces the dephasing that a full thermal ensemble or explicit phonon dynamics would produce—an assumption the authors validate only for aluminum's linear conductivity with ten configurations, not for silicon or diamond.

Editorial extensions

If this is right

Real-time TDDFT can predict dephasing times and spectral broadening from first principles, without empirical T2 parameters or configuration averaging.
High-harmonic spectra in dielectrics can be computed reliably using supercell rt-TDDFT with thermal disorder, potentially eliminating the need for macroscopic propagation effects to explain spectral cleanliness.
The primitive-cell density-matrix picture suggests that phenomenological dephasing models should include population relaxation effects, not just off-diagonal coherence decay.
The single-shot result implies that statistical typicality may hold: one representative disordered configuration can stand in for a full thermal ensemble in ultrafast electron dynamics.
The same framework should apply to other response functions, such as phonon-assisted absorption and nonlinear photocurrents, where electron-phonon coupling is relevant.

Reading between the lines

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

An explicit test of the single-shot equivalence would be to average the diamond HHG spectrum over many independently sampled ionic configurations and compare with the single-shot result; the paper only validates this robustness for aluminum linear response, not for nonlinear or dielectric cases.
The reported ~10 fs relaxation time for aluminum is likely supercell-size dependent because the authors do not provide an infinite-size extrapolation; a 5x5x5 or larger supercell calculation would indicate whether the damping time converges or keeps shifting with cell size.
The dominance of diagonal population dynamics suggests that a quantum master equation formulated in the primitive-cell basis might reproduce the same dephasing with a local-in-time dissipator, but this connection is not made in the paper and remains an inference.
The framework could be extended to finite-temperature ionic dynamics or quantum nuclear effects to test whether static disorder remains sufficient at longer time scales (beyond a few tens of femtoseconds) where phonon dynamics may contribute.

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Editorial analysis

A structured set of objections, weighed in public.

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

Desk Editor's Note

read the letter

Worth a careful read. The genuinely new piece is the time-dependent unfolding analysis: mapping the supercell wavefunction onto a primitive-cell density matrix and decomposing the current into diagonal and off-diagonal contributions. The claim that Drude-like damping in Al comes mostly from diagonal population dynamics, not off-diagonal coherence, is a real diagnostic advance and it is not in the cited prior work. The broader package—single-shot static disorder, Williams–Lax, no empirical T2—is a believable and useful explanation for why rt-TDDFT supercells show dephasing, and the Al size trend in Fig. 1 is suggestive in the right direction.

The soft spots are real and concentrated where the stress-test says they are. The 10 fs timescale is read off from three supercell sizes with no fit range, no uncertainty, and no L→∞ extrapolation. Since the supercell Hamiltonian is time-independent and finite, the current is a quasiperiodic sum over discrete eigenfrequencies, and an apparent exponential decay on a 50 fs window can be a level-spacing or beating artifact. The monotonic decrease of the long-time asymptotic value with supercell size argues that the damping is physical, but it does not quantify convergence. Si and diamond get no configuration statistics and no size convergence at all; the diamond HHG is a single 4×4×4 run. The 10-configuration test in Fig. S1 only shows shot-to-shot reproducibility for Al, not thermodynamic-limit behavior.

Two further caveats, both minor. The diagonal/off-diagonal decomposition is basis-dependent: it uses the conventional cubic primitive cell as the unfolding reference, and a different unfolding choice could shift weight between the two terms. So "populations dominate" should be read as a useful diagnostic in a chosen basis, not a basis-invariant microscopic fact. And the title overreaches a bit: the paper isolates static disorder and explicitly says phonon dynamics may add more at long times, but the title promises the microscopic origin of dephasing in solids. The HHG spectral cleaning itself was already reported in Ref. [22]; what is new here is the Williams–Lax attribution and the connection to the linear-response dephasing.

The authors are honest about the unitary, single-configuration nature of the calculation, and the conclusions do not oversell beyond what the numerics show internally. The missing piece is a controlled thermodynamic-limit test, which would make the quantitative timescale solid. As it stands, I read the paper as a strong qualitative mechanism plus a promising diagnostic, with the exact tau still open.

I would send this to peer review. The diagnostic and the framework deserve referee time, and the convergence question is exactly what a good referee should push on. I would not cite the 10 fs number as a material property, but I would cite the unfolding method for dephasing analysis.

Referee Report

4 major / 5 minor

Summary. The manuscript proposes that static lattice disorder, represented by frozen thermal and zero-point ionic displacements in a finite supercell, is sufficient to produce effective electronic dephasing in real-time TDDFT without an empirical T2. In the linear response of Al, supercell calculations show an apparent exponential decay of the time-domain conductivity σ(t) with τ ∼ 10 fs, whereas the primitive cell does not; similar damping is reported for Si. In the nonlinear regime, a 4×4×4 diamond supercell gives clean high-harmonic spectra, while the primitive cell shows irregular post-pulse oscillations. The authors introduce a time-dependent unfolding of supercell Bloch states onto primitive-cell Bloch states, and decompose the induced current into diagonal and off-diagonal contributions (Eqs. 6–10). They conclude that the dominant contribution to Drude-like damping is the diagonal/population part of the unfolded density matrix, not decay of off-diagonal coherence, and that dephasing emerges from phase mixing in a single disordered configuration rather than from ensemble averaging.

Significance. The paper addresses an important open problem—how to include dephasing in rt-TDDFT—and does so with a physically motivated, parameter-free prescription: ionic displacements are fixed by phonon amplitudes and temperature, and no relaxation time is fitted. The time-dependent unfolding diagnostic is a genuine conceptual contribution that could be useful beyond this work. If the finite-size and single-shot issues are resolved, the claim that static disorder alone gives Drude damping and HHG spectral cleaning would be a significant step. The current evidence is suggestive but not yet conclusive because the central mechanism is demonstrated on finite supercells without a thermodynamic-limit analysis.

major comments (4)

[Fig. 1 and Eq. (3)] The central result is the apparent Drude-like decay in Al, but the finite-size evidence is incomplete. Only 2×2×2, 3×3×3, and 4×4×4 supercells are shown; the fit giving 'τ ∼ 10 fs' is not described (fitting window, functional form, uncertainty), and no τ(L) values or L→∞ extrapolation are reported. The long-time value of σ(t) decreases with L, so the decay on the 50 fs window may still be a finite-size/level-spacing artifact. Please provide τ(L), fit details, and a larger-size or extrapolated result; this is essential to support the claim that a single static configuration represents the thermodynamic limit.
[Fig. S2 (Si)] The Si result is offered as corroboration, but it shows only 10 fs of dynamics and no configuration statistics. The statement that σ(t) damps on a 'similar timescale' is not supported by a fit, and the 4×4×4 curve is not shown to be converged. Without these, the silicon case does not independently strengthen the central mechanism.
[Fig. 3 (bottom) / §3] For the HHG claim, only a primitive cell and one 4×4×4 supercell are compared. Since the supercell Hamiltonian is finite and time-independent, the suppression of spurious high-frequency oscillations could be a consequence of the discrete spectrum rather than electron-phonon dephasing in the infinite system. Please show HHG spectra for at least two supercell sizes (and ideally a second independent configuration) to demonstrate that harmonic peak widths and relative intensities are converged with L.
[after Eq. (1); SM 'Computational Details'] The paper uses the special-displacement prescription of Ref. [15] with 'phonon amplitudes set equal to their standard deviations.' This is not a generic thermal ensemble; it fixes the amplitude and randomizes only phases. The authors validate it for Al linear response with ten configurations (Fig. S1), but no equivalent test is provided for Si or diamond, and no comparison with an explicit ensemble average over the amplitude distribution is made. Because the dephasing rate could be sensitive to the displacement statistics, this validation is load-bearing for the single-shot claim.

minor comments (5)

[Fig. 1] The legend uses '1x1x1' for the primitive cell; please relabel as 'primitive (1×1×1)' to avoid confusion with a genuine supercell.
[Eq. (7)] Define F_MK explicitly (initial occupations of supercell orbitals) and state how occupations are treated during time propagation, since in the velocity gauge the time-dependent KS orbitals carry the dynamics.
[Eq. (9)] Give the explicit expression for J_diamag, or state that it is the A(t)-dependent term; currently it is only described verbally.
[Si discussion / Fig. S2] The 'similar timescale' claim should be supported by a fit or a quantitative criterion; otherwise the wording is ambiguous.
[Figures] Conductivity is reported in atomic units without a conversion factor; adding one (e.g., 1 a.u. of conductivity) would improve readability for a broader audience.

Circularity Check

0 steps flagged · score 0.0 of 10

No circularity: dephasing is an emergent simulation output, not a fitted input or renamed known result.

full rationale

The paper's central claim is that static lattice disorder, inserted as thermally and zero-point displaced ionic positions, generates effective dephasing in real-time TDDFT without an empirical T2. The inputs to the calculation are physical choices (lattice temperature, supercell size, ionic displacement amplitudes taken from a prior external prescription, Ref. [15]) and the outputs (conductivity decay, density-matrix diagonal/off-diagonal decomposition, HHG spectra) are computed, not fitted. No equation reduces to a fitted parameter: the reported tau ~ 10 fs is extracted from the simulated decay rather than imposed. The unfolding projection (Eqs. 6-10) is an exact change of representation, and the dominance of the diagonal contribution is a numerical finding. The only self-citations are to the SALMON code (Ref. [17]) and to a prior observation that thermal disorder suppresses current oscillations (Ref. [22]); neither is load-bearing, because the present calculations independently demonstrate the effect. The finite-size and single-shot-convergence caveats identified by the reader are correctness/validation concerns, not circularity: the paper does not assume the dephasing time it reports. Therefore no circular step is present.

Assumptions & free parameters 2 free parameters · 4 assumptions · 1 invented entities

The central mechanism rests on familiar DFT ingredients plus two hand-chosen modeling inputs: the RMS-displacement single-configuration prescription and finite 4x4x4 supercells. The unfolding basis choice is an additional modeling decision that shapes the headline population-vs-coherence conclusion.

free parameters (2)

Phonon displacement amplitude prescription = standard deviations of harmonic modes (300 K plus zero-point)
Chosen by hand following Ref. [15]; all main results use this single displacement magnitude rather than sampling a full distribution. It affects the damping rate and the clean-spectrum claim.
Supercell size for main simulations = 4x4x4 (Al 256 atoms; Si/diamond 512 atoms)
Damping strength and long-time conductivity depend on supercell size in Fig. 1; 4x4x4 is the largest size computed, but no infinite-size extrapolation is provided, so the reported tau about 10 fs is finite-size dependent.

assumptions (4)

domain assumption ALDA plus norm-conserving pseudopotentials accurately describe electron dynamics in Al, Si, and diamond at the needed accuracy.
Invoked in SM 'Computational Details'; all quantitative claims depend on this approximate exchange-correlation and pseudopotential choice.
domain assumption Ionic positions are frozen during the electron dynamics because phonon periods are long compared with the femtosecond-scale electron dynamics.
Stated after Eq. (1): 'Since typical phonon periods are on the order of several tens of femtoseconds, the ionic positions can be treated as frozen during the electron dynamics on the timescale of interest.' If this fails, the dephasing mechanism changes.
domain assumption A single disordered configuration (single-shot Williams-Lax) is representative of the thermal ensemble for time-domain dephasing.
Motivated by Ref. [15] and asserted again in the Conclusions ('statistical typicality'); the paper validates it only for Al linear response with 10 configurations (Fig. S1).
ad hoc to paper The unfolded primitive-cell density matrix defined by Eqs. (6)-(8) is the relevant coarse-graining for comparing with phenomenological T2 descriptions.
This is the paper's own projection construction; the diagonal/off-diagonal decomposition and the central 'population dynamics' conclusion depend on this choice of basis and spatial averaging.

invented entities (1)

None
purpose: No new particles, fields, forces, or conserved quantities are introduced.
The unfolded primitive-cell density matrix is a projection/coarse-graining of the supercell state, not a new causal entity.

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Cite this review

Pith. "Pith review of Microscopic Origin of Dephasing in Solids from First-Principles Electron-Phonon Interactions." pith.science (2026). https://pith.science/paper/SRTF4XF7

@misc{pith2026260717109,
  author       = {Pith},
  title        = {Pith review of: Microscopic Origin of Dephasing in Solids from First-Principles Electron-Phonon Interactions},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/SRTF4XF7}},
  note         = {Machine review of arXiv:2607.17109}
}

read the original abstract

Electron-phonon interactions provide a microscopic origin of effective dephasing in solids within real -time TDDFT via a time-domain Williams-Lax framework. In metals, Drude -like damping emerges from a single disordered configuration; in dielectrics, the same mechanism yields clean high-harmonic spectra without introducing ultrashort phenomenological dephasing times. Mapping supercell dynamics onto a primitive-cell density matrix reveals that dephasing is governed primarily by population dynamics (diagonal elements) rather than by the decay of off-diagonal coherence.

Figures

Figures reproduced from arXiv: 2607.17109 by the authors.

**Figure 1.** shows the conductivity of aluminum computed using rt-TDDFT within the adiabatic local density approximation. All rt-TDDFT calculations are performed using the SALMON code [17]. Cubic supercells are utilised and numerical parameters adopted in the calculation are summarized in the supplemental material. The initial value σ(0) is determined by the instantaneous response of the electronic system (e.g., electron den… view at source ↗

**Figure 2.** FIG. 2. Decomposition of the conductivity into diagonal [PITH_FULL_IMAGE:figures/full_fig_p003_2.png] view at source ↗

**Figure 3.** FIG. 3. (Top) applied field and induced current for primitive [PITH_FULL_IMAGE:figures/full_fig_p004_3.png] view at source ↗

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Reference graph

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Pith tools

Reviewed August 1, 2026 · model on record in the stance chip above.

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