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arxiv: 2511.21539 · v3 · submitted 2025-11-26 · ❄️ cond-mat.str-el

Charge carrier relaxation dynamics in the one-dimensional Kondo lattice model

Arturo Perez-Romero , Mica Schwarm , Fabian Heidrich-Meisner This is my paper

Pith reviewed 2026-05-17 04:40 UTC · model grok-4.3

classification ❄️ cond-mat.str-el
keywords Kondo lattice modelrelaxation dynamicsthermalizationone-dimensional systemscharge carriersspin excitationsultrafast dynamicsLanczos method
0
0 comments X p. Extension

The pith

Charge carriers in the one-dimensional Kondo lattice reach a stationary state compatible with thermalization when filling is finite or the background spins form singlets.

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

The paper investigates the relaxation of optically excited charge carriers through coupling to magnetic excitations in the Kondo lattice model in one dimension. It contrasts the known absence of thermalization for one or two carriers in a ferromagnetic background with broader cases where the long-time state aligns with thermal expectations. Real-time simulations track spin polarization, local spin-spin correlations, and momentum distributions to show this compatibility. Direct comparison to finite-temperature values and spectral gap-ratio analysis supports the conclusion that thermalization occurs under these conditions.

Core claim

While in the well-studied cases of one or two charge carriers in a ferromagnetic background, no thermalization occurs, we demonstrate that the stationary state is compatible with thermalization if either the electronic filling is finite or the magnetic background is in the singlet sector.

What carries the argument

Time-dependent Lanczos evolution of the one-dimensional Kondo lattice Hamiltonian, with observables including conduction-electron spin polarization, localized-conduction spin-spin correlations, and electronic momentum distribution.

If this is right

  • At finite electron filling the relaxation channel to magnetic excitations produces a thermal stationary state.
  • Singlet magnetic backgrounds allow the same thermal outcome even at low carrier density.
  • The electronic momentum distribution in the stationary state matches the thermal distribution.
  • Level statistics via the gap ratio confirm the approach to a thermal ensemble.

Where Pith is reading between the lines

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

  • Similar relaxation-to-thermalization behavior may appear in other one-dimensional spin-charge coupled models when carrier density is not dilute.
  • The same observables could be tracked in higher-dimensional Kondo lattices to test whether the singlet versus ferromagnetic distinction persists.
  • Ultrafast optical experiments on real Kondo materials could check whether the observed momentum distributions match the predicted thermal form outside the dilute ferromagnetic limit.

Load-bearing premise

Finite-size chains and the Lanczos truncation in the simulations represent the thermodynamic-limit long-time stationary state without boundary or truncation effects that would change the apparent thermalization behavior.

What would settle it

A long-time momentum distribution or set of spin correlations that deviates from the corresponding finite-temperature thermal ensemble at the same energy density would show the stationary state is not thermal.

Figures

Figures reproduced from arXiv: 2511.21539 by Arturo Perez-Romero, Fabian Heidrich-Meisner, Mica Schwarm.

Figure 1
Figure 1. Figure 1: FIG. 1. (a) Sketch of the initial condition, Eq. (2), where [PITH_FULL_IMAGE:figures/full_fig_p003_1.png] view at source ↗
Figure 2
Figure 2. Figure 2: FIG. 2. Time evolution of several expectation values for various values of [PITH_FULL_IMAGE:figures/full_fig_p006_2.png] view at source ↗
Figure 4
Figure 4. Figure 4: FIG. 4. Sketch of the effective two-level system for the initial [PITH_FULL_IMAGE:figures/full_fig_p007_4.png] view at source ↗
Figure 3
Figure 3. Figure 3: FIG. 3. (a), (b): Logarithm of the electronic quasi [PITH_FULL_IMAGE:figures/full_fig_p007_3.png] view at source ↗
Figure 6
Figure 6. Figure 6: FIG. 6. Time dependence of the conduction electron’s spin [PITH_FULL_IMAGE:figures/full_fig_p008_6.png] view at source ↗
Figure 8
Figure 8. Figure 8: FIG. 8. Time-average [PITH_FULL_IMAGE:figures/full_fig_p009_8.png] view at source ↗
Figure 9
Figure 9. Figure 9: FIG. 9. Relaxation dynamics of the two-electron Kondo [PITH_FULL_IMAGE:figures/full_fig_p010_9.png] view at source ↗
Figure 11
Figure 11. Figure 11: FIG. 11. Time evolution of the conduction-electron spin po [PITH_FULL_IMAGE:figures/full_fig_p011_11.png] view at source ↗
Figure 12
Figure 12. Figure 12: FIG. 12. Average gap ratio [PITH_FULL_IMAGE:figures/full_fig_p011_12.png] view at source ↗
Figure 13
Figure 13. Figure 13: FIG. 13. Relaxation dynamics in the Kondo-Heisenberg [PITH_FULL_IMAGE:figures/full_fig_p012_13.png] view at source ↗
Figure 14
Figure 14. Figure 14: shows the spectral weight distribution of the initial state. For a strong Kondo coupling, the initial state has an equal contribution from the ground state and excited states. For arbitrary values of J/t0, since the local spin-spin correlation in the ground state stems from the singlet contribution (as shown in the inset of [PITH_FULL_IMAGE:figures/full_fig_p013_14.png] view at source ↗
read the original abstract

A generic question in the field of ultrafast dynamics is concerned with the relaxation dynamics and the subsequent thermalization of optically excited charge carriers. Among several possible relaxation channels available in a solid-state system, we focus on the coupling to magnetic excitations. In this paper, we study the real-time dynamics of a paradigmatic model, the Kondo lattice model in one dimension. We conduct a comprehensive study of the relaxation processes by evaluating the spin polarization of the conduction electron, the local spin-spin correlation between localized and conduction electrons, and the electronic momentum distribution. While in the well-studied cases of one or two charge carriers in a ferromagnetic background, no thermalization occurs, we demonstrate that the stationary state is compatible with thermalization if either the electronic filling is finite or the magnetic background is in the singlet sector. Our real-time simulations using the time-dependent Lanczos method are corroborated by a direct comparison with finite-temperature expectation values and an analysis of the spectrum in terms of the gap ratio.

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 investigates the real-time relaxation dynamics of charge carriers in the one-dimensional Kondo lattice model via time-dependent Lanczos simulations. It claims that, in contrast to the well-studied non-thermalizing cases of one or two carriers in a ferromagnetic background, the long-time stationary state becomes compatible with thermalization when the electronic filling is finite or the localized spins are in the singlet sector. This is supported by direct comparison of observables (spin polarization, local spin-spin correlations, momentum distribution) to finite-temperature thermal averages and by gap-ratio analysis of the many-body spectrum.

Significance. If the central numerical observations prove robust, the work clarifies the conditions under which coupling to magnetic excitations drives thermalization in Kondo systems, extending beyond the known non-thermalizing limits. The use of direct time evolution cross-checked against independent finite-temperature calculations and spectral statistics constitutes a methodological strength that strengthens the evidence for the filling- and sector-dependent claim.

major comments (3)
  1. [Methods] Methods section (time-dependent Lanczos implementation): the manuscript does not report the chain lengths N employed, the Krylov-subspace dimension, or any convergence tests with respect to subspace size. These omissions are load-bearing because the central claim of compatibility with thermalization rests on the long-time stationary values; without this information it is impossible to assess whether the observed relaxation is free of truncation artifacts or finite-size revivals.
  2. [Results] Results section (comparison to finite-T averages): the agreement between time-evolved observables and thermal expectation values is stated qualitatively but without quantitative error metrics, relative deviations, or uncertainty estimates on the stationary plateaus. This weakens the ability to judge how close the match actually is, particularly for the finite-filling and singlet-sector cases that underpin the main conclusion.
  3. [Spectral Analysis] Spectral analysis (gap-ratio discussion): while the gap ratio is used to infer chaotic level statistics, the text does not address whether this guarantees dynamical convergence on the simulated time scales or rules out slow revivals that could appear only at longer times or larger N. This is relevant because the skeptic concern about artifactual thermalization hinges on whether the finite-system dynamics faithfully represent the thermodynamic limit.
minor comments (2)
  1. [Abstract] Abstract: add a brief statement of typical system sizes and Lanczos subspace dimensions used; this is standard for numerical dynamics papers and would immediately address the reader's noted lack of information.
  2. [Figures] Figure captions: ensure all panels indicate the time window over which the stationary value is averaged and whether any smoothing or fitting was applied.

Simulated Author's Rebuttal

3 responses · 0 unresolved

We thank the referee for the positive assessment of our work and for the constructive comments that will help improve the manuscript. We address each major comment below and will make the corresponding revisions.

read point-by-point responses

  1. Referee: [Methods] Methods section (time-dependent Lanczos implementation): the manuscript does not report the chain lengths N employed, the Krylov-subspace dimension, or any convergence tests with respect to subspace size. These omissions are load-bearing because the central claim of compatibility with thermalization rests on the long-time stationary values; without this information it is impossible to assess whether the observed relaxation is free of truncation artifacts or finite-size revivals.

    Authors: We agree that these technical details are necessary for assessing the reliability of the results. In the revised manuscript we will explicitly report the chain lengths N employed in the simulations, the Krylov-subspace dimension used in the time-dependent Lanczos procedure, and the results of convergence tests with respect to subspace size. These tests confirm that the long-time stationary plateaus remain stable and are not affected by truncation artifacts on the time scales considered. revision: yes

  2. Referee: [Results] Results section (comparison to finite-T averages): the agreement between time-evolved observables and thermal expectation values is stated qualitatively but without quantitative error metrics, relative deviations, or uncertainty estimates on the stationary plateaus. This weakens the ability to judge how close the match actually is, particularly for the finite-filling and singlet-sector cases that underpin the main conclusion.

    Authors: We acknowledge that quantitative measures would strengthen the presentation. In the revised manuscript we will include relative deviation metrics and uncertainty estimates for the stationary values of the spin polarization, local spin-spin correlations, and momentum distribution compared with the finite-temperature thermal averages. This will be done for both the finite-filling and singlet-sector cases to allow a more precise judgment of the agreement. revision: yes

  3. Referee: [Spectral Analysis] Spectral analysis (gap-ratio discussion): while the gap ratio is used to infer chaotic level statistics, the text does not address whether this guarantees dynamical convergence on the simulated time scales or rules out slow revivals that could appear only at longer times or larger N. This is relevant because the skeptic concern about artifactual thermalization hinges on whether the finite-system dynamics faithfully represent the thermodynamic limit.

    Authors: We agree that the gap-ratio analysis alone does not guarantee the absence of slow revivals at longer times or in the thermodynamic limit. In the revised manuscript we will add an explicit discussion of this limitation, clarifying that the gap-ratio result is used only as supporting evidence for chaotic dynamics. We will emphasize that our main conclusions rest on the direct comparison of time-evolved observables with thermal averages together with the lack of revivals within the simulated window, and we will comment on the expected behavior for larger systems. revision: yes

Circularity Check

0 steps flagged

No circularity: direct numerical comparison to independent thermal benchmarks

full rationale

The paper's central result—that the long-time stationary state after charge-carrier relaxation is compatible with thermalization when electronic filling is finite or the magnetic background is in the singlet sector—is obtained by explicit time-dependent Lanczos evolution on finite chains, followed by direct comparison of observables (spin polarization, local spin-spin correlations, momentum distribution) to separately computed finite-temperature expectation values and by gap-ratio diagnostics of the spectrum. No parameter is fitted to a subset of data and then relabeled as a prediction, no self-citation supplies a load-bearing uniqueness theorem, and no ansatz or definition is smuggled in via prior work by the same authors. The derivation chain therefore remains self-contained against external numerical benchmarks rather than reducing to its own inputs by construction.

Axiom & Free-Parameter Ledger

1 free parameters · 2 axioms · 0 invented entities

The central claim rests on standard quantum mechanics and the definition of the Kondo lattice Hamiltonian. No new entities are postulated. The only potential free parameters are the model couplings (Kondo exchange J and hopping t) and the specific fillings and initial states chosen for simulation; these are standard inputs rather than fitted quantities invented for this work.

free parameters (1)
  • Kondo coupling J and hopping t
    Standard parameters of the Kondo lattice model; their ratio sets the energy scale but is not fitted to the relaxation data in the abstract.
axioms (2)
  • standard math The time-dependent Schrödinger equation governs the unitary evolution of the many-body wavefunction.
    Invoked implicitly by the use of the time-dependent Lanczos method.
  • standard math Finite-temperature expectation values can be computed by tracing over the canonical ensemble.
    Used for direct comparison to the long-time stationary state.

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    We conduct a comprehensive study of the relaxation processes by evaluating the spin polarization of the conduction electron, the local spin-spin correlation... Our real-time simulations using the time-dependent Lanczos method are corroborated by a direct comparison with finite-temperature expectation values and an analysis of the spectrum in terms of the gap ratio.

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Reference graph

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