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arxiv: 2511.02618 · v2 · submitted 2025-11-04 · ❄️ cond-mat.stat-mech · cond-mat.quant-gas· quant-ph

Post-quench relaxation dynamics of Gross-Neveu lattice fermions

Domenico Giuliano , Reinhold Egger , Bidyut Dey , Andrea Nava This is my paper

Pith reviewed 2026-05-18 01:04 UTC · model grok-4.3

classification ❄️ cond-mat.stat-mech cond-mat.quant-gasquant-ph
keywords Gross-Neveu modelpost-quench dynamicseigenstate thermalization hypothesisgeneralized Gibbs ensembleLindblad master equationlattice fermionsrelaxation dynamicsopen quantum systems
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The pith

In the thermodynamic limit the order parameter of the quenched Gross-Neveu lattice model reaches its post-quench value according to the eigenstate thermalization hypothesis.

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

The paper examines the relaxation of lattice fermions in the one-dimensional Gross-Neveu model after an interaction-parameter quench. A time-dependent self-consistent Lindblad master equation incorporates possible coupling to a reservoir. In closed finite systems the order parameter oscillates and revives, yet settles to a steady value in the large-system limit consistent with eigenstate thermalization. Finite-momentum correlations relax only when reservoir coupling is present. The results line up with relaxation to a generalized Gibbs ensemble instead of full thermal equilibrium.

Core claim

For a closed finite-size system the order parameter dynamics exhibits oscillations and revivals after an interaction parameter quench. In the thermodynamic limit the order parameter reaches its post-quench stationary value in accordance with the eigenstate thermalization hypothesis. Time-dependent finite-momentum correlation matrix elements equilibrate only if the system-reservoir coupling is nonzero. The findings are consistent with a pertinent Generalized Gibbs Ensemble.

What carries the argument

The time-dependent self-consistent Lindblad master equation that incorporates the system-reservoir coupling γ to describe the open-system dynamics of the lattice fermions.

If this is right

  • The order parameter equilibrates in the thermodynamic limit even for a closed system.
  • Finite-momentum correlations require nonzero reservoir coupling to reach equilibrium.
  • The post-quench state is captured by a generalized Gibbs ensemble.
  • Oscillations and revivals appear only in finite closed systems and vanish in the thermodynamic limit.

Where Pith is reading between the lines

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

  • Integrable models may routinely relax to a GGE rather than a fully thermal state after quenches.
  • Analogous behavior could appear in other lattice field theories subjected to interaction quenches.
  • Cold-atom experiments could directly test whether reservoir coupling is required for correlation equilibration.

Load-bearing premise

The time-dependent self-consistent Lindblad master equation accurately captures the open-system dynamics of the lattice fermions without introducing artifacts that alter the observed relaxation and equilibration behavior.

What would settle it

Numerical simulation or experiment on a closed system in the thermodynamic limit that checks whether finite-momentum correlations equilibrate in the absence of any reservoir coupling.

Figures

Figures reproduced from arXiv: 2511.02618 by Andrea Nava, Bidyut Dey, Domenico Giuliano, Reinhold Egger.

Figure 1
Figure 1. Figure 1: FIG. 1. Equilibrium phase diagram of the lattice GN model [PITH_FULL_IMAGE:figures/full_fig_p003_1.png] view at source ↗
Figure 2
Figure 2. Figure 2: FIG. 2. Post-quench order parameters [PITH_FULL_IMAGE:figures/full_fig_p005_2.png] view at source ↗
Figure 3
Figure 3. Figure 3: FIG. 3. Post-quench order parameters [PITH_FULL_IMAGE:figures/full_fig_p006_3.png] view at source ↗
Figure 4
Figure 4. Figure 4: FIG. 4. Post-quench dynamics of [PITH_FULL_IMAGE:figures/full_fig_p006_4.png] view at source ↗
Figure 6
Figure 6. Figure 6: FIG. 6. Post-quench dynamics of [PITH_FULL_IMAGE:figures/full_fig_p007_6.png] view at source ↗
Figure 8
Figure 8. Figure 8: (b) for the corresponding case with kBT = 0.05. These results were obtained from Eqs. (17) and (18). We observe unattenuated oscillations of the real and imaginary parts of this matrix element persisting for arbi￾trarily long times. A comprehensive understanding of the full nonequilibrium time evolution of the closed system therefore cannot rely on a few global observables like m(t) and/or δJ(t). The relax… view at source ↗
Figure 10
Figure 10. Figure 10: FIG. 10. Post-quench dynamics of the (a) real part and (b) [PITH_FULL_IMAGE:figures/full_fig_p009_10.png] view at source ↗
read the original abstract

We study the quantum relaxation dynamics for a lattice version of the one-dimensional (1D) $N$-flavor Gross-Neveu (GN) model after a Hamiltonian parameter quench. Allowing for a system-reservoir coupling $\gamma$, we numerically describe the system dynamics through a time-dependent self-consistent Lindblad master equation. For a closed ($\gamma=0$) finite-size system subjected to an interaction parameter quench, the order parameter dynamics exhibits oscillations and revivals. In the thermodynamic limit, our results imply that the order parameter reaches its post-quench stationary value in accordance with the eigenstate thermalization hypothesis (ETH). However, time-dependent finite-momentum correlation matrix elements equilibrate only if $\gamma>0$. Our findings are consistent with the system being described by a pertinent Generalized Gibbs Ensemble (GGE) and, accordingly, highlight subtle yet important aspects of the post-quench relaxation dynamics of quantum many-body 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

2 major / 2 minor

Summary. The manuscript examines the relaxation dynamics following a parameter quench in a lattice Gross-Neveu model of interacting fermions. Using a time-dependent self-consistent Lindblad master equation with tunable dissipation strength γ, the authors numerically simulate the evolution of the order parameter and correlation functions. They report oscillations and revivals in finite systems for γ=0, infer ETH-compliant equilibration of the order parameter in the thermodynamic limit, and find that finite-momentum correlations equilibrate only in the presence of dissipation (γ>0), consistent with a Generalized Gibbs Ensemble description.

Significance. If the numerical method is free of artifacts, the work provides useful insights into the role of dissipation in distinguishing full thermalization (via ETH) from GGE-like prethermalization in interacting 1D fermionic models. The reported γ dependence and revival behavior could inform broader studies of open quantum many-body systems and the applicability of ETH to order parameters versus correlation functions.

major comments (2)
  1. The time-dependent self-consistent Lindblad master equation is the sole tool used to generate all dynamical results. For γ=0 this equation must reduce exactly to unitary Schrödinger evolution, yet the self-consistent closure (mean-field factorization of the GN interaction) is not shown to preserve this property without introducing damping or premature stationarity. This directly affects the validity of the ETH claim for the order parameter in the closed-system thermodynamic limit and the GGE interpretation for correlations.
  2. The thermodynamic-limit statement that the order parameter reaches its post-quench stationary value in accordance with ETH rests on finite-size numerics and standard scaling assumptions. The manuscript does not present a systematic finite-size scaling analysis (e.g., revival amplitude versus system size or explicit extrapolation of the long-time value) that would confirm the absence of persistent oscillations in the infinite-volume limit.
minor comments (2)
  1. Abstract: the phrasing 'our results imply' for the thermodynamic-limit ETH statement should be softened to 'suggest' or 'are consistent with' to reflect the numerical and approximate nature of the evidence.
  2. Notation: the definition of the self-consistent closure and the precise form of the Lindblad operators should be stated with an explicit equation number so that readers can verify the γ=0 reduction.

Simulated Author's Rebuttal

2 responses · 0 unresolved

We thank the referee for the careful reading of our manuscript and the constructive comments. We address each major comment point by point below, indicating the revisions we will implement.

read point-by-point responses

  1. Referee: The time-dependent self-consistent Lindblad master equation is the sole tool used to generate all dynamical results. For γ=0 this equation must reduce exactly to unitary Schrödinger evolution, yet the self-consistent closure (mean-field factorization of the GN interaction) is not shown to preserve this property without introducing damping or premature stationarity. This directly affects the validity of the ETH claim for the order parameter in the closed-system thermodynamic limit and the GGE interpretation for correlations.

    Authors: We agree that the self-consistent closure is a mean-field factorization and does not correspond to the exact many-body unitary Schrödinger evolution. For γ=0 the equations reduce to the closed time-dependent Hartree-Fock dynamics of the one-body density matrix. Within this approximation the evolution is trace-preserving and does not introduce extraneous damping or artificial stationarity; any apparent relaxation in the thermodynamic limit arises from dephasing of an increasing number of modes. We will add an explicit derivation of the γ=0 reduction together with numerical checks of energy and norm conservation, and we will qualify the ETH and GGE statements as holding within the mean-field description. These clarifications will be placed in the Methods section and the discussion of the closed-system results. revision: yes

  2. Referee: The thermodynamic-limit statement that the order parameter reaches its post-quench stationary value in accordance with ETH rests on finite-size numerics and standard scaling assumptions. The manuscript does not present a systematic finite-size scaling analysis (e.g., revival amplitude versus system size or explicit extrapolation of the long-time value) that would confirm the absence of persistent oscillations in the infinite-volume limit.

    Authors: We concur that a systematic finite-size scaling analysis would strengthen the thermodynamic-limit claim. In the revised manuscript we will include additional data showing the revival amplitude versus system size L together with an explicit extrapolation of the long-time order-parameter value to L→∞. These results will be presented in a new figure and accompanying text demonstrating that persistent oscillations vanish in the infinite-volume limit, consistent with ETH expectations within our approach. revision: yes

Circularity Check

0 steps flagged

No circularity: claims follow from numerical integration of the master equation

full rationale

The paper obtains its results on order-parameter relaxation, ETH compliance in the thermodynamic limit, and GGE consistency by direct numerical integration of the time-dependent self-consistent Lindblad master equation after a parameter quench. No step fits a parameter to a target observable and then presents a closely related quantity as an independent prediction; the self-consistent closure is an explicit dynamical approximation whose output is computed rather than assumed. The distinction between γ=0 (oscillations/revivals) and γ>0 (equilibration of finite-momentum correlations) emerges from the integration itself and is not forced by definition or by a self-citation chain. The central claims therefore remain independent of the inputs.

Axiom & Free-Parameter Ledger

1 free parameters · 1 axioms · 0 invented entities

The central claims rest on the validity of the Lindblad approximation and on the assumption that finite-size data extrapolate cleanly to the thermodynamic limit; no new particles or forces are postulated.

free parameters (1)
  • γ
    System-reservoir coupling strength introduced to control dissipation; varied parametrically in the simulations.
axioms (1)
  • domain assumption The self-consistent Lindblad master equation provides a faithful description of the open quantum dynamics for the chosen parameter regime.
    Invoked to numerically evolve the system after the quench.

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Forward citations

Cited by 1 Pith paper

Reviewed papers in the Pith corpus that reference this work. Sorted by Pith novelty score.

  1. Dissipation Mechanisms and Dissipative Phase Transitions of two coupled Fully Connected Quantum Ising models

    cond-mat.stat-mech 2026-04 unverdicted novelty 5.0

    Different classes of dissipators in coupled quantum Ising models produce either equilibrium-like relaxation with protocol-dependent dynamics or nonequilibrium steady states featuring reentrant symmetry breaking.

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