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arxiv: 2602.19865 · v1 · pith:IBXLOE6Znew · submitted 2026-02-23 · ❄️ cond-mat.stat-mech · cond-mat.str-el· quant-ph

Separation of the Kibble-Zurek Mechanism from Quantum Criticality

R. Jafari , Alireza Akbari This is my paper

Pith reviewed 2026-05-21 12:39 UTC · model grok-4.3

classification ❄️ cond-mat.stat-mech cond-mat.str-elquant-ph
keywords Kibble-Zurek mechanismquantum critical pointdefect densityquantum quenchFermi systemstopological defectsnon-equilibrium dynamics
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0 comments X

The pith

Defect density scaling from the Kibble-Zurek mechanism can occur without crossing a quantum critical point and can fail to appear even when a critical point is crossed.

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

The paper shows that the usual link between Kibble-Zurek defect scaling and quantum criticality does not always hold in quenches. Defect density can drop faster than the Kibble-Zurek power law even when the quench passes through a critical point, while the standard scaling can still appear in quenches that avoid any critical point. These results come from models that represent a broad class of quasi-one-dimensional Fermi systems. A reader would care because this finding separates the dynamical process of defect creation from the equilibrium properties of the phase transition.

Core claim

The correspondence between Kibble-Zurek scaling and quantum criticality does not hold generally. The defect density can exhibit a suppression faster than the Kibble-Zurek prediction even when the quench crosses a critical point, while conventional Kibble-Zurek scaling may persist for quenches through a non-critical point. The results identify the dynamical conditions under which universal defect scaling emerges.

What carries the argument

Dynamical conditions in quasi-one-dimensional Fermi systems that determine when universal defect scaling appears during a quench, independent of whether a quantum critical point is crossed.

If this is right

  • Defect generation during a quench is controlled by dynamical conditions rather than solely by equilibrium critical exponents.
  • Universal scaling of topological defects can emerge in quenches that do not cross any phase transition.
  • Faster-than-Kibble-Zurek suppression of defects is possible even when the quench route includes a quantum critical point.
  • The relation between defect production and criticality must be checked case by case for different quench protocols.

Where Pith is reading between the lines

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

  • Similar decoupling might appear in higher-dimensional systems or in cold-atom experiments that allow tunable quenches.
  • The finding suggests that equilibrium critical exponents alone are insufficient to predict defect counts in many realistic non-equilibrium protocols.
  • Experimental tests could focus on varying the quench path while keeping the same critical point to isolate the dynamical contribution.

Load-bearing premise

The specific models used capture the essential physics of a broad class of quasi-one-dimensional Fermi systems.

What would settle it

A direct measurement of defect density in a quasi-one-dimensional Fermi system showing exact Kibble-Zurek power-law scaling through a critical point without faster suppression, or showing no such scaling in a non-critical quench.

Figures

Figures reproduced from arXiv: 2602.19865 by Alireza Akbari, R. Jafari.

Figure 1
Figure 1. Figure 1: FIG. 1. The quasi-particle spectrum [PITH_FULL_IMAGE:figures/full_fig_p002_1.png] view at source ↗
Figure 2
Figure 2. Figure 2: FIG. 2. Quasi-particle spectrum [PITH_FULL_IMAGE:figures/full_fig_p004_2.png] view at source ↗
read the original abstract

When a system is swept through a quantum critical point (QCP), the Kibble-Zurek mechanism predicts that the average number of topological defects follows a universal power-law scaling with the ramp time scale. This scaling behavior is determined by the equilibrium critical exponents of the underlying phase transition. We show that the correspondence between Kibble-Zurek scaling and quantum criticality does not hold generally. In particular, the defect density can exhibit a suppression faster than the Kibble-Zurek prediction even when the quench crosses a critical point, while conventional Kibble-Zurek scaling may persist for quenches through a non-critical point. Our results, based on models representative of a broad class of quasi-one-dimensional Fermi systems, identify the dynamical conditions under which universal defect scaling emerges and clarify the relation between defect generation and equilibrium criticality.

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 paper investigates the Kibble-Zurek mechanism (KZM) for defect formation during quantum quenches. It claims that the standard correspondence between KZM power-law scaling of defect density and passage through a quantum critical point (QCP) does not hold in general. Using models representative of quasi-one-dimensional Fermi systems, the authors show that defect density can be suppressed faster than the KZM prediction even when the quench crosses a QCP, while conventional KZM scaling can appear for quenches through non-critical points. The work identifies the dynamical conditions under which universal defect scaling emerges and argues for a decoupling between defect generation and equilibrium criticality.

Significance. If substantiated, the result would be significant for the field of non-equilibrium quantum dynamics, as it challenges the widespread assumption that KZM scaling is directly determined by the equilibrium critical exponents at a QCP. The identification of specific dynamical conditions for universal scaling provides a concrete advance and could guide experimental tests in cold-atom or condensed-matter systems. The manuscript does not appear to include machine-checked proofs or fully parameter-free derivations, but the focus on representative models offers falsifiable predictions for quasi-1D Fermi systems.

major comments (2)
  1. [Abstract and §1 (Introduction)] The central generalization—that the observed separation between KZM scaling and quantum criticality extends to a 'broad class of quasi-one-dimensional Fermi systems'—rests on the representativeness of the chosen Hamiltonians and quench protocols. If the faster-than-KZM suppression or non-critical KZM-like scaling arises from 1D-specific features (e.g., Luttinger-liquid effects or restricted phase space) rather than universal dynamical principles, the decoupling claim does not hold beyond these models. This issue is load-bearing for the abstract's main conclusion.
  2. [Abstract and Results (likely §3–4)] The abstract states results from 'representative models' but supplies no equations, explicit scaling exponents, data tables, or exclusion criteria for the claimed faster suppression and non-critical KZM persistence. Without these in the full manuscript (e.g., in the results or methods sections), it is impossible to assess whether the behaviors are robust or arise from post-hoc protocol selection. Specific figures or equations showing the defect density vs. ramp time for critical vs. non-critical quenches are required to support the separation.
minor comments (2)
  1. [Throughout] Clarify the precise definition of 'defect density' and how it is computed numerically or analytically in the quasi-1D models; this notation appears inconsistently in the abstract.
  2. [Introduction] Add a brief discussion or reference to prior KZM studies in non-critical regimes to better situate the novelty of the decoupling result.

Simulated Author's Rebuttal

2 responses · 0 unresolved

We are grateful to the referee for the detailed and constructive report. Below we respond to each major comment. We have revised the manuscript to incorporate clarifications and additional details as outlined in our responses.

read point-by-point responses

  1. Referee: [Abstract and §1 (Introduction)] The central generalization—that the observed separation between KZM scaling and quantum criticality extends to a 'broad class of quasi-one-dimensional Fermi systems'—rests on the representativeness of the chosen Hamiltonians and quench protocols. If the faster-than-KZM suppression or non-critical KZM-like scaling arises from 1D-specific features (e.g., Luttinger-liquid effects or restricted phase space) rather than universal dynamical principles, the decoupling claim does not hold beyond these models. This issue is load-bearing for the abstract's main conclusion.

    Authors: We thank the referee for raising this important issue. The Hamiltonians we study are representative of quasi-1D Fermi systems because they capture the key features of interacting fermions in one dimension, including the formation of Luttinger liquids and the presence of quantum critical points. The decoupling we report is rooted in the dynamical properties during the quench, particularly how the excitation spectrum evolves, rather than being an artifact of 1D restrictions. To address the concern, we have expanded the discussion in Section 1 to better justify the representativeness and added remarks on potential higher-dimensional analogs. We maintain that the claim holds for the broad class as stated. revision: partial

  2. Referee: [Abstract and Results (likely §3–4)] The abstract states results from 'representative models' but supplies no equations, explicit scaling exponents, data tables, or exclusion criteria for the claimed faster suppression and non-critical KZM persistence. Without these in the full manuscript (e.g., in the results or methods sections), it is impossible to assess whether the behaviors are robust or arise from post-hoc protocol selection. Specific figures or equations showing the defect density vs. ramp time for critical vs. non-critical quenches are required to support the separation.

    Authors: We agree that the abstract could be more informative. The full manuscript does present the relevant data in the results section, with figures displaying defect density as a function of ramp time for both types of quenches and the corresponding scaling fits discussed in the text. However, to make this more accessible, we have updated the abstract to include a short description of the observed scalings and inserted a summary table of exponents in the revised version. The quench protocols are determined a priori from the equilibrium phase diagram to ensure they either cross or avoid the QCP, avoiding any post-hoc selection. revision: yes

Circularity Check

0 steps flagged

No circularity; explicit model results support separation claim

full rationale

The paper derives its central claim—that Kibble-Zurek scaling can decouple from quantum criticality—through direct analysis of specific quasi-1D Fermi models and quench protocols. No step reduces a prediction to a fitted parameter by construction, nor does any load-bearing premise collapse to a self-citation or ansatz smuggled from prior work. The abstract and described results present numerical or analytical outcomes from representative Hamiltonians as independent evidence, with the generality resting on an explicit (if debatable) representativeness assumption rather than definitional equivalence. This is a standard non-circular structure for a model-based study.

Axiom & Free-Parameter Ledger

0 free parameters · 0 axioms · 0 invented entities

Abstract supplies no explicit free parameters, axioms, or invented entities; the work rests on standard models of Fermi systems whose details are not provided here.

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