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arxiv: 2606.24395 · v1 · pith:PL66AVZFnew · submitted 2026-06-23 · ❄️ cond-mat.stat-mech · hep-lat

Out-of-equilibrium scaling of the particle density in quantum fermionic wires after a critical quenching of the chemical potential

H. Panagopoulos , E. Vicari This is my paper

Pith reviewed 2026-06-25 22:19 UTC · model grok-4.3

classification ❄️ cond-mat.stat-mech hep-lat
keywords quantum quenchparticle densityKitaev wiredynamic scalingout-of-equilibriumchemical potentialcritical pointfermionic systems
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The pith

The difference between post-quench and critical particle density in fermionic wires scales with the dynamic variable θ = t/ξ^z.

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

This paper shows that in quantum fermionic Kitaev wires, quenching the chemical potential to the critical point causes the particle density minus its critical value to follow an out-of-equilibrium scaling law governed by the dynamic scaling variable θ ∼ t/ξ^z. In equilibrium the particle density is dominated by regular and logarithmic terms from mixing with the identity operator, but after the quench the subtracted quantity reveals clean dynamic scaling. A reader would care because this demonstrates how time evolution after a quench can uncover universal behavior hidden in static critical phenomena, supporting broader conjectures about post-quench dynamics.

Core claim

The difference between the post-QQ particle density and its critical value develops an out-of-equilibrium scaling behavior in terms of the dynamic scaling variable θ∼t/ξ^z. The scaling function has a peculiar singular behavior in the θ→0 limit, apparently related to the anomalous equilibrium scaling behavior of the particle density at the starting point of the QQ protocol. This provides analytical evidence of earlier conjectures on the general emergence of post-QQ dynamic scaling behaviors of the subtracted particle density, unlike their equilibrium counterpart which is dominated by nonuniversal contributions.

What carries the argument

The dynamic scaling variable θ ∼ t/ξ^z for the post-quench time evolution of the subtracted particle density.

If this is right

  • The scaling function exhibits a singular behavior as θ approaches 0.
  • This scaling is distinct from the equilibrium case dominated by nonuniversal terms.
  • Analytical evidence supports conjectures on post-quench dynamic scaling of subtracted particle density.
  • The emergence of scaling is tied to the initial state being within the critical region.

Where Pith is reading between the lines

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

  • If this scaling holds, it suggests that quench protocols can isolate universal critical behavior in systems where equilibrium quantities are masked by analytic backgrounds.
  • Extensions to other initial states or different quench protocols could test the generality of the singular θ→0 behavior.
  • Similar subtracted quantities might reveal hidden scaling in other nonequilibrium critical dynamics.

Load-bearing premise

That the regular and logarithmic terms from mixing with the identity operator do not dominate the time-dependent difference in particle density after the quench.

What would settle it

Numerical computation of the particle density at small post-quench times showing that the subtracted density does not follow the predicted scaling function or its singular limit as θ→0.

Figures

Figures reproduced from arXiv: 2606.24395 by E. Vicari, H. Panagopoulos.

Figure 1
Figure 1. Figure 1: FIG. 1: We show the scaling function Γ( [PITH_FULL_IMAGE:figures/full_fig_p005_1.png] view at source ↗
Figure 2
Figure 2. Figure 2: FIG. 2: We show the exact expression (55) (full line) for [PITH_FULL_IMAGE:figures/full_fig_p007_2.png] view at source ↗
read the original abstract

We study the out-of-equilibrium scaling behavior of the particle density in quantum fermionic Kitaev wires, after instantaneous quantum quenches (QQs) of the chemical potential within their quantum critical region. The critical scaling of the ground-state particle density is known to be subleading at its Ising-like quantum transition, hidden by regular and logarithmic terms arising from peculiar mixings with the identity operator. This situation changes along the out-of-equilibrium dynamics arising from QQs of the chemical potential to the critical point, starting from the ground state for Hamiltonian parameters within the critical region. We analytically show that the difference between the post-QQ particle density and its critical value develops an out-of-equilibrium scaling behavior, in terms of the dynamic scaling variable $\theta\sim t/\xi^z$ (where $t>0$ is the post-QQ time, $\xi$ is the length scale of the initial state, and $z$ is the dynamic critical exponent) associated with the post-QQ time evolution. The scaling function turns out to have a peculiar singular behavior in the $\theta\to 0$ limit, apparently related to the anomalous equilibrium scaling behavior of the particle density at the starting point of the QQ protocol. This provides analytical evidence of earlier conjectures on the general emergence of post-QQ dynamic scaling behaviors of the subtracted particle density (supported by numerical finite-size scaling analyses), unlike their equilibrium counterpart which turns out to be dominated by nonuniversal contributions.

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 out-of-equilibrium dynamics of the particle density in Kitaev fermionic wires following an instantaneous quench of the chemical potential to the critical point, starting from the ground state inside the critical region. It claims an analytical derivation that the subtracted density Δn(t) = n(t) − n_crit obeys dynamic scaling in the variable θ ∼ t/ξ^z (with z the dynamic exponent), and that the associated scaling function is singular as θ → 0, in contrast to the equilibrium density which is dominated by regular and logarithmic contributions from identity-operator mixing.

Significance. If the explicit cancellation of non-universal terms is demonstrated, the result supplies analytical evidence that post-quench subtracted observables can exhibit clean dynamic scaling even when their equilibrium counterparts are masked by operator mixing. This would support earlier numerical conjectures and illustrate how time evolution can isolate universal pieces that are inaccessible at equilibrium.

major comments (2)
  1. [out-of-equilibrium dynamics section (referenced in abstract)] The central analytical claim rests on showing that the regular and logarithmic identity-mixing contributions to the equilibrium density cancel (or become ξ-independent) in the post-quench difference Δn(t). The out-of-equilibrium section must contain the explicit mode-sum (or CFT) calculation demonstrating that the time-evolution operator applied to the initial state does not reintroduce time-dependent pieces proportional to these operators that survive subtraction for finite t; without this step the clean θ scaling is not established.
  2. [scaling-function analysis] The singular θ → 0 behavior of the scaling function is asserted to be related to the anomalous equilibrium scaling at the initial point. The derivation must explicitly connect the small-θ expansion to the known equilibrium mixing coefficients; otherwise the claimed relation remains conjectural rather than derived.
minor comments (2)
  1. Clarify the precise definition of the initial length scale ξ and the dynamic exponent z used in θ; state whether they are taken from the equilibrium Ising universality class or renormalized by the quench protocol.
  2. Provide the explicit form of the scaling function f(θ) or at least its leading small-θ and large-θ asymptotics to allow direct comparison with future numerics.

Simulated Author's Rebuttal

2 responses · 0 unresolved

We thank the referee for the careful reading and constructive suggestions. We agree that the out-of-equilibrium section requires more explicit derivations to fully substantiate the analytical claims. We will revise the manuscript to incorporate the requested calculations.

read point-by-point responses

  1. Referee: [out-of-equilibrium dynamics section (referenced in abstract)] The central analytical claim rests on showing that the regular and logarithmic identity-mixing contributions to the equilibrium density cancel (or become ξ-independent) in the post-quench difference Δn(t). The out-of-equilibrium section must contain the explicit mode-sum (or CFT) calculation demonstrating that the time-evolution operator applied to the initial state does not reintroduce time-dependent pieces proportional to these operators that survive subtraction for finite t; without this step the clean θ scaling is not established.

    Authors: We agree that an explicit mode-sum calculation is essential. In the revised manuscript we will add the full fermionic mode expansion (Bogoliubov-de Gennes quasiparticles) for the post-quench time evolution, explicitly demonstrating the cancellation of the regular and logarithmic identity-mixing terms in Δn(t) and confirming that no time-dependent non-universal contributions survive the subtraction for finite t. revision: yes

  2. Referee: [scaling-function analysis] The singular θ → 0 behavior of the scaling function is asserted to be related to the anomalous equilibrium scaling at the initial point. The derivation must explicitly connect the small-θ expansion to the known equilibrium mixing coefficients; otherwise the claimed relation remains conjectural rather than derived.

    Authors: We accept that the connection must be derived rather than asserted. The revised version will contain an explicit small-θ expansion of the scaling function, obtained from the mode-sum expression, and will directly match its leading singular term to the known equilibrium mixing coefficients of the identity operator at the initial point. revision: yes

Circularity Check

0 steps flagged

No significant circularity; analytical derivation stands independently

full rationale

The paper claims an explicit analytical demonstration that the subtracted post-quench density difference Δn(t) = n(t) − n_crit obeys dynamic scaling in θ = t/ξ^z, with a singular θ→0 limit. This is presented as arising from the mode-sum or CFT time evolution applied to the initial critical-region ground state, after the identity-mixing terms that dominate equilibrium are subtracted. No equation is shown reducing the scaling function to a fitted parameter or to a prior self-citation by definition. The reference to 'earlier conjectures' (supported by numerics) is contextual; the present work supplies the independent analytical step. The derivation chain therefore remains self-contained against external benchmarks and does not collapse by construction.

Axiom & Free-Parameter Ledger

0 free parameters · 2 axioms · 0 invented entities

Based solely on the abstract; the work relies on standard assumptions of the Kitaev chain and its Ising-like critical point but introduces no new free parameters or invented entities.

axioms (2)
  • domain assumption The Kitaev wire exhibits an Ising-like quantum critical point with known dynamic exponent z
    Invoked when defining the scaling variable θ ~ t/ξ^z and referring to the critical region.
  • domain assumption The initial state is the ground state inside the critical region before the instantaneous quench
    Stated as the starting point of the QQ protocol in the abstract.

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