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Fate of dynamical quantum phase transitions from sudden quench to slow quench limit

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

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Pith's one-line read Slow quenches, not just sudden ones, leave dynamical quantum phase transitions intact only when the ramp crosses an equilibrium quantum critical point; within-phase 'accidental' DQPTs are erased.

desk verdict Plausible filter mechanism, convincingly illustrated in three models, but the general argument is a heuristic and the abstract overstates it. read the letter →

arxiv 2607.15649 v1 pith:AIBKDGYV submitted 2026-07-17 quant-ph cond-mat.stat-mech

Xiang Zhang , Fuxiang Li This is my paper · ORCID
classification quant-phcond-mat.stat-mech
keywords dynamicalquantumphasetransitionsLoschmidtechoslowquenchLandau-ZenertransitioncriticalityXYchainAubry-AndrémodeltrimerSu-Schrieffer-Heeger
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

Sudden quenches produce dynamical quantum phase transitions (DQPTs) both when a system is driven across an equilibrium phase boundary and when it is not; the latter, dubbed accidental DQPTs, muddy the connection between dynamical and equilibrium criticality. This paper contends that ramping the control parameter slowly—rather than switching it abruptly—separates the two: DQPTs survive slow ramps that cross a gap-closing equilibrium transition, while accidental DQPTs generated inside a single phase disappear as the ramp rate goes to zero. The mechanism is a generalized equal-overlap condition for the Loschmidt echo, combined with Landau-Zener suppression of excitations in gapped phases. The authors demonstrate the effect numerically in the XY chain, the Aubry-André model, and the trimer Su-Schrieffer-Heeger model, and show that the surviving DQPT critical times scale with ramp rate through the equilibrium critical exponent zν. If right, this turns DQPT into a dynamical tool for locating equilibrium quantum critical points and exponents.

What carries the argument

The central identity is the equal-overlap condition for the Loschmidt echo under slow quench: |p_{k_c,1}||c_{k_c,1}| = |p_{k_c,2}||c_{k_c,2}|, where p_{k,i} are the instantaneous eigenstate occupation amplitudes and c_{k,i} the overlaps of those eigenstates with the initial state. Its behavior is controlled by the Landau-Zener formula P = exp(−π Δ_k²/β), giving the excitation probability for a two-band model ramped linearly at rate β through an avoided crossing of size Δ_k. The argument uses the vanishing of Δ_k at a gap-closing critical point to guarantee a solution for k_c, and the uniform exponential suppression of P in a gapped phase to rule one out.

What would settle it

Find a gapped quantum phase in which a momentum sector has a Landau-Zener parameter Δ_k that is exactly or effectively zero without the system crossing an equilibrium phase boundary; a slow quench within that phase would then still generate a k_c satisfying the equal-overlap condition, producing a DQPT and disproving the filter. Numerically, this can be checked by computing |p_{k,2}(t)| for a very slow ramp in a model with an accidental band touching point.

Watch

Extended reading notes

Core claim

For a two-band system initialized in its ground state and driven by a linear ramp, the Loschmidt amplitude factorizes over momenta and a DQPT occurs at a critical momentum k_c when |p_{k_c,1}||c_{k_c,1}| = |p_{k_c,2}||c_{k_c,2}|, the product of the instantaneous-state occupation amplitude and the initial/final overlap amplitude. When the ramp stays within a gapped phase, the Landau-Zener excitation amplitude |p_{k,2}| is exponentially small for all k at slow ramp rates, so this equality cannot be met and accidental DQPTs vanish. When the ramp crosses an equilibrium transition, the gap closes at some k_0, the excitation amplitude reaches one there, and the equality is guaranteed for some k_c

Load-bearing premise

The filter assumes that for a slow ramp inside a gapped phase the excitation amplitude |p_{k,2}| is uniformly small for all momenta at all times of interest, and that for a ramp crossing a gap-closing transition a critical momentum k_c satisfying the equal-overlap condition always exists—justified only by the infinite-time Landau-Zener formula and an existence statement, not by a proof, and known to fail when a transition lacks bulk gap closing.

Editorial extensions

If this is right

  • DQPTs that survive a slow ramp pinpoint equilibrium quantum critical points, so a dynamical measurement can locate a static phase boundary without crossing it adiabatically.
  • The first DQPT critical time scales with the ramp rate as τ_c ∼ β^{-zν/(1+zν)}, allowing extraction of the equilibrium critical exponent product zν from dynamics.
  • Accidental DQPTs reported in the XY chain (same-ferromagnetic-phase quenches) and in the Aubry-André model (same-extended-phase quenches) are predicted to vanish under slow ramps, a directly testable prediction.
  • The filter works only when the transition is accompanied by bulk gap closing; a topological transition without gap closing, as in the non-mirror-symmetric trimer SSH model, does not produce slow-quench DQPT.
  • The mechanism extends beyond two-band to multiband models, demonstrated by the mirror-symmetric trimer SSH case.

Reading between the lines

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

  • A practical corollary the authors leave implicit: the threshold ramp rate below which accidental DQPTs vanish should be set by the smallest gap along the ramp path, so finite-size or quasiperiodic systems with tiny but nonzero gaps may require impractically slow ramps.
  • The same criterion offers a dynamical classifier for whether a given equilibrium phase transition is accompanied by bulk gap closing: observe whether DQPT survives slow driving.
  • The Landau-Zener argument is for noninteracting bands; whether the filtering survives interactions, where the Loschmidt echo does not factorize over momenta, is an open extension suggested by the paper's framing.
  • Because the equal-overlap condition is stated per momentum, lattice translation invariance is needed; a disorder-induced or position-dependent ramp would require a different formulation.
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Editorial analysis

A structured set of objections, weighed in public.

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

Referee Report

4 major / 4 minor

Summary. The paper studies dynamical quantum phase transitions (DQPTs) under slow linear quenches, using the first Loschmidt-amplitude convention G(t)=⟨ψ(t_i)|ψ(t)⟩, and claims two main results: (i) DQPTs remain robust when the ramp crosses an equilibrium quantum phase transition, and (ii) 'accidental' DQPTs, which occur under sudden quenches within the same equilibrium phase, are filtered out in the slow-quench limit. The general argument in Sec. II is based on a two-band Landau-Zener picture and the condition |p_{k_c,1}||c_{k_c,1}|=|p_{k_c,2}||c_{k_c,2}| of Eq. (11). The claims are illustrated numerically for the XY chain, the Aubry-André model, and the trimer Su-Schrieffer-Heeger model, and the authors also extract a critical-time scaling τ_c∼β^{-σ} with σ related to equilibrium exponents. The paper is clearly written and the numerical examples are relevant, but the general argument is heuristic in ways that are load-bearing for the central claim.

Significance. If the central claim were rigorously established, it would provide a practical and physically appealing connection between DQPTs and equilibrium quantum criticality, and it would give a dynamical route to locating quantum critical points and extracting critical exponents. The choice of three distinct models—a spin-chain, a quasiperiodic model, and a multiband topological model—makes the intended scope broad. The paper is also honest about a limitation: the SSH3 no-bulk-gap-closing case does not produce slow-quench DQPTs, which the authors correctly attribute to the absence of gap closing. However, the paper's own general argument is not a proof: it relies on asymptotic Landau-Zener formulas at finite times and treats time-dependent overlaps as constants. The numerical demonstrations are suggestive rather than conclusive, as no finite-size scaling or convergence analysis is provided. The critical-time scaling law is largely inherited from the authors' previous work (Ref. [70]) and is presented without fit details.

major comments (4)
  1. [Sec. II, Eqs. (10)-(14)] The filtering argument uses the Landau-Zener probability P=exp(-πΔ_k²/β), which is an asymptotic t→±∞ transition probability. In the first approach defining G(t) in Eq. (7), DQPT critical times are evaluated at finite t during the slow ramp (e.g., Figs. 2 and 4). The statement that for a same-phase quench |p_{k,2}| is 'always very small' for small β is therefore not established for the times τ_c where Eq. (11) is actually needed. The paper's own Fig. 3(a2) shows a finite |p_{k,2}|² at β=0.08, which contradicts the 'always very small' assertion. This is a load-bearing gap in the general argument.
  2. [Sec. II, Eq. (11)] The coefficients |c_{k,i}(t)|=⟨u_i^-|u_k^±(t)⟩ are time-dependent through the instantaneous eigenstates, so the statement that they 'can be seen as a constant' is not correct. Eq. (11) is therefore a condition at the finite time τ_c, not a condition on asymptotic occupation amplitudes. The existence of a k_c for gap-crossing quenches, argued from |p_{k_0,2}|=1 at k_0 and small |p_{k,2}| away from k_0, does not by itself guarantee that |p_{k,1}||c_{k,1}|=|p_{k,2}||c_{k,2}| holds at the same time τ_c. The three numerical examples support the claim as a numerical observation, but they do not fill this logical gap.
  3. [Sec. III, Figs. 2, 5, 7] DQPTs are defined by nonanalyticities of the rate function in the thermodynamic limit. The manuscript does not report system-size dependence or finite-size scaling for any of the three models. For finite chains, an exact zero of G(t) occurs only if the critical momentum k_c lies on the discrete momentum grid; otherwise only sharp dips appear. Showing that no DQPT is visible at one system size and one quench rate (e.g., Fig. 2(b) for β=0.05) does not establish the claimed filtering in the thermodynamic limit. This is central to the numerical demonstration of the filter mechanism.
  4. [Sec. III, Figs. 4 and 8, Eq. (24)] The universal scaling τ_c∼β^{-σ} and the extraction of zν=1 are used to argue that DQPTs can identify equilibrium critical exponents. However, the paper gives no fit procedure, no fit range, no error bars, and no finite-size checks for the extracted exponents. Moreover, the XY chain result is quoted as τ_c∼β^{-1/2} while the SSH3 result in Eq. (24) includes a constant shift τ_0; the relation between these forms and the derivation in Ref. [70] is asserted rather than demonstrated. As written, this part of the claim is not independently supported by the data presented.
minor comments (4)
  1. [Eq. (10)] The notation is inconsistent: the left-hand side writes G_k(t) as a product over k, which should presumably read G(t)=∏_k G_k(t). Please correct.
  2. [Throughout] There are numerous typos, e.g., 'qunech', 'Hamltonians', 'depictes', 'presentes', and 'DA T AA V AILABILITY'. A careful proofread is needed.
  3. [Sec. II, around Eq. (11)] Eq. (11) is only a necessary condition for a zero of G_k(t); the phase condition Φ_{k,1}-Φ_{k,2}=π mod 2π is also required. The text should state this explicitly to avoid implying that the magnitude condition alone defines a DQPT.
  4. [Sec. II, Eq. (15)] The second Loschmidt-amplitude convention is dismissed in one sentence. Since some slow-quench DQPT literature uses that convention, a brief quantitative comparison or explicit statement of why it is not applicable would strengthen the presentation.

Circularity Check

0 steps flagged · score 0.0 of 10

No exhibit-able circular reduction; the filtering claim rests on direct numerics, and the self-cited scaling relation is checked against the paper's own data.

full rationale

I walked the paper's derivation chain from Eq. (10) to Eq. (11) and through the three model studies. The slow-quench DQPT condition (11) is algebraically derived from the Loschmidt-amplitude decomposition; it is not a restatement of the conclusion. The central 'filtering' claim—same-phase sudden-quench DQPTs disappear in the slow-quench limit while gap-crossing DQPTs persist—is supported by explicit numerical solution of the time-dependent Schrödinger equation (Eq. 12) with the same endpoints as the sudden-quench protocols, not by fitting a parameter and renaming it a prediction. The Landau-Zener formula (14) is used heuristically to motivate small transition amplitudes, and the finite-time use of an asymptotic formula is a legitimate correctness concern, but it is not a circular reduction: the existence of a k_c satisfying Eq. (11) is not defined into existence, and the paper's own figures provide the independent numerical check. The 'genuine DQPT' language is a stated criterion, but the substantive result is that the criterion selects gap-crossing quenches, which is an empirical finding rather than a tautology. The self-citations to Ref. [70] supply the scaling relation σ=zν/(1+zν); the paper then compares that relation to its own τ_c(β) data (Figs. 4 and 8). Thus the self-citation is not the sole content of the critical-exponent claim and is not load-bearing in a circular way. Under the hard rule requiring an explicit equation-to-equation reduction or a fitted parameter renamed as prediction, I find no exhibit-able circular step.

Assumptions & free parameters 3 free parameters · 3 assumptions · 0 invented entities

The central claim rests on the Landau-Zener approximation for finite-time slow ramps, an asserted existence of a critical momentum satisfying Eq. (11), and a definition of 'genuine' DQPT as robust under slow quench. The threshold quench rate and scaling exponent are extracted from numerics rather than predicted from the general argument, and the scaling law itself is inherited from self-cited Ref. [70]. No new entities are introduced.

free parameters (3)
  • threshold quench rate β_th = 0.09 (XY, γ=0.3, h_i=0, h_f=0.9)
    Numerically determined boundary between DQPT and no-DQPT behavior in Fig. 3; defines 'sufficiently slow' for that model, with no analytic prediction.
  • critical-time scaling exponent σ = 1/2
    Extracted from log-log plots of τ_c versus β in XY (Fig. 4) and SSH3 (Fig. 8); used to infer zν=1 via self-cited Ref. [70], with no error bars reported.
  • constant shift τ0 = not specified
    Introduced in Eq. (24) for the SSH3 scaling fit τ_c ~ β^{-1/2} + τ0; its value and fitting procedure are not reported.
assumptions (3)
  • domain assumption The infinite-time Landau-Zener formula P = exp(-πΔ_k²/β) is a good approximation for the finite-time slow linear quenches considered here.
    Sec. II after Eq. (14) states the formula 'can serve as a good approximation'; the filtering argument relies on the resulting exponential suppression of excitations, but no bounds or finite-time corrections are given.
  • domain assumption For a ramp crossing a gap-closing quantum phase transition, in the thermodynamic limit there is always a critical momentum k_c satisfying Eq. (11).
    Sec. II: 'In the thermodynamic limit... we can always find a special point k_c such that condition (11) is satisfied.' This is asserted, not proven.
  • ad hoc to paper A 'genuine' DQPT is one that is robust under slow quench and independent of initial state and microscopic details.
    Introduction states 'genuine DQPT should remain robust and is independent of both the initial state preparation and microscopic details of the Hamiltonian.' This definitional postulate shapes what the paper counts as real versus accidental.

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Pith. "Pith review of Fate of dynamical quantum phase transitions from sudden quench to slow quench limit." pith.science (2026). https://pith.science/paper/AIBKDGYV

@misc{pith2026260715649,
  author       = {Pith},
  title        = {Pith review of: Fate of dynamical quantum phase transitions from sudden quench to slow quench limit},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/AIBKDGYV}},
  note         = {Machine review of arXiv:2607.15649}
}
read the original abstract

Previous investigations of dynamical quantum phase transition (DQPT) have predominantly focused on sudden quench protocols. In this work, we systematically explore the fate of DQPT from the sudden to the slow quench regime. We establish that DQPT remains robust under slow quenching when the protocol crosses an equilibrium quantum phase transition. Conversely, we show that accidental DQPTs,which occur when the pre and post quench Hamiltonians reside in the same equilibrium phase, can be filtered out in the slow quench limit. This demonstrates that slow quenches can reveal the intrinsic connection between DQPT and equilibrium quantum phase transitions, thereby enabling DQPT to serve as a dynamical probe for identifying equilibrium quantum critical points. We illustrate these findings with examples from the XY chain, the Aubry-Andr\'e model, and the trimer Su-Schrieffer-Heeger model.

Figures

Figures reproduced from arXiv: 2607.15649 by the authors.

Figure 1
Figure 1. FIG. 1. Schematic of the quench protocols: Sudden quench [PITH_FULL_IMAGE:figures/full_fig_p002_1.png] view at source ↗
Figure 2
Figure 2. FIG. 2. DQPTs in the XY chain under sudden and slow [PITH_FULL_IMAGE:figures/full_fig_p005_2.png] view at source ↗
Figure 3
Figure 3. FIG. 3. The condition ( [PITH_FULL_IMAGE:figures/full_fig_p006_3.png] view at source ↗
Figures from the paper (4 more)
Figure 4
Figure 4. Figure 4: FIG. 4. The scaling behavior of critical time of DQPT when [PITH_FULL_IMAGE:figures/full_fig_p006_4.png]
Figure 5
Figure 5. Figure 5: FIG. 5. Loschmidt echo [PITH_FULL_IMAGE:figures/full_fig_p007_5.png]
Figure 6
Figure 6. Figure 6: FIG. 6. The spectrum of the bulk Hamiltonian of SSH3 in the [PITH_FULL_IMAGE:figures/full_fig_p008_6.png]
Figure 7
Figure 7. Figure 7: FIG. 7. Sudden and slow quench dynamics in the SSH3 model [PITH_FULL_IMAGE:figures/full_fig_p008_7.png]

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