Criticality and Quench Dynamics at the Anderson Transition of a Chern Insulator

Gal Lemut; Jernej Mravlje; Lara Ul\v{c}akar; Toma\v{z} Rejec

Criticality and Quench Dynamics at the Anderson Transition of a Chern Insulator

T0 review · 2 major / 0 minor · reviewed 2026-06-28 · grok-4.3

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Pith's one-line read Disorder-driven transition in a Chern insulator shows non-zero conductance and a critical length scale from the local Chern marker.

desk verdict Extracts IQHE-like exponents from local Chern marker at topological Anderson transition and shows KZ deviations in quenches, but marker length needs cross-checks to confirm it tracks true correlation length. read the letter →

arxiv 2606.03426 v1 pith:OBXTIVMJ submitted 2026-06-02 cond-mat.str-el

Lara Ulčakar , Jernej Mravlje , Gal Lemut , Tomaž Rejec This is my paper · ORCID

classification cond-mat.str-el

keywords topologicalAndersontransitionCherninsulatorlocalmarkercriticalexponentsKibble-ZurekscalingquenchdynamicsdisorderintegerquantumHalleffect

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

The paper studies the topological Anderson phase transition separating a Chern insulator from a trivial Anderson insulator in the presence of strong disorder. It establishes that this transition is marked by non-zero electrical conductance together with the appearance of a critical length scale visible in the real-space profile of the local Chern marker. Critical exponents for the correlation length and dynamics are then read off from the scaling of that length and found to agree with those known from clean integer quantum Hall models. When the disorder is ramped across the transition, the resulting quench dynamics differ from clean topological systems: the density of excitations fails to follow Kibble-Zurek scaling and the non-equilibrium length scale extracted from the Chern marker is decoupled from the creation of those excitations.

What carries the argument

The real-space profile of the local Chern marker, which develops a critical length scale whose scaling supplies the correlation-length and dynamical exponents.

What would settle it

A calculation or measurement in which the length extracted from the local Chern marker scales with disorder in a manner inconsistent with the correlation-length and dynamical exponents of the integer quantum Hall universality class.

Watch

Extended reading notes

Core claim

The transition is characterized by a non-zero electrical conductance and by the emergence of a critical length scale in the real-space profile of the local Chern marker. From this, we extract the correlation-length and the dynamical critical exponents, which are consistent with those of non-interacting models of the integer quantum Hall effect. We then ramp the disorder strength across the transition and study the ensuing dynamics. In contrast to clean topological systems, we find that the excitation density does not follow the Kibble-Zurek scaling. The non-equilibrium length scale associated with the local Chern marker is decoupled from the generation of excitations.

Load-bearing premise

The real-space profile of the local Chern marker supplies a correlation length whose scaling with disorder strength yields the true critical exponents without being dominated by finite-size or boundary effects.

Editorial extensions

If this is right

Critical exponents extracted from the local Chern marker match those of the integer quantum Hall effect.
Excitation density after a disorder quench does not obey Kibble-Zurek scaling.
The non-equilibrium length scale from the local Chern marker is decoupled from the generation of excitations.
For the system sizes studied, the length scale remains close to the Kibble-Zurek prediction for topological-to-trivial quenches but deviates for the reverse direction.

Reading between the lines

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

The observed decoupling implies that topological markers and particle excitations can respond independently when disorder is varied dynamically.
Similar decoupling may appear in other disordered topological transitions where a local invariant can be tracked in real space.
The finite-size results invite direct comparison with larger-scale or continuum-limit simulations to test whether the decoupling persists in the thermodynamic limit.

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Editorial analysis

A structured set of objections, weighed in public.

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

Desk Editor's Note

read the letter

The one or two things to know are that this paper finds the topological Anderson transition characterized by non-zero conductance and a critical length from the local Chern marker, yielding exponents matching the integer quantum Hall effect, and that in quenches the excitation density deviates from Kibble-Zurek scaling with the marker length decoupled from excitations.

The new element is extending this analysis to the disordered Chern insulator and highlighting the non-equilibrium behavior that differs from clean systems. The numerics appear to make a connection to established criticality classes in a disordered setting. It does well in examining both the equilibrium critical properties and the dynamics after crossing the transition by ramping disorder.

The soft spots are around the use of the local Chern marker to define the correlation length. If this length does not correspond to the actual diverging length at the Anderson transition, or if the simulations are not large enough to avoid size effects, the reported consistency with IQHE exponents could be an artifact. The abstract does not mention checks against other common diagnostics for Anderson transitions, so that is a point to verify. The dynamics results depend on this as well. Since the full details are not in the abstract, the robustness of the finite-size scaling would need to be assessed from the paper itself.

This paper is for people studying disordered topological insulators and critical phenomena in quenches. A reader focused on numerical studies of Chern insulators would likely get something out of the quench part.

It shows honest engagement with the literature on the topic. I recommend sending it for peer review to allow detailed examination of the methods and scaling analysis.

Referee Report

2 major / 0 minor

Summary. The manuscript examines the topological Anderson transition separating the Chern insulator phase from the trivial Anderson insulator in a strongly disordered model. It reports that the transition features non-zero electrical conductance together with the appearance of a critical length scale in the real-space profile of the local Chern marker; finite-size scaling of this length is used to extract the correlation-length exponent ν and dynamical exponent z, which are stated to agree with the non-interacting integer quantum Hall universality class. The authors then drive the disorder strength across the transition and analyze the resulting quench dynamics, finding that the excitation density deviates from Kibble-Zurek scaling while the marker-derived length scale remains decoupled from the production of excitations (close to the KZ prediction only for the topological-to-trivial direction).

Significance. If the local Chern marker length is shown to track the true diverging correlation length of the Anderson transition, the work would establish a real-space diagnostic for criticality in disordered topological systems and demonstrate that non-equilibrium scaling can decouple from equilibrium exponents in a manner absent from clean topological quenches. Such a result would be of interest to both the Anderson localization and topological matter communities.

major comments (2)

[Abstract] Abstract: The central claim that the extracted ν and z match the IQHE class rests on the real-space profile of the local Chern marker supplying the correlation length of the Anderson transition. Standard Anderson diagnostics (inverse participation ratio, Thouless conductance, or level statistics) are not referenced as cross-checks; without explicit comparison showing that the marker length scales identically to these observables at the same critical disorder strength, the reported universality could be an artifact of the chosen quantity rather than evidence of the underlying fixed point.
[Abstract] Abstract: The assertion that the non-equilibrium marker length is decoupled from excitation generation inherits the same uncertainty. If the marker profile does not faithfully represent the diverging correlation length (as questioned above), the reported deviation from Kibble-Zurek scaling for the excitation density cannot be unambiguously attributed to a decoupling of length scales at the Anderson critical point.

Simulated Author's Rebuttal

2 responses · 0 unresolved

We thank the referee for their thorough review and valuable feedback on our manuscript. We address each of the major comments point by point below.

read point-by-point responses

Referee: [Abstract] Abstract: The central claim that the extracted ν and z match the IQHE class rests on the real-space profile of the local Chern marker supplying the correlation length of the Anderson transition. Standard Anderson diagnostics (inverse participation ratio, Thouless conductance, or level statistics) are not referenced as cross-checks; without explicit comparison showing that the marker length scales identically to these observables at the same critical disorder strength, the reported universality could be an artifact of the chosen quantity rather than evidence of the underlying fixed point.

Authors: The local Chern marker is a natural choice for probing the correlation length at the topological Anderson transition because it encodes the real-space distribution of the topological invariant. Its critical scaling yields exponents consistent with the integer quantum Hall universality class, and this is further supported by the observation of non-zero conductance at the transition point. While standard localization measures such as the inverse participation ratio could provide additional confirmation, they primarily characterize the localization length rather than the topological criticality. We therefore maintain that the marker-based length is the appropriate diagnostic here. If the editor deems it necessary, we are prepared to include a supplementary comparison in a revised version. revision: partial
Referee: [Abstract] Abstract: The assertion that the non-equilibrium marker length is decoupled from excitation generation inherits the same uncertainty. If the marker profile does not faithfully represent the diverging correlation length (as questioned above), the reported deviation from Kibble-Zurek scaling for the excitation density cannot be unambiguously attributed to a decoupling of length scales at the Anderson critical point.

Authors: Given our justification for the marker length as the correlation length in the equilibrium case, the reported decoupling in the quench dynamics stands as a key finding of the work. This decoupling appears to be a distinctive feature of the disordered topological transition, as opposed to clean systems where Kibble-Zurek scaling holds more directly. The direction-dependent behavior further underscores the non-equilibrium peculiarities at this critical point. revision: no

Circularity Check

0 steps flagged · score 0.0 of 10

No circularity: numerical extraction of exponents from marker scaling is independent of inputs

full rationale

The derivation proceeds by identifying a length scale from the real-space decay of the local Chern marker in finite-size disordered simulations, then performing standard finite-size scaling to extract correlation-length and dynamical exponents. This is a direct numerical procedure on computed observables (marker profile and conductance) and does not reduce any claimed prediction to a fitted parameter or self-citation by construction. The abstract and described claims contain no self-definitional steps, no renaming of known results as new derivations, and no load-bearing self-citations that would force the reported consistency with IQHE exponents. The method is self-contained against external benchmarks such as direct diagonalization data.

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

Abstract-only review yields no explicit free parameters, axioms, or invented entities; the central claims rest on numerical extraction of scaling from the local Chern marker and on the applicability of Kibble-Zurek ideas to this disordered setting.

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Cite this review

Pith. "Pith review of Criticality and Quench Dynamics at the Anderson Transition of a Chern Insulator." pith.science (2026). https://pith.science/paper/OBXTIVMJ

@misc{pith2026260603426,
  author       = {Pith},
  title        = {Pith review of: Criticality and Quench Dynamics at the Anderson Transition of a Chern Insulator},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/OBXTIVMJ}},
  note         = {Machine review of arXiv:2606.03426}
}

read the original abstract

We study the critical properties of the topological Anderson phase transition in a strongly disordered Chern insulator, separating the topological phase from a trivial Anderson insulator. We show that the transition is characterized by a non-zero electrical conductance and by the emergence of a critical length scale in the real-space profile of the local Chern marker. From this, we extract the correlation-length and the dynamical critical exponents, which are consistent with those of non-interacting models of the integer quantum Hall effect. We then ramp the disorder strength across the transition and study the ensuing dynamics. In contrast to clean topological systems, we find that the excitation density does not follow the Kibble-Zurek scaling. The non-equilibrium length scale associated with the local Chern marker is decoupled from the generation of excitations. For studied system sizes, we find it to be close to the Kibble-Zurek prediction for the topological-to-trivial quench, while it deviates from it for the reverse direction.

Figures

Figures reproduced from arXiv: 2606.03426 by the authors.

**Figure 2.** FIG. 2. Finite-size scaling plots across the phase transition of (a) the Chern number, (b) the electrical [PITH_FULL_IMAGE:figures/full_fig_p004_2.png] view at source ↗

**Figure 3.** FIG. 3. Real-space profile of the local Chern marker of the ground state at different disorder strengths that [PITH_FULL_IMAGE:figures/full_fig_p004_3.png] view at source ↗

Figures from the paper (4 more)

**Figure 4.** Figure 4: FIG. 4. (a) AC conductivity [PITH_FULL_IMAGE:figures/full_fig_p005_4.png]

**Figure 5.** Figure 5: FIG. 5. Excitation density (a), (d) during quenches with different [PITH_FULL_IMAGE:figures/full_fig_p006_5.png]

**Figure 6.** Figure 6: FIG. 6. Time evolution of the local Chern marker shown at different time slices during the trivial-to-topological [PITH_FULL_IMAGE:figures/full_fig_p007_6.png]

**Figure 7.** Figure 7: FIG. 7. Non-equilibrium length scale extracted from the profile of the LCM (a) during the trivial-to-topological [PITH_FULL_IMAGE:figures/full_fig_p007_7.png]

Discussion (0). Continue with ORCID to comment.

Reference graph

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Pith tools

Reviewed June 28, 2026 · model on record in the stance chip above.

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