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

Abstract

We study the critical properties and non-equilibrium dynamics of the topological Anderson phase transition in a strongly disordered Chern insulator. We show that a critical length scale emerges in the real-space profile of the local Chern marker and matches the corresponding correlation-length critical exponent found in the literature. We further determine the dynamical critical exponent from the frequency-dependent conductivity, finding values consistent with those of non-interacting models in the integer quantum Hall universality class. We then ramp the disorder strength across the phase transition and investigate the ensuing non-equilibrium dynamics. In contrast to clean topological systems, the spectral gap is closed due to localized states and consequently the generation of excitations does not exhibit Kibble-Zurek scaling. Despite this, we find that the non-equilibrium length scale extracted from the local Chern marker shows signatures of the Kibble-Zurek scaling. Our results demonstrate that the non-equilibrium dynamics of the topological Anderson transition features decoupling between the excitations and the emergent length scale as known from clean systems, and establish the local Chern marker as a probe of the emergent length scale during the quench.

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BibTeX RIS

BibTeX

@misc{ulcakar2026criticality,
  title = {{Criticality and Quench Dynamics at the Anderson Transition of a Chern Insulator}},
  author = {Lara Ulčakar and Jernej Mravlje and Gal Lemut and Tomaž Rejec},
  howpublished = {arXiv},
  year = {2026},
  month = nov,
  doi = {10.48550/arxiv.2606.03426},
  eprint = {2606.03426},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2606.03426},
}

RIS

TY  - UNPB
TI  - Criticality and Quench Dynamics at the Anderson Transition of a Chern Insulator
AU  - Lara Ulčakar
AU  - Jernej Mravlje
AU  - Gal Lemut
AU  - Tomaž Rejec
PY  - 2026
DA  - 2026/11/04
PB  - arXiv
DO  - 10.48550/arxiv.2606.03426
UR  - https://arxiv.org/abs/2606.03426
AB  - We study the critical properties and non-equilibrium dynamics of the topological Anderson phase transition in a strongly disordered Chern insulator. We show that a critical length scale emerges in the real-space profile of the local Chern marker and matches the corresponding correlation-length critical exponent found in the literature. We further determine the dynamical critical exponent from the frequency-dependent conductivity, finding values consistent with those of non-interacting models in the integer quantum Hall universality class. We then ramp the disorder strength across the phase transition and investigate the ensuing non-equilibrium dynamics. In contrast to clean topological systems, the spectral gap is closed due to localized states and consequently the generation of excitations does not exhibit Kibble-Zurek scaling. Despite this, we find that the non-equilibrium length scale extracted from the local Chern marker shows signatures of the Kibble-Zurek scaling. Our results demonstrate that the non-equilibrium dynamics of the topological Anderson transition features decoupling between the excitations and the emergent length scale as known from clean systems, and establish the local Chern marker as a probe of the emergent length scale during the quench.
ER  -

Abstract

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