We study topological insulators under dephasing noise. With examples of both a $2d$ Chern insulator and a $3d$ topological insulator protected by time-reversal symmetry, we demonstrate that there is a phase transition at finite dephasing strength between phases with nontrivial and trivial topological indices. Here, the topological index is defined through the correlation matrix. The transition can be diagnosed through the spectrum of the whole correlation matrix or of a local subsystem. Interestingly, even if the topological insulator is very close to the topological-trivial critical point in its Hamiltonian, it still takes finite strength of dephasing to change the topological index, suggesting the robustness of topological insulators under dephasing. We further consider Chern insulators in the presence of real-space disorder, which exhibit a ground-state transition between topological and Anderson insulating phases. We find that even strongly disordered Chern insulators, close to the critical disorder strength, exhibit robustness with respect to dephasing.We study topological insulators under dephasing noise. With examples of both a $2d$ Chern insulator and a $3d$ topological insulator protected by time-reversal symmetry, we demonstrate that there is a phase transition at finite dephasing strength between phases with nontrivial and trivial topological indices. Here, the topological index is defined through the correlation matrix. The transition can be diagnosed through the spectrum of the whole correlation matrix or of a local subsystem. Interestingly, even if the topological insulator is very close to the topological-trivial critical point in its Hamiltonian, it still takes finite strength of dephasing to change the topological index, suggesting the robustness of topological insulators under dephasing. We further consider Chern insulators in the presence of real-space disorder, which exhibit a ground-state transition between topological and Anderson insulating phases. We find that even strongly disordered Chern insulators, close to the critical disorder strength, exhibit robustness with respect to dephasing.

arXiv:2506.04102Physical review. B./Physical review. BNov 13, 20250 citations

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

Lara Ulčakar, Jernej Mravlje, G. Lemut +1 more

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.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.

arXiv:2606.03426Jun 2, 20260 citations

Disordered topological quantum critical points in three-dimensional systems

Shuichi Murakami

Jan 1, 20100 citations

Kibble-Zurek Behavior in Disordered Chern Insulators

Lara Ulčakar, Jernej Mravlje, Tomaž Rejec

Even though no local order parameter in the sense of the Landau theory exists for topological quantum phase transitions in Chern insulators, the highly nonlocal Berry curvature exhibits critical behavior near a quantum critical point. We investigate the critical properties of its real space analog, the local Chern marker, in weakly disordered Chern insulators. Because of disorder, inhomogeneities appear in the spatial distribution of the local Chern marker. Their size exhibits power-law scaling with the critical exponent matching the one extracted from the Berry curvature of a clean system. We drive the system slowly through such a quantum phase transition. The characteristic size of inhomogeneities in the nonequilibrium postquench state obeys the Kibble-Zurek scaling. In this setting, the local Chern marker thus does behave in a similar way as a local order parameter for a symmetry breaking second order phase transition. The Kibble-Zurek scaling also holds for the inhomogeneities in the spatial distribution of excitations and of the orbital polarization.Even though no local order parameter in the sense of the Landau theory exists for topological quantum phase transitions in Chern insulators, the highly nonlocal Berry curvature exhibits critical behavior near a quantum critical point. We investigate the critical properties of its real space analog, the local Chern marker, in weakly disordered Chern insulators. Because of disorder, inhomogeneities appear in the spatial distribution of the local Chern marker. Their size exhibits power-law scaling with the critical exponent matching the one extracted from the Berry curvature of a clean system. We drive the system slowly through such a quantum phase transition. The characteristic size of inhomogeneities in the nonequilibrium postquench state obeys the Kibble-Zurek scaling. In this setting, the local Chern marker thus does behave in a similar way as a local order parameter for a symmetry breaking second order phase transition. The Kibble-Zurek scaling also holds for the inhomogeneities in the spatial distribution of excitations and of the orbital polarization.

arXiv:2003.08439Physical Review LettersNov 18, 202034 citations

We study topological insulators under dephasing noise. With examples of both a

2d

Chern insulator and a

3d

topological insulator protected by time-reversal symmetry, we demonstrate that there is a phase transition at finite dephasing strength between phases with nontrivial and trivial topological indices. Here, the topological index is defined through the correlation matrix. The transition can be diagnosed through the spectrum of the whole correlation matrix or of a local subsystem. Interestingly, even if the topological insulator is very close to the topological-trivial critical point in its Hamiltonian, it still takes finite strength of dephasing to change the topological index, suggesting the robustness of topological insulators under dephasing. We further consider Chern insulators in the presence of real-space disorder, which exhibit a ground-state transition between topological and Anderson insulating phases. We find that even strongly disordered Chern insulators, close to the critical disorder strength, exhibit robustness with respect to dephasing.