Dephasing-induced Quantum Hall Criticality in the Quantum Anomalous Hall system

TL;DR

The paper shows that pure dephasing, without static disorder, can realize quantum Hall criticality by preserving a topological $\theta$-term in an open-system NL$\sigma$M. Using a Keldysh-Lindblad framework, they derive the effective action for a dephasing QAH system and demonstrate a two-parameter RG flow in $(\sigma_{xx},\sigma_{xy})$ with a quantum Hall critical line at $|\theta|=\pi$, yielding a finite $\sigma_{xx}^*$ at criticality. Boundary-driven simulations of the Qi-Wu-Zhang lattice confirm the predicted phase structure and provide a practical protocol to extract Hall transports from potential maps. The work reframes plateau physics in open platforms and cold atoms, offering a self-contained route to Hall criticality via dephasing and guiding experimental diagnostics of topological transport in nonunitary systems.

Abstract

Conventional wisdom holds that static disorder is indispensable to the integer quantum Hall effect, underpinning both quantized plateaus and the plateau-plateau transition. We show that pure dephasing, without elastic disorder, is sufficient to generate the same $θ$ driven criticality. Starting from a Keldysh formulation, we derive an open system nonlinear $σ$ model (NL$σ$M) for class A with a topological $θ$ term but no Cooperon sector, and we demonstrate that nonperturbative instantons still govern a two parameter flow of $(σ_{xx},σ_{xy})$. Evaluating $θ$ in a dephasing quantum anomalous Hall setting, we predict a quantum Hall critical point at $σ_{xy}=1/2$ with finite $σ_{xx}$ the hallmark of the integer quantum Hall universality class realized without Anderson localization. Boundary driven simulations of the Qi_Wu_Zhang model with local dephasing confirm this prediction and provide an experimentally aligned protocol to extract $(σ_{xx},σ_{xy})$ from Hall potential maps. By establishing dephasing as a self contained route to Hall criticality, our framework reframes plateau physics in open solid state and cold atom platforms and offers practical diagnostics for topological transport in nonunitary matter.

Figures (6)

• Figure 1: (a) The trajectories of two parameter renormalization group flow of dephasing quantum anomalous hall systems, where the numerical constant $D_0=2$. (b) The phase diagram of dephasing Qi-Wu-Zhang model for $E = 0$, in which there are two phases, denoted as $|\theta|>\pi$ and $|\theta|<\pi$ correspondingly, where $\gamma$ is the rate of dephasing, $u$ is the staggering potential of the model, $\theta = \theta_1 + \theta_2$ is the topological angle. We observed a dephasing-indeced quantum phase transition when the band topology is nontrivial (that $|u|<2$), where the quantum Hall critical points are those $|\theta|=\pi$ (mengta-solid line).
• Figure 2: (a) The contour plot of chemical potential $\mu(x,y)$ and the current distribution in the steady-state of the boundary driven Qi-Wu-Zhang model with dephasing, that the system is in open boundary conditions and the source is marked in yellow while drain is marked in blue, where $\gamma= 0.2$, $u=0.6$ and $L=12$. The coupling between the system and source/drain is set to a constant $\Gamma=0.1$. (b) The trajectories of two parameters $(\sigma_{xy},\lambda)$ renormalization group flow, it obvious that $\beta_\lambda<0$ for $\sigma_{xy}\leq1/2$, while $\beta_\lambda>0$ can only be satisfied when $\sigma_{xy}> 1/2$, where the numerical constant $D_0=2$. (c) The inverse $\beta$-function $\beta_\lambda^{-1}$ versus $u$ for $\gamma=0.1, 0.15, 0.2, 0.4$, (d) The inverse $\beta$-function $\beta_\lambda^{-1}$ versus $\gamma$ for $u=0.5, 0.7, 1.5, 2.1$, where $\beta_\lambda$ is the fitting parameter of the function $\lambda(L) = \beta_\lambda \ln L + \alpha$ for $L = 8, 12, 16, 20$.
• Figure 3: The phase diagram of dephasing Qi-Wu-Zhang model for $E = 0.5$, in which there are two phases, denoted as $|\theta|>\pi$ and $|\theta|<\pi$ correspondingly, where $\gamma$ is the rate of dephasing, $u$ is the staggering potential of the model, $\theta = \theta_1 + \theta_2$ is the topological angle. Where the quantum Hall critical points are those $|\theta|=\pi$ (mengta-solid line), and the black dotted line are critical points for $E = 0$.
• Figure 4: The contour plot of steady-state chemical potential $\mu(x,y)$ for $u=0.6$ (the first column) and $2.4$ (the second column), three values of dephasing rate are studied, $\gamma=0.05$ (the first line), $0.1$ (the second line), and $0.3$ (the third line). Where $\Gamma = 0.1$, source/drain is marked in yellow/blue, the green region at the center of sample where $L/4< x/y \leq 3L/4$ are selected to evaluate $\mu_x$ and $\mu_y$.
• Figure 5: Finite scaling of $\lambda$ for $\gamma = 0.1, 0.15, 0.2, 0.4$, where triangles mark the numerical value of $\lambda$ for each values of $u$, and the solid lines are the corresponding fitting curve that $\lambda(L) = \beta_\lambda \ln L +\alpha$.