Interaction-enhanced integer quantum Hall effect in disordered systems

We study transport properties and topological phase transition in two-dimensional interacting disordered systems. We derive the Hall conductance within real-space dynamical mean-field theory, which is quantized and serves as a topological invariant for insulators, even when the energy gap is closed by localized states. In the spinful Harper-Hofstadter-Hatsugai model, in the trivial insulator regime, we find that the repulsive on-site interaction can assist weak disorder to induce the integer quantum Hall effect, while in the topologically nontrivial regime, it impedes Anderson localization. Generally, the interaction broadens the regime of the topological phase in the disordered system.

Figure 1

The density plot (upper) and error list plot (lower) of $\chi /2$ as a function of disorder strength and interaction strength, for $\mathrm{\Lambda }=0$. The inset shows the disorder strength where $\chi /2=0.5$, as a function of $1/L^2$ and for different interaction strengths, where $L^2$ is the size of the supercell with $n_x=n_y=L$ (from left to right: $L=44,28,24,14,10$).

Figure 2

The density plot (upper) and error list plot (lower) of $\chi /2$ as a function of disorder strength and interaction strength, for $\mathrm{\Lambda }=2.2t$. The dashed black line shown in the upper figure is given by the EMT; see Eq. (30). The inset in the lower figure shows how the value of $\chi /2$ depends on the size of supercell, where the blue (red) lines are for $U=0.0t\left(0.5t\right)$.