Interacting Chern Insulator in Infinite Spatial Dimensions

We study a generic model of a Chern insulator supplemented by a Hubbard interaction in arbitrary even dimension $D$ and demonstrate that the model remains well defined and nontrivial in the $D\to \infty$ limit. Dynamical mean-field theory is applicable and predicts a phase diagram with a continuum of topologically different phases separating a correlated Mott insulator from the trivial band insulator. We discuss various features, such as the elusive distinction between insulating and semimetal states, which are unconventional already in the noninteracting case. Topological phases are characterized by a nonquantized Chern density replacing the Chern number as $D\to \infty$.

Figure 1

Left: band structure $\epsilon (k)={\epsilon }_{\pm }(k)$ of the $D=4$ model along straight shortest lines in the BZ connecting HSPs characterized by $n_0$. Results for different $m$, see color code. Middle: different topological phases with Chern numbers $C_D(n_0)$ (green), separated by critical $m$ values (red dots) for different $D$. Right: $U=0$ DOS on the $A$ orbitals at $m=-1.5$ for $D=\infty$. Inset: orbital polarization as function of $m$ for $D=\infty$. Nearest-neighbor hopping: $t=t^{*}/\sqrt{D}$, $t^{*}=1$ sets the energy scale.

Figure 2

$m\text{−}U$ phase diagram of the $D\to \infty$ model. The color codes the Chern density.