Topological order in a correlated Chern insulator

We study the effect of electron-electron interactions in a spinful Chern insulator. For weak on-site repulsive interactions at half-filling, the system is a weakly correlated Chern insulator adiabatically connected to the noninteracting ground state, while in the limit of infinitely strong repulsion the system is described by an effective spin model recently predicted to exhibit a chiral spin liquid ground state. In the regime of large but finite repulsion, we find an exotic gapped phase with characteristics partaking of both the noninteracting Chern insulator and the chiral spin liquid. This phase has an integer quantized Hall conductivity $2e^2/h$ and quasiparticles with electric charges that are integer multiples of the electron charge $e$, but the ground state on the torus is fourfold degenerate and quasiparticles have fractional statistics. We discuss how these unusual properties affect the outcome of a charge pumping experiment and, by deriving the topological field theory, elucidate that the topological order is of the exotic ${\mathbb{Z}}_2$ double-semion type.

Figure 1

(a) Topological ground state degeneracy in the CI*: energy difference between two different global ${\mathbb{Z}}_2$ flux configurations on finite tori with $L\times L$ unit cells. The dashed curve is a fit corresponding to an exponential dependence on $L$. (b) Spin-charge separation in the CI*: a single hole splits into two anyons, a charge $-e$ particle without spin (quasiparticle $l_1$ in Table ), and a neutral particle with spin 1/2 (bound state of quasiparticle $l_1$ and $l_4$). Results are obtained from self-consistent calculations on the honeycomb lattice model with Hubbard $U=26t$ and $t_2=it$.

Figure 2

(a) Charge pumping between two hexagons threaded by external fluxes $\varphi$ and $-\varphi$ and separated by $D$ unit cells. (b) Transferred charge as a function of $\varphi$ in the CI (dashed curve) and the CI* (blue circles), in units of the flux quantum ${\varphi }_0=h/e$ for $D=8$. The shaded area denotes the parameter range where a spontaneously created ${\mathbb{Z}}_2$ vortex pair (semion/antisemion) partly screens the external fluxes.