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Integer and Fractional Quantum Anomalous Hall Effect in a Strip of Stripes Model

We study the quantum anomalous Hall effect in a strip of stripes model coupled to a magnetic texture with zero total magnetization and in the presence of strong electron-electron interactions. A helical magnetization along the stripes and a spin-selective coupling between the stripes gives rise to a bulk gap and chiral edge modes. Depending on the ratio between the period of the magnetic structure and the Fermi wavelength, the system can exhibit the integer or fractional quantum anomalous Hall effect. In the fractional regime, the quasiparticles have fractional charges and non-trivial Abelian braid statistics.