Synthetic ladders pierced by a magnetic field realized with one-dimensional alkaline-earth(-like) fermionic gases represent a promising environment for the investigation of quantum-Hall physics with ultracold atoms. We unveil the existence of a hierarchy of insulating and conducting states which appear at fractional filling factors by means of both analytical and numerical methods based on the density-matrix renormalization group algorithm. Analogously to the original quantum Hall effect, we show that such states can be exploited for constructing a topological Thouless pump where the charge transported after one cycle is quantized to fractional values and demonstrate this behavior with a full many-body time-dependent calculation. We conclude with some results on Laughlin-like states in both fermionic and bosonic systems.
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