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AbstractTopological spaces have numerous applications for quantum matter with protected chiral edge modes related to an integer-valued Chern number, which also characterizes the global response of a spin-1/2 particle to a magnetic field. Such spin-1/2 models can also describe topological Bloch bands in lattice Hamiltonians. Here we introduce interactions in a system of spin-1/2s to reveal a class of topological states with rational-valued Chern numbers for each spin providing a geometrical anddoi:10.1038/s42005-021-00641-0 fatcat:udi4vj7yu5fd7hu5h4nya4xxny