Understanding the interplay between the topological nature and the symmetryproperty of interacting systems has been a central matter of condensed matterphysics in recent years. In this Letter, we establish nonperturbativeconstraints on the quantized Hall conductance of many-body systems witharbitrary interactions. Our results allow one to readily determine themany-body Chern number modulo a certain integer without performing anyintegrals, solely based on the rotation eigenvalues and the average particledensity of the many-body ground state.
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