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The field of quantum chaos originated in the study of spectral statistics forinteracting many-body systems, but this heritage was almost forgotten whensingle-particle systems moved into the focus. In recent years new interestemerged in many-body aspects of quantum chaos. We study a chain of interacting,kicked spins and carry out a semiclassical analysis that is capable ofidentifying all kinds of genuin many-body periodic orbits. We show that thecollective many-body periodic orbits can fully dominate the spectra in certaincases.

Collectivity and Periodic Orbits in a Chain of Interacting, Kicked Spins