We consider rotating finite-size vortex arrays in Bose-Einstein condensates that are confined by cylindrically symmetric external potentials. We show that such systems possess two exact Nambu-Goldstone zero modes associated with two spontaneously broken continuous symmetries of the system. We verify our analytical result via direct numerical diagonalizations of the Bogoliubov–de Gennes equations. We conclude by comparing rotating vortex lattices in superfluids to supersolids and discrete time crystals.

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• Bose-Einstein condensates
• Vortex lattices