The influence of Berry curvature on the motion of Bloch electrons is a well-established quantum geometric effect.However,the diverse collective behaviors within condensed matter systems,along with their coupling to electron dynamics,offer an even broader platform for exploring quantum geometric phenomena.In this article,we provide a concise review and outlook on the study of quantum geometric effects across several typical symmetry-breaking states,including lattice vibrations and phonons,magnetization dynamics and spin waves,Bose-Einstein condensates and quantum vortices,superconducting order parameters and quasiparticles,as well as lattice deformations and artificial gravity.
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