Particles and collective behavior

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.