We investigate the postquench dynamics of the quantum geometric tensor (QGT) of one-dimensional periodic systems with a suddenly changed Hamiltonian and make connections to physical observables. The diagonal component with respect to the crystal momentum gives a metric corresponding to the variance of the time-evolved position, and its coefficient of the quadratic term in time is the group-velocity variance, signaling ballistic wavepacket dispersion. The other diagonal QGT component with respect to time reveals the energy variance. The off-diagonal QGT component features a real part as a covariance and an imaginary part representing a quench-induced curvature. Using the Su-Schrieffer-Heeger model as an example, our numerical results of different quenches confirm that the postquench QGT is governed by physical quantities and local geometric objects from the initial state and postquench bands, such as the Berry connection, group velocities, and energy variance. Furthermore, the connections between the QGT and physical observables suggest the QGT as a comprehensive probe for nonequilibrium phenomena.

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• Geometric & topological phases
• 1-dimensional systems
• Su-Schrieffer-Heeger model