Evolution of quantum geometric tensor of 1D periodic systems after a quench

TL;DR

This paper studies how the quantum geometric tensor evolves after a sudden change in Hamiltonian in 1D systems, linking it to physical observables and demonstrating its use as a probe for nonequilibrium dynamics.

Contribution

It introduces a detailed analysis of the post-quench quantum geometric tensor in 1D systems, connecting it to physical quantities like Berry connection and energy variance, with numerical validation using the SSH model.

Findings

Post-quench QGT components relate to physical observables.

QGT evolution reflects wavepacket dispersion and energy variance.

Numerical results confirm QGT's role as a probe for nonequilibrium phenomena.

Abstract

We investigate the post-quench dynamics of the quantum geometric tensor (QGT) of 1D periodic systems with a suddenly changed Hamiltonian. 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 (SSH) model as an example, our numerical results of different quenches confirm that the post-quench QGT is governed by physical quantities and local geometric objects from the initial state and post-quench 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.