Global Quenches after Localised Perturbations

TL;DR

This paper studies how a single local spin flip affects the long-term dynamics of a quantum spin chain after a global quench, revealing persistent effects linked to topological properties.

Contribution

It demonstrates that local perturbations can have lasting impacts on global dynamics due to topological features, challenging assumptions of eventual translational invariance restoration.

Findings

Local spin flip influences infinite time limit behavior.

Translational invariance remains broken after the quench.

Topological properties, like semilocal charges, underlie the phenomenon.

Abstract

We investigate the effect of a single spin flip preceding a global quench between translationally invariant local Hamiltonians in spin-$\tfrac{1}{2}$ chains. The effect of the localised perturbation does not fade away however large the distance from the perturbation is. In particular, translational invariance is not restored and the infinite time limit depends on whether the spin was flipped or not. We argue that this phenomenon is more general than the particular example considered and we conjecture that it is triggered by topological properties, specifically, the existence of "semilocal charges".