Survival and Detection of Symmetry-Protected Topology in Loop Quenches

Abstract: We explore a class of dynamical protocols - that we term loop quenches - which are tailored for the study of symmetry-protected topological (SPT) systems. In loop quenches, SPT phases can survive even out of equilibrium, thus evading the dynamical violation of their protecting symmetry. Moreover, we demonstrate that employing loop quenches allows to detect the equilibrium topology via measurable dynamical quantities. Focusing on chiral-SPT phases, we introduce the Loschmidt chirality amplitude as a key observable that encodes the equilibrium topological invariant. We exemplify our method for chiral-symmetric one-dimensional two-band insulators and propose a pump-probe measurement scheme which allows to extract the amplitude in question. Our protocol uncovers a direct dynamical signature of SPT phases and, most importantly, paves the way for a general diagnostic framework that can be extended to other symmetry classes and dimensions.