We study conventional and out-of-time-ordered correlators (OTOCs) for a wide variety of transverse field Ising chains: classical and quantum, clean and disordered, and integrable and generic. The setting we consider is that of a quantum quench. We find a remarkably rich phenomenology, ranging from stable periodic signals to ones decaying with varying rates. This variety is due to a complex interplay of constraints on thermalization imposed by integrability and symmetry. A process we term dynamical domain wall relocalization provides a long-lived signal in the clean, integrable case, which can be degraded by the addition of disorder even without interactions. Our results shed light on a proposal to use an OTOC as a dynamical diagnostic of a quantum phase more powerful than a standard observable.
@article{arxiv.2207.09502,
title = {Dynamical correlations and domain wall relocalization in transverse field Ising chains},
author = {Philippe Suchsland and Benoît Douçot and Vedika Khemani and Roderich Moessner},
journal= {arXiv preprint arXiv:2207.09502},
year = {2025}
}