Operator dependence and robustness of spacetime-localized response in a quantum critical spin chain

We investigate the phenomenon of spacetime-localized response in a quantum critical spin system, with particular attention to how it depends on the spatial profile and operator content of the applied perturbation, as well as its robustness against increase of amplitude and temporal discretization. Motivated by recent theoretical proposals linking such response patterns to the anti-de Sitter/conformal field theory correspondence, we numerically analyze the real-time dynamics of the one-dimensional transverse-field Ising model at criticality using the time-evolving block decimation algorithm. We find that sharply localized and periodically recurring responses emerge only for specific types of perturbations, namely those that correspond to local density fields in the continuum limit. In contrast, perturbations involving other spin components produce conventional propagating excitations without localization. Furthermore, we demonstrate that the response remains qualitatively robust when the time-dependent perturbation is approximated by a piecewise-linear function, highlighting the practical relevance of our findings for quantum simulation platforms with limited temporal resolution. Our results clarify the operator dependence of emergent bulk-like dynamics in critical spin chains and offer guidance for probing holographic physics in experimental settings.