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We study the dynamics of the quantum Ising chain following a zero-temperaturequench of the transverse field strength. Focusing on the behavior of two-pointspin correlation functions, we show that the correlators of the order parameterdisplay an effective asymptotic thermal behavior, i.e., they decayexponentially to zero, with a phase coherence rate and a correlation lengthdictated by the equilibrium law with an effective temperature set by the energyof the initial state. On the contrary, the two-point correlation functions ofthe transverse magnetization or the density-of-kinks operator decay as apower-law and do not exhibit thermal behavior. We argue that the differentbehavior is linked to the locality of the corresponding operator with respectto the quasi-particles of the model: non-local operators, such as the orderparameter, behave thermally, while local ones do not. We study which featuresof the two-point correlators are a consequence of the integrability of themodel by analizing their robustness with respect to a sufficiently strongintegrability-breaking term.

Long time dynamics following a quench in an integrable quantum spin chain: local versus non-local operators and effective thermal behavior