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We discuss the emergence of nonadiabatic behavior in the dynamics of theorder parameter in a low-dimensional quantum many-body system subject to alinear ramp of one of its parameters. While performing a ramp within a gappedphase seems to be the most favorable situation for adiabaticity, we show thatsuch a change leads eventually to the disruption of the order, no matter howslowly the ramp is performed. We show this in detail by studying the dynamicsof the one-dimensional quantum Ising model subject to linear variation of thetransverse magnetic field within the ferromagnetic phase, and then propose ageneral argument applicable to other systems.

Nonadiabatic stationary behaviour in a driven low-dimensional gapped system