  We study the dynamics of an interacting quantum spin chain under the
application of a linearly increasing field. This model exhibits a type of
localization known as Stark many-body localization. The dynamics shows a strong
dependence on the initial conditions, indicating that the system violates the
conventional ("strong") eigenstate thermalization hypothesis at any finite
gradient of the field. This is contrary to reports of a numerically observed
ergodic phase. Therefore, the localization is crucially distinct from
disorder-driven many-body localization, in agreement with recent predictions on
the basis of localization via Hilbert-space shattering.
