  We report some nonsmooth dynamics of a Bloch state in a one-dimensional tight
binding model with the periodic boundary condition. After a sudden change of
the potential of an arbitrary site, quantities like the survival probability of
the particle in the initial Bloch state show cusps periodically, with the
period being the Heisenberg time associated with the energy spectrum. This
phenomenon is a \emph{nonperturbative} counterpart of the nonsmooth dynamics
observed previously (Zhang and Haque, arXiv:1404.4280) in a periodically driven
tight binding model. Underlying the cusps is an exactly solvable model, which
consists of equally spaced levels extending from $-\infty$ to $+\infty $,
between which two arbitrary levels are coupled to each other by the same
strength.
