  When a spatially localized stress is applied to a growing one-dimensional
interface, the interface deforms. This deformation is described by the
effective surface tension representing the stiffness of the interface. We
present that the stiffness exhibits divergent behavior in the large system size
limit for a growing interface with thermal noise, which has never been observed
for equilibrium interfaces. Furthermore, by connecting the effective surface
tension with a space-time correlation function, we elucidate the mechanism that
anomalous dynamical fluctuations lead to divergent stiffness.
