  Driving a homogeneous system across a quantum phase transition in a
quench-time $\tau_Q$ generates excitations on wavelengths longer than the
Kibble-Zurek (KZ) length $\hat\xi\propto\tau_Q^{\nu/(1+z\nu)}$ within the KZ
time window $\hat t\propto\tau_Q^{z\nu/(1+z\nu)}$, where $z$ and $\nu$ are the
critical exponents. Quenches designed with local time-dependent inhomogeneity
can introduce a gap in the spectrum. For a variety of setups with short-range
interactions, they have been shown to suppress excitations if the spatial
velocity of the inhomogenous front is below the characteristic KZ velocity
$\hat v \propto \hat\xi/\hat t$. Ising-like models with long-range interactions
can have no sonic horizon, spreading information instantaneously across the
system. Usually, this should imply that inhomogenous transitions will render
the dynamics adiabatic regardless of the front velocity. However, we show that
we get an adiabatic transition with no defects only when the inhomogeneous
front moves slower than a characteristic crossover velocity $\tilde v \propto
\theta^{(z-1)\nu/(1+\nu)}$, where $\theta$ is the slope of the inhomogeneous
front at the critical point. The existence of this crossover velocity and
adiabaticity of the model is a consequence of the energy gap in the
quasiparticle spectrum that is opened by the inhomogeneity. This effect can be
employed for efficient adiabatic quantum state preparation in systems with
long-range interactions.
