  We study solvable spin chains where either fields or couplings vary linearly
in space and create a sandwich-like structure of the ground state. We find that
the entanglement entropy between two halves of a chain varies logarithmically
with the interface width. After quenching to a homogeneous critical system, the
entropy grows logarithmically in time in the XX model, but quadratically in the
transverse Ising chain. We explain this behaviour and indicate generalizations
to other power laws.
