  We consider the XXZ spin chain with a magnetic field gradient and study the
profiles of the magnetization as well as the entanglement entropy. For a slowly
varying field it is shown that, by means of a local density approximation, the
ground-state magnetization profile can be obtained with standard Bethe ansatz
techniques. Furthermore, it is argued that the low-energy description of the
theory is given by a Luttinger liquid with slowly varying parameters. This
allows us to obtain a very good approximation of the entanglement profile using
a recently introduced technique of conformal field theory in curved spacetime.
Finally, the front dynamics is also studied after the gradient field has been
switched off, following arguments of generalized hydrodynamics for integrable
systems. While for the XX chain the hydrodynamic solution can be found
analytically, the XXZ case appears to be more complicated and the magnetization
profiles are recovered only around the edge of the front via an approximate
numerical solution.
