  We study the explicit breaking of a $SU(2)$ symmetry to a $U(1)$ subgroup
employing the entanglement asymmetry, a recently introduced observable that
measures how much symmetries are broken in a part of extended quantum systems.
We consider as specific model the critical XXZ spin chain, which breaks the
$SU(2)$ symmetry of spin rotations except at the isotropic point, and is
described by the massless compact boson in the continuum limit. We examine the
$U(1)$ subgroup of $SU(2)$ that is broken outside the isotropic point by
applying conformal perturbation theory, which we complement with numerical
simulations on the lattice. We also analyse the entanglement asymmetry of the
full $SU(2)$ group. By relying on very generic scaling arguments, we derive an
asymptotic expression for it.
