  In this work, we explore the interplay of confinement, string breaking and
entanglement asymmetry on a 1D quantum Ising chain. We consider the evolution
of an initial domain wall and show that, surprisingly, while the introduction
of confinement through a longitudinal field typically suppresses entanglement,
it can also serve to increase it beyond a bound set for free particles. Our
model can be tuned to conserve the number of domain walls, which gives an
opportunity to explore entanglement asymmetry associated with link variables.
We study two approaches to deal with the non-locality of the link variables,
either directly or following a Kramers-Wannier transformation that maps bond
variables (kinks) to site variables (spins). We develop a numerical procedure
for computing the asymmetry using tensor network methods and use it to
demonstrate the different types of entanglement and entanglement asymmetry.
