Kramers--Wannier intertwiner

For a one-dimensional periodic spin chain, a Kramers--Wannier intertwiner maps vertex spins in the $X$ basis to edge domain walls. It obeys $D(X_i{X}_{i+1})={\tilde{Z}}_{i+1/2}D$ and $D{Z}_i=({\tilde{X}}_{i-1/2}{\tilde{X}}_{i+1/2})D$ and identifies spin configurations related by the global ${\mathbb{Z}}_2$ symmetry.