Free fermionic and parafermionic multispin quantum chains with non-homogeneous interacting ranges

A large family of multispin interacting one-dimensional quantum spin models with $Z(N)$ symmetry and a free-particle eigenspectra are known in the literature. They are free-fermionic ($N=2$) and free-parafermionic ($N\geq 2$) quantum chains. The essential ingredient that implies the free-particle sp