Free-fermionic quantum chains with inhomogeneous couplings

A new family of free-fermionic quantum spin chains with multispin interactions was recently introduced. In this work, we argue that it is possible to build quantum Ising chains with inhomogeneous couplings with the same spectrum of the multispin chains. This is done by associating an antisymmetric tridiagonal matrix to the polynomials that characterize the quasi-energies of the system via a modified Euclidean algorithm. The phase diagram of the inhomogeneous models is investigated numerically and a formula for the order parameter is conjectured. The phase diagram is characterized by gapped phases separated by critical hyperplanes with order-disorder transitions depending on the parity of the number of generators of the Hamiltonian, pointing out an underlying topological phenomena.