Ising analogues of quantum spin chains with multispin interactions

Understand

A new family of free fermionic quantum spin chains with multispin interactions was recently introduced.

• Here we show that it is possible to build standard quantum Ising chains -- but with inhomogeneous couplings -- which have the same spectra as the novel spin chains with multispin interactions.
• The Ising models are obtained by associating an antisymmetric tridiagonal matrix to the polynomials that characterize the quasienergies of the system via a modified Euclidean algorithm.
• For the simplest non-trivial case, corresponding to the Fendley model, the phase diagram of the inhomogeneous Ising model is investigated numerically.