Conformally invariant free-parafermionic quantum chains with multispin interactions

We calculate the spectral properties of two related families of non-Hermitian free-particle quantum chains with N-multispin interactions (N=2,3,...). The first family have a Z(N) symmetry and are described by free parafermions. The second have a U(1) symmetry and are generalizations of XX quantum chains described by free fermions. The eigenspectra of both free-particle families are formed by the combination of the same pseudo-energies. The models have a multicritical point with dynamical critical exponent z=1. The finite-size behavior of their eigenspectra, as well as the entanglement properties of their ground-state wave function, indicate the models are conformally invariant. The models with open and periodic boundary conditions show quite distinct physics due to their non-Hermiticity. The models defined with open boundaries have a single conformal invariant phase, while the XX multispin models show multiple phases with distinct conformal central charges in the periodic case.