Free Parafermionic Spin Chains

Abstract

It has been proved that a certain Z_n generalization of the Transverse Field Ising model has a ”free” parafermionic spectrum, in the sense that the entire spectrum is found in terms of independent energy levels, with the striking feature that there are n possibilities for occupying each level. However, this proof holds only for open boundary conditions. Here, we investigate the effect of imposing periodic boundary conditions on the system.