Energy spectrum and critical exponents of the free parafermion Z(N) spin chain

Results are given for the ground state energy and excitation spectrum of a simple N-state Z(N) spin chain described by free parafermions. The model is non-Hermitian for N >= 3 with a real ground state energy and a complex excitation spectrum. Although having a simpler Hamiltonian than the superintegrable chiral Potts model, the model is seen to share some properties with it, e.g. the specific heat exponent alpha = 1 - 2/N and the anisotropic correlation length exponents nu(parallel to) = 1 and nu(perpendicular to) = 2/N.The work of FCA was supported in part by the Brazilian agencies FAPESP and CNPq. MTB acknowledges support from the 1000 Talent Plan and Chongqing University in China. The work of MTB has also been supported by National Natural Science Foundation of China Grant No. 11574405 and Australian Research Council Discovery Project DP130102839