Free-parafermionic Z(N) and free-fermionic XY quantum chains.

@article{Alcaraz2021FreeparafermionicZA,
  title={Free-parafermionic Z(N) and free-fermionic XY quantum chains.},
  author={F. C. Alcaraz and Rodrigo A Pimenta},
  journal={Physical review. E},
  year={2021},
  volume={104 5-1},
  pages={
          054121
        }
}
The relationship between the eigenspectrum of Ising and XY quantum chains is well known. Although the Ising model has a Z(2) symmetry and the XY model a U(1) symmetry, both models are described in terms of free-fermionic quasiparticles. The fermionic quasienergies are obtained by means of a Jordan-Wigner transformation. On the other hand, there exists in the literature a huge family of Z(N) quantum chains whose eigenspectra, for N>2, are given in terms of free parafermions, and they are not… 
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