# 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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