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arXiv · 1802.06061

Z4 parafermions in one-dimensional fermionic lattices

Alessio Calzona·Tobias Meng·Maura Sassetti·Thomas L. Schmidt
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Abstract

Parafermions are emergent excitations which generalize Majorana fermions and are potentially relevant to topological quantum computation. Using the concept of Fock parafermions, we present a mapping between lattice $\mathbb{Z}_4$ parafermions and lattice spin-$1/2$ fermions which preserves the locality of operators with $\mathbb{Z}_4$ symmetry. Based on this mapping, we construct an exactly solvable, local, and interacting one-dimensional fermionic Hamiltonian which hosts zero-energy modes obeying parafermionic algebra. We numerically show that this parafermionic phase remains stable in a wide range of parameters, and discuss its signatures in the fermionic spectral function.

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Alessio Calzona, Tobias Meng, Maura Sassetti, Thomas L. Schmidt. 2018-02-16. Z4 parafermions in one-dimensional fermionic lattices. https://doi.org/10.1103/physrevb.98.201110

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