Archive ouverte HAL – Nontopological parafermions in a one-dimensional fermionic model with even multiplet pairing

Leonardo Mazza 1, 2 Fernando IeminiMarcello DalmonteChristophe Mora 3

Phys.Rev.B, 2018, 98 (20), pp.201109. 〈10.1103/PhysRevB.98.201109〉

We discuss a one-dimensional fermionic model with a generalized ZN even multiplet pairing extending Kitaev Z2 chain. The system shares many features with models believed to host localized edge parafermions, the most prominent being a similar bosonized Hamiltonian and a ZN symmetry enforcing an N-fold degenerate ground state robust to certain disorders. Interestingly, we show that the system supports a pair of parafermions but they are nonlocal instead of being boundary operators. As a result, the degeneracy of the ground state is only partly topological and coexists with spontaneous symmetry breaking by a (two-particle) pairing field. Each symmetry-breaking sector is shown to possess a pair of Majorana edge modes encoding the topological twofold degeneracy. Surrounded by two band insulators, the model exhibits for N=4 the dual of an 8π fractional Josephson effect highlighting the presence of parafermions.

  • 1. LPTMS - Laboratoire de Physique Théorique et Modèles Statistiques
  • 2. FRDPENS - Fédération de recherche du Département de physique de l'Ecole Normale Supérieure - ENS Paris
  • 3. LPA - Laboratoire Pierre Aigrain