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Topological phases of parafermions: a model with exactly-solvable ground states
Parafermions are emergent excitations that generalize Majorana fermions and
can also realize topological order. In this paper we present a non-trivial and
quasi-exactly-solvable model for a chain of parafermions in a topological
phase. We compute and characterize the ground-state wave-functions, which are
matrix-product states and have a particularly elegant interpretation in terms
of Fock parafermions, reflecting the factorized nature of the ground states.
Using these wavefunctions, we demonstrate analytically several signatures of
topological order. Our study provides a starting point for the non-approximate
study of topological one-dimensional parafermionic chains with
spatial-inversion and time-reversal symmetry in the absence of strong edge
modes.Comment: 6 + 9 pages, 3 figure
Non-topological parafermions in a one-dimensional fermionic model with even multiplet pairing
We discuss a one-dimensional fermionic model with a generalized
even multiplet pairing extending Kitaev
chain. The system shares many features with models believed to host localized
edge parafermions, the most prominent being a similar bosonized Hamiltonian and
a symmetry enforcing an -fold degenerate ground state
robust to certain disorder. Interestingly, we show that the system supports a
pair of parafermions but they are non-local 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 the dual of an
fractional Josephson effect highlighting the presence of parafermions.Comment: 12 pages, 3 figure
Prólogo
Prólogo del libro: Pérez Marín, M. Dolores (2010), Paula Montal Fornés. Biografía, espiritualidad y carisma. Córdoba, Servicio de Publicaciones de la Universidad, 2010.-- Este documento se ha editado con el permiso del titular de los Derechos, el Servicio de Publicaciones de la Universidad de Córdoba
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