Related papers: Parafermionic phases with symmetry-breaking and to…
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…
We discuss a one-dimensional fermionic model with a generalized $\mathbb{Z}_{N}$ even multiplet pairing extending Kitaev $\mathbb{Z}_{2}$ chain. The system shares many features with models believed to host localized edge parafermions, the…
We concisely review the recent evolution in the study of parafermions -- exotic emergent excitations that generalize Majorana fermions and similarly underpin a host of novel phenomena. First we illustrate the intimate connection between…
Recently, it has been proposed that exotic one-dimensional phases can be realized by gapping out the edge states of a fractional topological insulator. The low-energy edge degrees of freedom are described by a chain of coupled parafermions.…
We study the topological classification of parafermionic chains in the presence of a modified time reversal symmetry that satisfies ${\cal T}^2=1 $. Such chains can be realized in one dimensional structures embedded in fractionalized two…
Parafermions are a natural generalization of Majorana fermions. We consider a breathing Kagome lattice with complex hoppings by imposing $\mathbb{Z}_{3}$ clock symmetry in the complex energy plane. It is a non-Hermitian generalization of…
Parafermion zero modes are generalizations of Majorana modes that underlie comparatively rich non-Abelian-anyon properties. We introduce exact mappings that connect parafermion chains, which can emerge in two-dimensional fractionalized…
We classify the gapped phases of Z_N parafermions in one dimension and construct a representative of each phase. Even in the absence of additional symmetries besides parafermionic parity, parafermions may be realized in a variety of phases,…
One-dimensional topological phases can host localized zero-energy modes that enable high-fidelity storage and manipulation of quantum information. Majorana fermion chains support a classic example of such a phase, having zero modes that…
We study a chain of ferromagnetic nano-particles or ferromagnetic molecule/atoms on a substrate of fully gapped superconductors. We find that under quite realistic conditions, the fermion-number-parity symmetry $Z_2^f$ can spontaneously…
A sign of topological order in a gapped one-dimensional quantum chain is the existence of edge zero modes. These occur in the Z_2-invariant Ising/Majorana chain, where they can be understood using free-fermion techniques. Here I discuss…
Topological phases which host Majorana fermions can not be identified via local order parameters. We give simple nonlocal order parameters to distinguish quasi-one-dimensional (1D) topological superconductors of spinless fermions, for any…
Topological orders and associated topological protected excitations satisfying non-Abelian statistics have been widely explored in various platforms. The $\mathbb{Z}_3$ parafermions are regarded as the most natural generation of the…
Topological phases of matter remain a focus of interest due to their unique properties -- fractionalisation, ground state degeneracy, and exotic excitations. While some of these properties can occur in systems of free fermions, their…
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 are generalizations of Majorana fermions that may appear in interacting topological systems. They are known to be powerful building blocks of topological quantum computers. Existing proposals for realizations of parafermions…
For systems of lattice anyons like Majorana and parafermions, the unconventional quantum statistics determines a set of global symmetries (e.g., fermion parity for Majoranas) admitting no relevant perturbations. Any operator that breaks…
It has recently been realized that zero modes with projective non-Abelian statistics, generalizing the notion of Majorana bound states, may exist at the interface between a superconductor and a ferromagnet along the edge of a fractional…
We show that the single-mode parafermionic type systems possess supersymmetry, which is based on the symmetry of characteristic functions of the parafermions related to the generalized deformed oscillator of Daskaloyannis et al. The…
We study the properties of one-dimensional topological superconductors under the influence of generic boundary conditions mimicking the coupling with external environments. We identify a general four-parameters classification of the…