Related papers: Changing anyonic ground degeneracy with engineered…
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…
The Kitaev chain model exhibits topological order that manifests as topological degeneracy, Majorana edge modes and $Z_{2}$ topological invariance of the abulk spectrum. This model can be obtained from a transverse field Ising model(TFIM)…
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…
Parafermions are Zn generalisations of Majorana quasiparticles, with fractional non-Abelian statistics. They can be used to encode topological qudits and perform Clifford operations by their braiding. We study the simplest case of the Z3…
Parafermions are the simplest generalizations of Majorana fermions that realize topological order. We propose a less restrictive notion of topological order in 1D open chains, which generalizes the seminal work by Fendley [J. Stat. Mech.,…
Parafermions modes are non-Abelian anyons which were introduced as $\mathbb{Z}_N$ generalizations of $\mathbb{Z}_2$ Majorana states. In particular, $\mathbb{Z}_3$ parafermions can be used to produce Fibonacci anyons, laying a path towards…
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…
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 degeneracy is the degeneracy of the ground states in a many-body system in the large-system-size limit. Topological degeneracy cannot be lifted by any local perturbation of the Hamiltonian. The topological degeneracies on closed…
Topologically ordered quantum systems have robust physical properties, such as quasiparticle statistics and ground-state degeneracy, which do not depend on the microscopic details of the Hamiltonian. We consider topological phase…
Exotic topologically protected zero modes with parafermionic statistics (also called fractionalized Majorana modes) have been proposed to emerge in devices fabricated from a fractional quantum Hall system and a superconductor. The…
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…
Non-Abelian anyons--particles whose exchange noncommutatively transforms a system's quantum state--are widely sought for the exotic fundamental physics they harbor as well as for quantum computing applications. There now exist numerous…
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…
We study the phase diagrams of a family of 3D "Walker-Wang" type lattice models, which are not topologically ordered but have deconfined anyonic excitations confined to their surfaces. We add a perturbation (analogous to that which drives…
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…
Parafermions, which can be viewed as a fractionalized version of Majorana modes, exhibit profound non-Abelian statistics and emerge in topologically ordered systems, while their realization in experiment has been challenging. Here we…
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 analyse an exactly solvable spin-$1/2$ chain which is a generalised version of Kitaev's honeycomb model. We show that every state of the system has a $2^{N/4}$ fold degeneracy, where $N$ is the number of sites. We present analytic…
The Haldane phase represents one of the most important symmetry protected states in modern physics. This state can be realized using spin-1 and spin-${1\over 2}$ Heisenberg models and bosonic particles. Here we explore the emergent Haldane…