Related papers: Parafermionic phases with symmetry-breaking and to…
Three dimensional topological superconductors (TScs) protected by time reversal (T) symmetry are characterized by gapless Majorana cones on their surface. Free fermion phases with this symmetry (class DIII) are indexed by an integer n, of…
We propose a procedure that characterizes free-fermion or interacting multipolar higher-order topological phases via their bulk entanglement structure. To this end, we construct nested entanglement Hamiltonians by first applying an…
We develop a framework to analyze one-dimensional topological superconductors with charge conservation. In particular, we consider models with $N$ flavors of fermions and $(\mathbb{Z}_2)^N$ symmetry, associated with the conservation of the…
The effect of interactions on topological insulators and superconductors remains, to a large extent, an open problem. Here, we describe a framework for classifying phases of one-dimensional interacting fermions, focusing on spinless…
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…
In this letter we present, in a number conserving framework, a model of interacting fermions in a two-wire geometry supporting non-local zero-energy Majorana-like edge excitations. The model has an exactly solvable line, on varying the…
We extend the twisted gauge theory model of topological orders in three spatial dimensions to the case where the three spaces have two dimensional boundaries. We achieve this by systematically constructing the boundary Hamiltonians that are…
Parafermions that generalize (Majorana or usual) fermions appear as interacting quasi-particles because of their nature. Although attempts to develop models with free (non-interacting) parafermions have been undertaken, existing proposals…
In this work, we propose a modern view of the integer spin simple currents which have played a central role in discrete torsion. We reintroduce them as nonanomalous composite particles constructed from $Z_{N}$ parafermionic field theories.…
It is well known that two-dimensional fermionic systems with a nonzero Chern number must break the time reversal symmetry, manifested by the appearance of chiral edge modes on an open boundary. Such an incompatibility between topology and…
Parafermionic zero modes are a novel set of excitations displaying non-Abelian statistics somewhat richer than that of Majorana modes. These modes are predicted to occur when nearby fractional quantum Hall edge states are gapped by an…
We show that a topological superconductor made of four chains of superconducting spinless fermions characterized by four Majorana edge states can adiabatically be deformed into a trivial band insulator. To unwind this time-reversal…
Topological phases of matter are usually realized in deconfined phases of gauge theories. In this context, confined phases with strongly fluctuating gauge fields seem to be irrelevant to the physics of topological phases. For example, the…
Parafermion zero modes are exotic emergent excitations that can be considered as $\mathbb{Z}_n$ generalizations of Majorana fermions. Present in fractional quantum Hall-superconductor hybrid systems, among others, they can serve as…
Lattice models with supersymmetry are known to exhibit a variety of remarkable properties that do not exist in the relativistic models. In this paper, we introduce an interacting generalization of the Kitaev chain of Majorana fermions with…
Based on the recently established parafermionic matrix product states, we study the classification of one-dimensional gapped phases of parafermions with the time reversal (TR) symmetry satisfying $T^{2}=1$. Without extra symmetry, it has…
A preon-based composite model of the fundamental fermions is discussed, in which the fermions are bound states of smaller entities -- primitive charges (preons). The preon is regarded as a dislocation in a dual 3-dimensional manifold -- a…
We introduce a model of interacting Majorana fermions that describes a superconducting phase with a topological order characterized by the Fibonacci topological field theory. Our theory, which is based on a $SO(7)_1/(G_2)_1$ coset…
In this article we outline the historical development and key results obtained to date for free parafermionic spin chains. The concept of free parafermions provides a natural N-state generalization of free fermions, which have long…
A characteristic feature of topological systems is the presence of robust gapless edge states. In this work the effect of time-dependent perturbations on the edge states is considered. Specifically we consider perturbations that can be…