Related papers: Stability of zero modes in parafermion chains
We prove that quantum information encoded in some topological excitations, including certain Majorana zero modes, is protected in closed systems for a time scale exponentially long in system parameters. This protection holds even at…
I explicitly construct a strong zero mode in the XYZ chain or, equivalently, Majorana wires coupled via a four-fermion interaction. The strong zero mode is an operator that pairs states in different symmetry sectors, resulting in identical…
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…
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…
The prospects for realizing a topological quantum computer have brightened since the apparent detection of Majorana fermions at the ends of semiconducting nanowires. These Majorana zero-modes persist in the presence of the strong disorder…
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.,…
Topological excitations in many-body systems are one of the paradigmatic cornerstones of modern condensed matter physics. In particular, parafermions are elusive fractional excitations potentially emerging in fractional quantum…
Experimental signatures of Majorana zero modes in a single superconducting quantum wire with spin-orbit coupling have been reported as zero bias peaks in the tunneling spectroscopy. We study whether these zero modes can persist in an array…
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…
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 show that the $\nu=8$ integer quantum Hall state can support Majorana zero modes at domain walls between its two different stable chiral edge phases without superconductivity. This is due to the existence of an edge phase that does not…
One-dimensional topological superconductors are known to host Majorana zero modes at domain walls terminating the topological phase. Their nonabelian nature allows for processing quantum information by braiding operations which are…
One promising avenue to study one-dimensional ($1$D) topological phases is to realize them in synthetic materials such as cold atomic gases. Intriguingly, it is possible to realize Majorana boundary modes in a $1$D number-conserving system…
We show that a one dimensional ultra-cold Fermi gas with Rashba-like spin orbit coupling, a Zeeman field and intrinsic attractive interactions exhibits a novel topological superfluid state, which forms in spite of total number conservation…
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 derive the zero mode solutions for a Majorana fermion in the background of a cosmic string and contrast it with the zero mode solution for a (neutral) Dirac fermion. A Majorana zero mode carries no vector or axial charge, and it cannot…
Majorana modes and fractional fermions are two types of edge zero modes appearing separately in topological superconductors and dimerized chains. Here we reveal how to harvest both types of edge modes simultaneously in an exotic chain. Such…
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…
Numerical calculations for Majorana zero modes on a one-dimensional chain are performed using the technique of block diagonalization for general parameter settings. It is found that Majorana zero modes occur near the ends of the chain and…
The remarkable properties and potential applications of Majorana fermions have led to considerable efforts in recent years to realize topological matters that host these excitations. For a number-conserving system, there have been a few…