Related papers: First quantization of braided Majorana fermions
Let $\hat{\frak g}$ be an untwisted affine Kac-Moody algebra. The quantum group $U_h(\hat{\frak g})$ (over $\mathbb{C}[[h]]$) is known to be a quasitriangular Hopf algebra: in particular, it has a universal $ R $--matrix, which yields an $…
We propose a scheme in semiconducting quantum nanowires structure to demonstrate the non-Abelian statistics for Majorana fermions in terms of braid group. The Majorana fermions are localized at the endpoints of semiconducting wires, which…
In this paper we outline an approach to calculus over quasitriangular Hopf algebras. We study differential operators in the framework of monoidal categories equipped with a braiding or symmetry. To be more concrete, we choose as an example…
We introduce a quasitriangular Hopf algebra or `quantum group' $U(B)$, the {\em double-bosonisation}, associated to every braided group $B$ in the category of $H$-modules over a quasitriangular Hopf algebra $H$, such that $B$ appears as the…
Majorana fermions are long-sought exotic particles that are their own antiparticles. Here we propose to utilize superconducting circuits to construct two superconducting-qubit arrays where Majorana modes can occur. A so-called Majorana…
We study super-braided Hopf algebras $\Lambda$ primitively generated by finite-dimensional right crossed (or Drinfeld-Radford-Yetter) modules $\Lambda^1$ over a Hopf algebra $A$ which are quotients of the augmentation ideal $A^+$ under…
This is an introduction for algebraists to the theory of algebras and Hopf algebras in braided categories. Such objects generalise super-algebras and super-Hopf algebras, aswell as colour-Lie algebras. Basic facts about braided categories C…
We classify braided tensor categories over C of exponential growth which are quasisymmetric, i.e., the squared braiding is the identity on the product of any two simple objects. This generalizes the classification results of Deligne on…
This is a survey on pointed Hopf algebras over algebraically closed fields of characteristic 0. We propose to classify pointed Hopf algebras $A$ by first determining the graded Hopf algebra $\gr A$ associated to the coradical filtration of…
We present a theoretical framework that integrates Majorana's infinite-component relativistic equation within the algebraic structure of paraparticles through the minimal nontrivial $\mathbb{Z}_2 \times \mathbb{Z}_2$--graded Lie algebras…
We consider universal statistical properties of systems that are characterized by phase states with macroscopic degeneracy of the ground state. A possible topological order in such systems is described by non-linear discrete equations. We…
In this talk I discuss a recently developed "Unfolded Quantization Framework". It allows to introduce a Hamiltonian Second Quantization based on a Hopf algebra endowed with a coproduct satisfying, for the Hamiltonian, the physical…
Parafermions are non-Abelian anyons which generalize Majorana fermions and hold great promise for topological quantum computation. We study the braiding of $\mathbb{Z}_{2n}$ parafermions which have been predicted to emerge as bound states…
Certain one-dimensional Fermi systems have an energy gap in the bulk spectrum while boundary states are described by one Majorana operator per boundary point. A finite system of length $L$ possesses two ground states with an energy…
We study a possibility to define the (braided) comultiplication for the GLq(N)-covariant differential complexes on some quantum spaces. We discover such `differential bialgebras' (and Hopf algebras) on the bosonic and fermionic quantum…
Non-Abelian quasiparticles have been predicted to exist in a variety of condensed matter systems. Their defining property is that an adiabatic braid between two of them results in a nontrivial change of the quantum state of the system. To…
Demonstration of a nontrivial result of quasiparticle exchange (or braiding) is usually considered the definitive proof of a topological phase with nonabelian excitations, such as Majorana bound states (MBSs). However, in finite systems…
We study the non-abelian statistics characterizing systems where counter-propagating gapless modes on the edges of fractional quantum Hall states are gapped by proximity-coupling to superconductors and ferromagnets. The most transparent…
A braided Frobenius algebra is a Frobenius algebra with braiding that commutes with the operations, that are related to diagrams of compact surfaces with boundary expressed as ribbon graphs. A heap is a ternary operation exemplified by a…
We propose the concept of a device based on a square-shaped sample of a two-dimensional second-order topological helical superconductor which hosts two zero-dimensional Majorana quasiparticles at the corners. The two zero-energy modes rely…