Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Log inSign up
Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Blog
Job Board
Q3AS

© 2026 Aqora Quantum S.A.S.

TermsPrivacyLegal Notice

arXiv:hep-th/9309120 · Journal of Physics A Mathematical and General

On the class of possible non-local anyon-like operators and quantum groups

Масуд Чайчиан, R Gonzalez Felipe, C Montonen

Published Nov 7, 1993• 3 citations
arXivHTMLPDF

Abstract

We find a class of non-local operators constructed by attaching a disorder operator to fermionic degrees of freedom, which can be used to generate q-deformed algebras following the Schwinger approach. This class includes anyonic operators defined on a lattice.
DOI
10.1088/0305-4470/26/21/003

Related papers

On the class of possible nonlocal anyon-like operators and quantum groups

Масуд Чайчиан, González-Felipe, R, Montonen, Claus

We find a class of nonlocal operators constructed by attaching a disorder operator to fermionic degrees of freedom, which can be used to generate q-deformed algebras following the Schwinger approach. This class includes the recently proposed anyonic operators defined on a lattice.

•Jan 1, 1993•4 citations

Anyons and Deformed Lie Algebras

M. Frau, Alberto Lerda A, S. Sciuto

We discuss the connection between anyons (particles with fractional statistics) and deformed Lie algebras (quantum groups). After a brief review of the main properties of anyons, we present the details of the anyonic realization of all deformed classical Lie algebras in terms of anyonic oscillators. The deformation parameter of the quantum groups is directly related to the statistics parameter of the anyons. Such a realization is a direct generalization of the Schwinger construction in terms of fermions and is based on a sort of bosonization formula which yields the generators of the deformed algebra in terms of the undeformed ones. The entire procedure is well defined on two-dimensional lattices, but it can be consistently reduced also to one-dimensional chains.

arXiv:hep-th/9407161•Jul 25, 1994•2 citations

q-deformed classical Lie algebras and their anyonic realization

M Frau, M A R-Monteiro, S Sciuto

All classical Lie algebras can be realized a la Schwinger (1965) in terms of fermionic oscillators. We show that the same can be done for their q-deformed counterparts by simply replacing the fermionic oscillators with anyonic ones defined on a two-dimensional lattice. The deformation parameter q is a phase related to the anyonic statistical parameter. A crucial role in this construction is played by a sort of bosonization formula which gives the generators of the quantum algebras in terms of the undeformed ones. The entire procedure works even on one-dimensional chains; in such a case q can also be real.

arXiv:hep-th/9304108•Journal of Physics A Mathematical and General•Feb 7, 1994•9 citations

$q$-Deformed Classical Lie Algebras and their Anyonic Realization

M. Frau, Monteiro, M A, S. Sciuto

All classical Lie algebras can be realized \\`a la Schwinger in terms of fermionic oscillators. We show that the same can be done for their $q$-deformed counterparts by simply replacing the fermionic oscillators with anyonic ones defined on a two dimensional lattice. The deformation parameter $q$ is a phase related to the anyonic statistical parameter. A crucial r\\^ole in this construction is played by a sort of bosonization formula which gives the generators of the quantum algebras in terms of the underformed ones. The entire procedure works even on one dimensional chains; in such a case $q$ can also be real.

•Jan 1, 1994•7 citations

Quantum computation from fermionic anyons on a one-dimensional lattice

Allan Tosta, Daniel J. Brod, Ernesto F. Galvão

Fermionic linear optics corresponds to the dynamics of free fermions and is known to be efficiently simulable classically. We define fermionic anyon models by deforming the fermionic algebra of creation and annihilation operators, and consider the dynamics of number-preserving, quadratic Hamiltonians on these operators. We show that any such deformation results in an anyonic linear-optical model which allows for universal quantum computation.

arXiv:1812.06807•Physical Review A•Jun 27, 2019•7 citations

Non-locality of non-Abelian anyons

Gavin K. Brennen, S. Iblisdir, Jiannis K. Pachos +1 more

Entangled states of quantum systems can give rise to measurement correlations of separated observers that cannot be described by local hidden variable theories. Usually, it is assumed that entanglement between particles is generated due to some distance-dependent interaction. Yet anyonic particles in two dimensions have a nontrivial interaction that is purely topological in nature. In other words, it does not depend on the distance between two particles, but rather on their exchange history. The information encoded in anyons is inherently non-local even in the single subsystem level making the treatment of anyons non-conventional. We describe a protocol to reveal the non-locality of anyons in terms of correlations in the outcomes of measurements in two separated regions. This gives a clear operational measure of non-locality for anyonic states and it opens up the possibility to test Bell inequalities in quantum Hall liquids or spin lattices.

arXiv:0810.4319•New Journal of Physics•Oct 12, 2009•12 citations
We discuss the connection between anyons (particles with fractional statistics) and deformed Lie algebras (quantum groups). After a brief review of the main properties of anyons, we present the details of the anyonic realization of all deformed classical Lie algebras in terms of anyonic oscillators. The deformation parameter of the quantum groups is directly related to the statistics parameter of the anyons. Such a realization is a direct generalization of the Schwinger construction in terms of fermions and is based on a sort of bosonization formula which yields the generators of the deformed algebra in terms of the undeformed ones. The entire procedure is well defined on two-dimensional lattices, but it can be consistently reduced also to one-dimensional chains.
All classical Lie algebras can be realized a la Schwinger (1965) in terms of fermionic oscillators. We show that the same can be done for their q-deformed counterparts by simply replacing the fermionic oscillators with anyonic ones defined on a two-dimensional lattice. The deformation parameter q is a phase related to the anyonic statistical parameter. A crucial role in this construction is played by a sort of bosonization formula which gives the generators of the quantum algebras in terms of the undeformed ones. The entire procedure works even on one-dimensional chains; in such a case q can also be real.
qqq-Deformed Classical Lie Algebras and their Anyonic Realization
All classical Lie algebras can be realized \\`a la Schwinger in terms of fermionic oscillators. We show that the same can be done for their qqq-deformed counterparts by simply replacing the fermionic oscillators with anyonic ones defined on a two dimensional lattice. The deformation parameter qqq is a phase related to the anyonic statistical parameter. A crucial r\\^ole in this construction is played by a sort of bosonization formula which gives the generators of the quantum algebras in terms of the underformed ones. The entire procedure works even on one dimensional chains; in such a case qqq can also be real.
Entangled states of quantum systems can give rise to measurement correlations of separated observers that cannot be described by local hidden variable theories. Usually, it is assumed that entanglement between particles is generated due to some distance-dependent interaction. Yet anyonic particles in two dimensions have a nontrivial interaction that is purely topological in nature. In other words, it does not depend on the distance between two particles, but rather on their exchange history. The information encoded in anyons is inherently non-local even in the single subsystem level making the treatment of anyons non-conventional. We describe a protocol to reveal the non-locality of anyons in terms of correlations in the outcomes of measurements in two separated regions. This gives a clear operational measure of non-locality for anyonic states and it opens up the possibility to test Bell inequalities in quantum Hall liquids or spin lattices.