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Related papers: Non-Abelian Fusion Rules from an Abelian System

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We propose a scheme to probe the non-Abelian statistics of the collective anyonic excitation in Kitaev's honeycomb model with cold atoms in an optical lattice. The generation of the anyonic excitation can be realized by simple rotating…

Quantum Physics · Physics 2013-05-31 Sheng Liu , Zheng-Yuan Xue

Motivated by the possibility of creating non-Abelian fields using cold atoms in optical lattices, we explore the richness and complexity of non-interacting two-dimensional electron gases (2DEGs) in a lattice, subjected to such fields. In…

Mesoscale and Nanoscale Physics · Physics 2008-04-17 Indubala I. Satija , Daniel C. Dakin , J. Y. Vaishnav , Charles W. Clark

Topological quantum states of matter, both Abelian and non-Abelian, are characterized by excitations whose wavefunctions undergo non-trivial statistical transformations as one excitation is moved (braided) around another. Topological…

Quantum Physics · Physics 2009-11-13 Chuanwei Zhang , V. W. Scarola , Sumanta Tewari , S. Das Sarma

It is well known that the abelian $Z_2$ anyonic model (toric code) can be realized on a highly entangled two-dimensional spin lattice, where the anyons are quasiparticles located at the endpoints of string-like concatenations of Pauli…

Statistical Mechanics · Physics 2008-11-05 James R. Wootton , Ville Lahtinen , Zhenghan Wang , Jiannis K. Pachos

We study two families of quantum models which have been used previously to investigate the effect of topological symmetries in one-dimensional correlated matter. Various striking similarities are observed between certain $\mathbf{Z}_n$…

Statistical Mechanics · Physics 2018-02-09 Peter E. Finch , Michael Flohr , Holger Frahm

We suggest a class of two-dimensional lattice spin Hamiltonians describing non-Abelian SU(2) chiral spin liquids - spin-analogues of fractional non-Abelian quantum Hall states- with gapped bulk and gapless chiral edge excitations described…

Strongly Correlated Electrons · Physics 2017-05-03 P. Lecheminant , A. M. Tsvelik

We study the emergence of topological matter in two-dimensional systems of neutral Rydberg atoms in Ruby lattices. While Abelian anyons have been predicted in such systems, non-Abelian anyons, which would form a substrate for fault-tolerant…

Quantum Physics · Physics 2023-06-21 Nora M. Bauer , Elias Kokkas , Victor Ale , George Siopsis

Non-Abelian topological order (TO) is a coveted state of matter with remarkable properties, including quasiparticles that can remember the sequence in which they are exchanged. These anyonic excitations are promising building blocks of…

We use the moduli matrix approach to study the moduli space of 1/4 BPS kinks supported by vortices in the Higgs phase of N = 2 supersymmetric U(N) gauge theories when non-zero masses for the matter hypermultiplets are introduced. We focus…

High Energy Physics - Theory · Physics 2011-03-30 Muneto Nitta , Walter Vinci

Non-Abelian topological charges (NATCs), characterized by their noncommutative algebra, offer a framework for describing multigap topological phases beyond conventional Abelian invariants. While higher-order topological phases (HOTPs) host…

Mesoscale and Nanoscale Physics · Physics 2026-05-15 Jiaxin Pan , Longwen Zhou

Non-Abelian anyons can exist as point-like particles in two-dimensional systems, and have particle exchange statistics which are neither bosonic nor fermionic. Like in spin systems, the role of fusion (Heisenberg-like) interactions between…

Strongly Correlated Electrons · Physics 2018-08-08 Babatunde M. Ayeni , Robert N. C. Pfeifer , Gavin K. Brennen

Non-Abelian Lattice Gauge Theory in Euclidean space-time of dimension d>=2 whose gauge group is any compact Lie group is related to a Spin Foam Model by an exact strong-weak duality transformation. The group degrees of freedom are…

High Energy Physics - Lattice · Physics 2008-11-26 Hendryk Pfeiffer , Robert Oeckl

We consider a two-dimensional spin system that exhibits abelian anyonic excitations. Manipulations of these excitations enable the construction of a quantum computational model. While the one-qubit gates are performed dynamically the model…

Quantum Physics · Physics 2007-08-28 Jiannis K. Pachos

We study the collective states of interacting non-Abelian anyons that emerge in Kitaev's honeycomb lattice model. Vortex-vortex interactions are shown to lead to the lifting of the topological degeneracy and the energy is discovered to…

Mesoscale and Nanoscale Physics · Physics 2011-09-27 Ville Lahtinen

Kitaev's toric code is an exactly solvable model with $\mathbb{Z}_2$-topological order, which has potential applications in quantum computation and error correction. However, a direct experimental realization remains an open challenge.…

Quantum Physics · Physics 2021-08-23 Lukas Homeier , Christian Schweizer , Monika Aidelsburger , Arkady Fedorov , Fabian Grusdt

Lattice gauge theories are fundamental to such distinct fields as particle physics, condensed matter or quantum information theory. The recent progress in the control of artificial quantum systems already allows for studying Abelian lattice…

Quantum Physics · Physics 2021-06-30 Valentin Kasper , Torsten V. Zache , Fred Jendrzejewski , Maciej Lewenstein , Erez Zohar

Non-abelian lattice spin models with symmetry group SU(N) or U(N) can be formulated in terms of link variables which are subject to the Bianchi constraints. Using this representation we derive exact and local dual formulation for the…

High Energy Physics - Lattice · Physics 2009-11-10 O. Borisenko , V. Kushnir

We construct two-dimensional non-Abelian topologically ordered states by strongly coupling arrays of one-dimensional quantum wires via interactions. In our scheme, all charge degrees of freedom are gapped, so the construction can use either…

Strongly Correlated Electrons · Physics 2016-05-18 Po-Hao Huang , Jyong-Hao Chen , Pedro R. S. Gomes , Titus Neupert , Claudio Chamon , Christopher Mudry

Non-Abelian physics, originating from noncommutative sequences of operations, unveils novel topological degrees of freedom for advancing band theory and quantum computation. In photonics, significant efforts have been devoted to developing…

Optics · Physics 2026-02-02 Gyunghun Kim , Jensen Li , Xianji Piao , Namkyoo Park , Sunkyu Yu

The design of quantum many body systems, which have to fulfill an extensive number of constraints, appears as a formidable challenge within the field of quantum simulation. Lattice gauge theories are a particular important class of quantum…