Anyons in an exactly solved model and beyond
TLDR
In this article, a spin-1/2 system on a honeycomb lattice is studied, where the interactions between nearest neighbors are of XX, YY or ZZ type, depending on the direction of the link; different types of interactions may differ in strength.About:
This article is published in Annals of Physics.The article was published on 2006-01-01 and is currently open access. It has received 4032 citations till now. The article focuses on the topics: Anyon & Topological quantum computer.read more
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Many-Body Physics with Ultracold Gases
TL;DR: In this article, a review of recent experimental and theoretical progress concerning many-body phenomena in dilute, ultracold gases is presented, focusing on effects beyond standard weakcoupling descriptions, such as the Mott-Hubbard transition in optical lattices, strongly interacting gases in one and two dimensions, or lowest-Landau-level physics in quasi-two-dimensional gases in fast rotation.
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Non-Abelian Anyons and Topological Quantum Computation
TL;DR: In this article, the authors describe the mathematical underpinnings of topological quantum computation and the physics of the subject are addressed, using the ''ensuremath{
u}=5∕2$ fractional quantum Hall state as the archetype of a non-Abelian topological state enabling fault-tolerant quantum computation.
Non-Abelian Anyons and Topological Quantum Computation
TL;DR: In this article, the authors describe the mathematical underpinnings of topological quantum computation and the physics of the subject using the nu=5/2 fractional quantum Hall state as the archetype of a non-Abelian topological state enabling fault-tolerant quantum computation.
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Spin liquids in frustrated magnets
TL;DR: This exotic behaviour of frustrated magnets is now being uncovered in the laboratory, providing insight into the properties of spin liquids and challenges to the theoretical description of these materials.
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Classification of topological insulators and superconductors in three spatial dimensions
TL;DR: In this paper, the authors systematically studied topological phases of insulators and superconductors in three dimensions and showed that there exist topologically nontrivial (3D) topologically nonsmooth topological insulators in five out of ten symmetry classes introduced in the context of random matrix theory.
References
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Categories for the Working Mathematician
TL;DR: In this article, the authors present a table of abstractions for categories, including Axioms for Categories, Functors, Natural Transformations, and Adjoints for Preorders.
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Quantum Groups
TL;DR: In this paper, the authors introduce the theory of quantum groups with emphasis on the spectacular connections with knot theory and Drinfeld's recent fundamental contributions and present the quantum groups attached to SL2 as well as the basic concepts of the Hopf algebras.
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The resonating valence bond state in La2CuO4 and superconductivity
TL;DR: The oxide superconductors, particularly those recently discovered that are based on La2CuO4, have a set of peculiarities that suggest a common, unique mechanism: they tend in every case to occur near a metal-insulator transition into an odd-electron insulator with peculiar magnetic properties.
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Quantum field theory and the Jones polynomial
TL;DR: In this paper, it was shown that 2+1 dimensional quantum Yang-Mills theory with an action consisting purely of the Chern-Simons term is exactly soluble and gave a natural framework for understanding the Jones polynomial of knot theory in three dimensional terms.