scholarly journals Dispersive toric code model with fusion and defusion

2020 ◽  
Vol 101 (11) ◽  
Author(s):  
Bruno Nachtergaele ◽  
Nicholas E. Sherman
Keyword(s):  
2011 ◽  
Vol 23 (04) ◽  
pp. 347-373 ◽  
Author(s):  
PIETER NAAIJKENS

We consider various aspects of Kitaev's toric code model on a plane in the C*-algebraic approach to quantum spin systems on a lattice. In particular, we show that elementary excitations of the ground state can be described by localized endomorphisms of the observable algebra. The structure of these endomorphisms is analyzed in the spirit of the Doplicher–Haag–Roberts program (specifically, through its generalization to infinite regions as considered by Buchholz and Fredenhagen). Most notably, the statistics of excitations can be calculated in this way. The excitations can equivalently be described by the representation theory of [Formula: see text], i.e. Drinfel'd's quantum double of the group algebra of ℤ2.


2019 ◽  
Vol 99 (5) ◽  
Author(s):  
Mohammad Hossein Zarei ◽  
Afshin Montakhab

2019 ◽  
Vol 31 (10) ◽  
pp. 1950038
Author(s):  
Péter Vrana ◽  
Máté Farkas

We study a generalization of Kitaev’s abelian toric code model defined on CW complexes. In this model, qudits are attached to [Formula: see text]-dimensional cells and the interaction is given by generalized star and plaquette operators. These are defined in terms of coboundary and boundary maps in the locally finite cellular cochain complex and the cellular chain complex. We find that the set of energy-minimizing ground states and the types of charges carried by certain localized excitations depends only on the proper homotopy type of the CW complex. As an application, we show that the homological product of a CSS code with the infinite toric code has excitations with abelian anyonic statistics.


2020 ◽  
Vol 2020 (12) ◽  
Author(s):  
Liang Kong ◽  
Yin Tian ◽  
Zhi-Hao Zhang

Abstract It was well known that there are e-particles and m-strings in the 3-dimensional (spatial dimension) toric code model, which realizes the 3-dimensional ℤ2 topological order. Recent mathematical result, however, shows that there are additional string-like topological defects in the 3-dimensional ℤ2 topological order. In this work, we construct all topological defects of codimension 2 and higher, and show that they form a braided fusion 2-category satisfying a braiding non-degeneracy condition.


2009 ◽  
Vol 80 (8) ◽  
Author(s):  
Julien Vidal ◽  
Ronny Thomale ◽  
Kai Phillip Schmidt ◽  
Sébastien Dusuel

2012 ◽  
Vol 85 (19) ◽  
Author(s):  
Fengcheng Wu ◽  
Youjin Deng ◽  
Nikolay Prokof'ev

This book explores the value for literary studies of relevance theory, an inferential approach to communication in which the expression and recognition of intentions plays a major role. Drawing on a wide range of examples from lyric poetry and the novel, nine of the ten chapters are written by literary specialists and use relevance theory both as an overall framework and as a resource for detailed analysis. The final chapter, written by the co-founder of relevance theory, reviews the issues addressed by the volume and explores their implications for cognitive theories of how communicative acts are interpreted in context. Originally designed to explain how people understand each other in everyday face-to-face exchanges, relevance theory—described in an early review by a literary scholar as ‘the makings of a radically new theory of communication, the first since Aristotle’s’—sheds light on the whole spectrum of human modes of communication, including literature in the broadest sense. Reading Beyond the Code is unique in using relevance theory as a prime resource for literary study, and is also the first to apply the model to a range of phenomena widely seen as supporting an ‘embodied’ conception of cognition and language where sensorimotor processes play a key role. This broadened perspective serves to enhance the value for literary studies of the central claim of relevance theory: that the ‘code model’ is fundamentally inadequate to account for human communication, and in particular for the modes of communication that are proper to literature.


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