scholarly journals Haag Duality and the Distal Split Property for Cones in the Toric Code

2012 ◽  
Vol 101 (3) ◽  
pp. 341-354 ◽  
Author(s):  
Pieter Naaijkens
Keyword(s):  
Haag Duality ◽  
Split Property ◽  
Toric Code

Superselection Structure of Massive Quantum Field Theories in 1+1 Dimensions

1998 ◽  
Vol 10 (08) ◽  
pp. 1147-1170 ◽  
Author(s):  
Michael Müger
Keyword(s):  
Large Class ◽  
Field Theories ◽  
Positive Energy ◽  
Quantum Field Theories ◽  
Quantum Field ◽  
Haag Duality ◽  
Conformally Invariant ◽  
Split Property

We show that a large class of massive quantum field theories in 1+1 dimensions, characterized by Haag duality and the split property for wedges, does not admit locally generated superselection sectors in the sense of Doplicher, Haag and Roberts. Thereby the extension of DHR theory to 1+1 dimensions due to Fredenhagen, Rehren and Schroer is vacuous for such theories. Even charged representations which are localizable only in wedge regions are ruled out. Furthermore, Haag duality holds in all locally normal representations. These results are applied to the theory of soliton sectors. Furthermore, the extension of localized representations of a non-Haag dual net to the dual net is reconsidered. It must be emphasized that these statements do not apply to massless theories since they do not satisfy the above split property. In particular, it is known that positive energy representations of conformally invariant theories are DHR representations.

scholarly journals Quantum critical phase transition between two topologically ordered phases in the Ising toric code bilayer

2020 ◽  
Vol 102 (21) ◽  
Author(s):  
Raymond Wiedmann ◽  
Lea Lenke ◽  
Matthias R. Walther ◽  
Matthias Mühlhauser ◽  
Kai Phillip Schmidt
Keyword(s):  
Phase Transition ◽  
Ordered Phases ◽  
Critical Phase ◽  
Quantum Critical ◽  
Toric Code

scholarly journals Four-dimensional toric code with non-Clifford transversal gates

2021 ◽  
Vol 3 (1) ◽  
Author(s):  
Tomas Jochym-O'Connor ◽  
Theodore J. Yoder
Keyword(s):  
Toric Code

scholarly journals Z2 lattice gauge theories and Kitaev's toric code: A scheme for analog quantum simulation

2021 ◽  
Vol 104 (8) ◽  
Author(s):  
Lukas Homeier ◽  
Christian Schweizer ◽  
Monika Aidelsburger ◽  
Arkady Fedorov ◽  
Fabian Grusdt
Keyword(s):  
Gauge Theories ◽  
Quantum Simulation ◽  
Lattice Gauge ◽  
Lattice Gauge Theories ◽  
Toric Code

scholarly journals Topological line in frustrated toric code models

2021 ◽  
Vol 104 (11) ◽  
Author(s):  
M. H. Zarei ◽  
J. Abouie
Keyword(s):  
Toric Code

scholarly journals Dynamical quantum phase transitions in extended toric-code models

2019 ◽  
Vol 100 (14) ◽  
Author(s):  
Vatshal Srivastav ◽  
Utso Bhattacharya ◽  
Amit Dutta
Keyword(s):  
Phase Transitions ◽  
Quantum Phase Transitions ◽  
Quantum Phase ◽  
Toric Code

scholarly journals Localization of Toric Code Defects

2011 ◽  
Vol 107 (3) ◽  
Author(s):  
Cyril Stark ◽  
Lode Pollet ◽  
Ataç Imamoğlu ◽  
Renato Renner
Keyword(s):  
Toric Code
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