scholarly journals Topological order in a three-dimensional toric code at finite temperature

2008 ◽  
Vol 78 (15) ◽  
Author(s):  
Claudio Castelnovo ◽  
Claudio Chamon
Keyword(s):  
Finite Temperature ◽  
Three Dimensional ◽  
Topological Order ◽  
Toric Code

scholarly journals A pedagogical overview on 2D and 3D Toric Codes and the origin of their topological orders

2019 ◽  
Vol 32 (02) ◽  
pp. 2030002
Author(s):  
M. F. Araujo de Resende
Keyword(s):  
Ground State ◽  
Three Dimensional ◽  
Topological Order ◽  
Two Dimensional ◽  
Dimensional Model ◽  
Dimensional Torus ◽  
Three Dimensional Model ◽  
2D And 3D ◽  
New Situation ◽  
Toric Code

In this work, we will show how the topological order of the Toric Code appears when the lattice on which it is defined discretizes a three-dimensional torus. In order to do this, we will present a pedagogical review of the traditional two-dimensional Toric Code, with an emphasis on how its quasiparticles are conceived and transported. With that, we want to make clear not only how all these same quasiparticle conception and transportation fit into this three-dimensional model, but to make it clear how topology controls the degeneracy of ground state in this new situation.

scholarly journals Geometric phases for mixed states of the Kitaev chain

2016 ◽  
Vol 374 (2068) ◽  
pp. 20150231 ◽  
Author(s):  
Ole Andersson ◽  
Ingemar Bengtsson ◽  
Marie Ericsson ◽  
Erik Sjöqvist
Keyword(s):  
Finite Temperature ◽  
Geometric Phase ◽  
Berry Phase ◽  
Condensed Matter ◽  
Order Parameters ◽  
Topological Order ◽  
Mixed States ◽  
Geometric Phases

The Berry phase has found applications in building topological order parameters for certain condensed matter systems. The question whether some geometric phase for mixed states can serve the same purpose has been raised, and proposals are on the table. We analyse the intricate behaviour of Uhlmann's geometric phase in the Kitaev chain at finite temperature, and then argue that it captures quite different physics from that intended. We also analyse the behaviour of a geometric phase introduced in the context of interferometry. For the Kitaev chain, this phase closely mirrors that of the Berry phase, and we argue that it merits further investigation.

scholarly journals Rényi entropy perspective on topological order in classical toric code models

2015 ◽  
Vol 92 (12) ◽  
Author(s):  
Johannes Helmes ◽  
Jean-Marie Stéphan ◽  
Simon Trebst
Keyword(s):  
Renyi Entropy ◽  
Rényi Entropy ◽  
Topological Order ◽  
Toric Code

scholarly journals Three-dimensional finite temperature gauge theory in the confined region and the string picture

2010 ◽  
Vol 836 (1-2) ◽  
pp. 91-99 ◽  
Author(s):  
P. Bialas ◽  
L. Daniel ◽  
A. Morel ◽  
B. Petersson
Keyword(s):  
Gauge Theory ◽  
Finite Temperature ◽  
Three Dimensional
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