Content deleted Content added
refimprove |
example |
||
Line 7:
For strings labeled by the positive integers, string-nets are the [[spin networks]] studied in [[loop quantum gravity]]. This has led to the proposal by Levin and Wen,<ref>Photons and electrons as emergent phenomena Michael Levin, Xiao-Gang Wen http://arxiv.org/abs/cond-mat/0407140 page 8 "loop quantum gravity appears to be a string net condensation..."</ref> and Smolin, Markopoulou and Konopka<ref>{{cite arxiv |eprint=hep-th/0611197|quote=we argue, but do not prove, that loop quantum gravity's spin networks can reproduce Levin and Wen's string net condensation in quantum gravity... |author1=Tomasz Konopka |author2=Fotini Markopoulou |author3=Lee Smolin |title=Quantum Graphity |class=hep-th |year=2006}}</ref> that loop quantum gravity's spin networks can give rise to the [[standard model]] of [[particle physics]] through this mechanism, along with [[fermi statistics]] and [[gauge interactions]]. To date, a rigorous derivation from LQG's spin networks to Levin and Wen's spin lattice has yet to be done, but the project to do so is called "[[quantum graphity]]", and in a more recent paper, Tomasz Konopka, [[Fotini Markopoulou]], [[Simone Severini]] argued that there are some similarities to spin networks (but not necessarily an exact equivalence) that gives rise to U(1) gauge charge and electrons in the string net mechanism.<ref>Quantum Graphity: a model of emergent locality http://arxiv.org/abs/0801.0861 page #19 "the excitation of the ground state...is expected to give rise to U(1) gauge charge, ...main difference between this model and the original model of Levin and Wen is that in the present case the background is dynamical, and has hexagonal rather than square plaquettes</ref>
[[Herbertsmithite]] may be the only known example of String-net matter.<ref name=eureka>{{cite web|last=Bowles|first=Claire|title=Have researchers found a new state of matter?|url=http://www.eurekalert.org/pub_releases/2007-03/ns-hrf031407.php|publisher=Eureka Alert|accessdate=29 January 2012}}</ref>
==Examples==
===The toric code===
The [[toric code]] is a two dimensional spin lattice, that acts as a quantum error-correcting code. It is defined on a two dimensional lattice with [[torus|toric]] [[boundary conditions]] with a spin-1/2 on each link. It can be shown that the ground state of the standard toric code Hamiltonian is an ''equal weight superposition'' of closed string states.<ref name=kitaevlaumann>{{cite journal|last=Kitaev|first=Alexei, Y.|coauthors=Chris Laumann|title=Topological phases and quantum computation|journal=ArXiv|year=2009|url=http://arxiv.org/abs/0904.2771}}</ref> Such a ground state is an example of a string-net condensate.<ref>{{cite journal|last=Morimae|first=Tomoyuki|title=Quantum computational tensor network on string-net condensate|journal=ArXiv|year=2011|url=http://arxiv.org/pdf/1012.1000v2.pdf}}</ref>
==References==
| |||